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Thomas Dehaeze
2025-11-27 17:53:13 +01:00
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23 changed files with 5857 additions and 398 deletions
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12
inkscape/tikz.org
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@@ -175,15 +175,15 @@
#+begin_src latex :file detail_kinematics_centralized_control.pdf
\begin{tikzpicture}
\node[block] (Jt) at (0, 0) {$\bm{J}^{-\intercal}$};
\node[block, right= of Jt] (G) {$\bm{G}$};
\node[block, right= of G] (J) {$\bm{J}^{-1}$};
\node[block, left= of Jt] (Kx) {$\bm{K}_{\mathcal{X}}$};
\node[block, right=0.5 of Jt] (G) {$\bm{G}$};
\node[block, right=0.5 of G] (J) {$\bm{J}^{-1}$};
\node[block, left=0.7 of Jt] (Kx) {$\bm{K}_{\mathcal{X}}$};
\draw[->] (Kx.east) -- node[midway, above]{$\bm{\mathcal{F}}$} (Jt.west);
\draw[->] (Kx.east) node[above right]{$\bm{\mathcal{F}}$} -- (Jt.west);
\draw[->] (Jt.east) -- (G.west) node[above left]{$\bm{\tau}$};
\draw[->] (G.east) -- (J.west) node[above left]{$\bm{\mathcal{L}}$};
\draw[->] (J.east) -- ++(1.0, 0);
\draw[->] ($(J.east) + (0.5, 0)$)node[]{$\bullet$} node[above]{$\bm{\mathcal{X}}$} -- ++(0, -1) -| ($(Kx.west) + (-0.5, 0)$) -- (Kx.west);
\draw[->] (J.east) -- ++(0.8, 0);
\draw[->] ($(J.east) + (0.4, 0)$)node[]{$\bullet$} node[above]{$\bm{\mathcal{X}}$} -- ++(0, -1) -| ($(Kx.west) + (-0.4, 0)$) -- (Kx.west);
\begin{scope}[on background layer]
\node[fit={(Jt.south west) (J.north east)}, fill=black!20!white, draw, dashed, inner sep=4pt] (Px) {};

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paper/asmejour/README.md Normal file
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#asmejour: A template for ASME journal papers#
Version 1.26 dated 2025/04/18.
####Overview####
This class provides a template to format preprints in the style of journal papers published by the American Society of Mechanical Engineers.
The layout and reference formats follow the style of published papers in 2025.
This work is not a publication of ASME.
Files in this distribution are:
``` README.md -- this file
asmejour.cls -- the class file
asmejour.bst -- bibtex style for ASME journal references
asmejour-template.tex -- a latex template/example for this class
asmejour-template.pdf -- documentation/sample paper
asmejour-sample.bib -- a sample bibliography file
*
sample-figure-1.pdf,
sample-figure-2a.pdf,
sample-figure-2b.pdf -- figures for the example template
/asmewide_example -- directory includes asmewide.sty and examples of wide equations```
The .tex and .cls files are commented and should be self-explanatory.
This template was designed to approach the following aims:
- closely approximate ASME's fonts and layout, including author/title/abstract design
- match ASME's current reference formats, including hyperlinked DOI and URL (replaces asmems4.bst)
- support hyperlinks to figures, tables, equations, references, and external URLs
- support pdf bookmarks and metadata
- provide line numbers for editing and review
- support balancing of columns on last page
- support PDF/A (archival) standards if desired
- support copyright notices for federal employees and contractors
- support bold-face math and citations in section headings and captions
- enable various math and text features with newtxmath, newtxtext, and inconsolata packages
- enable passages in other languages, e.g., for a translation of the abstract or a quotation
####Author####
John H. Lienhard V
Department of Mechanical Engineering
Massachusetts Institute of Technology
Cambridge, MA 02139-4307 USA
---
####Change log####
v1.26 (2025/04/18)
- Disable loading of exscale package by extarticle.cls (was causing spurious formula tag in section headings)
- Correct order of setting the lsmgreek and fsmgreek symbol fonts
- Move \\allowdisplaybreaks out of .cls and into .tex file, to allow user to control
- Drop unnecessary bookmark "Appendices"
- Add additional code/text around dropped option \[mathalfa=ccc=ddd\]
- Replace Figure 1 with a new pdf to end A-3u validation problem in pdfTeX
- Other minor changes in code and documentation
v1.25 (2025/04/07)
- Add support for unicode-math, using fonts from TeX Live. LuaLaTeX now loads unicode-math by default.
- Drop these packages: titlesec, enumitem, ifthen, iftex, totcount, hyperxmp, inputenc, bookmark, glyphtounicode
- Move hologo package loading from .cls file to .tex file
- Drop \[mathalfa\] class option. User can instead load mathalpha in the preamble when using pdfTeX
- Drop legacy PDF/A options \[pdf-a, pdfaconformance, pdfapart\]. Use \\DocumentMetadata instead
- Select larger small caps from newtxtext by default, drop \[largesc\] option
- Switch to LaTeX's native keyvalue mechanism; load kvoptions package only for backward compatibility
- Change vertical skip adjustment on multline environment from 7pt to 10pt (= \\jot in this class)
- Reduce use of etoolbox in favor of LaTeX's hook mechanisms; this limits asmejour to LaTeX formats dated 2020/10 or later
- Fixed operator encoding for sans and sansbold math versions (to OT1)
- Add pages and chapter to @book{.. entry in asmejour.bst; use pages= rather than eid= in sample .bib
- Reduce space between items in lists
- This version is backward compatible to the 2020/10 LaTeX format. Older formats will not compile this version.
- Convert sample images to PDF/A-3u
- Convert remaining title block code to expl3
- Add error message for unused \\author command
- Construct \\@author token list for consistency with standard classes
- Revise documentation
- v1.25 is PDF/UA-2 compliant if: \[captionpatch\] option is used; subcaptions are not used; figures are compliant; and \[nolists\] option is called or \\ref\* is used in optional argument of captions. Validation: Arlington model and demo.vera.org.
v1.24 (2025/01/26)
- Drop metalogo package
- Add optional line numbers to author and title text
- Rescale roman, helvetica, and typewriter fontdimens under fontspec to match pdftex
- Define \\@title
- Replace xcoffin package by expl3 coffins, and resolve related tagging problem
- Edits to asmewide.sty: set \\@RuleWidth at end of \\maketitle; add \\ignorespacesafterend
- Minor code clean-up
v1.23 (2024/07/24)
- Add class option for single-column formatting, \[singlecolumn\], as sometimes requested for review (thanks Lennart Hultgren)
- Change language sample from French to German, to avoid active characters (from Fourier to Pohlhausen)
- Reduce size of line number font
- Adjust code for \\appendix to better accommodate tagged pdf
- Correct bug in babel main language selection
- Miscellaneous code clean up and simplification
v1.22 (2024/02/06)
- The newtx package has dropped superiors option, so asmejour has dropped the \[superiors\] option and related code.
- Dropped legacy options \[lang, lang-second, lang-third\]
- Remove several other blocks of legacy code
- Refresh sample figures
- Edits to asmejour.bst: fix punctuation and spacing in journal title macros
- Edit asmejour-sample.bib
v1.21 (2023/10/22)
- Adjust loading order of hyperxmp and hyperref to accommodate v5.12 of hyperxmp package
- Change code that italicizes letters in subequation numbers to avoid conflict with hyperref
- Adjust font loading under luaLaTeX, now requiring that TeX Gyre Termes, TeX Gyre Heros, and Inconsolatazi4 are available
- Enable line numbers in abstract
- Revise code handling footnotes (now protected); revise code handling most package options; remove some legacy code.
- Minor correction to asmejour.bst for \\hrefurl when used separately from asmejour.cls
- Edit documentation
v1.20 (2022/12/30)
- Include patch for bug in hyperxmp.
- Italicize letters in subequation numbers, to match ASME style.
- Add macro "jhmt" to asmejour.bst for "ASME J Heat Mass Transfer"; add figures from jhmt and cite in asmejour-template.tex.
v1.19 (2022/06/26)
- Correct typo in asmejour.cls (line 359): \\protec should be \\protect
- Force T1 encoding of qhvc font under LuaLaTeX (for title and author blocks)
- Update code for Inconsolata and Helvetica fonts under LuaLaTeX to ensure T1 encoding. Adjust scale factors.
- Scale Helvetica font to 0.91, to better match roman font.
- Add option to asmewide.sty to suppress final page column balancing, [raggedend], expand error message text.
v1.18 (2022/01/10)
- Introduce asmewide.sty, an experimental package for setting page-width equations in a two column format. A document with examples of use is included.
v1.17 (2021/12/26):
- Add code to warn about obsolete LaTeX installations. TeX Live 2020 or later is recommended for the asmejour package.
v1.16 (2021/12/23):
- suppress warnings about unused options when calling mathalfa and/or barcolor
- eliminate use of \\entry{} with a single argument to produce subheadings in nomenclature; use \\EntryHeading{} instead. (**not backward compatible**)
- incorporate pending changes to LaTeX pdf management in relation to pdf-a color profile loading and recently deprecated \\pdfcatalog command
- load xparse only for older kernels
- edit documentation; mention \\mathversion sans and sansbold
- add upright, sans serif Greek letters for math
- minor edits to class file code; correct calls for pdfminorversion; edit warnings
- minor edits to asmejour.bst in relation to hyperlinks, \\href, \\hrefurl; update jht macro to latest style
v1.15 (2021/02/01):
- fix issue with math accents in mathversion sansbold (for captions)
- add optional copyright notices for government employees and contractors
- add \\EntryHeading command for nomenclature
- provide additional options for typewriter font
- simplify language options for babel
- make subfigure example consistent with ASME's labeling
- make abstract environment tolerant of blank lines
- edit sample bib file; include example of @manual
- update some usage of xparse; internal changes to \\PaperYear, \\CorrespondingAuthor and \\keywords commands.
- edit code for keys and options; correct largesc option; slightly increase interword shrink; remove legacy code;
- substantially edit documentation
v1.14 (2020/08/12): Set pdf page layout to a single page, rather than a two-page spread.
v1.13 (2020/08/10): Add support for PDF/A archival standards (1b, 2b, 2u, 3b, 3u), as the newtx fonts have recently gained complete unicode maps; also, restore varl and varqu as default options of the inconsolata font.
v1.12 (2020/04/12): Change subfigure \\ref labels to have parentheses around italic letters; remove space between consecutive numerical citations; add macro to adjust vertical space below abstract; edit documentation; remove varl and varqu options of inconsolata font; extensively edit/document asmejour-sample.bib file.
Many changes to asmejour.bst (v1.03) to improve consistency with ASME reference formats for collections, technical reports, and conference papers, to better manage hyperlinks, and to warn for missing fields. These includes: move venue, eventdate, and paper number to end of @inproceedings; move paper number after address of @techreport; hyperlink technical report numbers and conference numbers, and provide fallback for missing numbers; separate serial collection parenthetical layout from @incollection into new @inserialcollection; add default name for @inproceedings paper number, "Paper No.", changed by type ={} (this alternation is not backward compatible!); add oclc macro for archive field; complete the set of macros for ASME journal names.
v1.11: ensure T1 font encoding, utf-8 input, and LuaLaTeX compatibility; edit documentation.
v1.10: update asmejour.bst to most recent Crossref standard prefix for doi (https://doi.org/); remove xpatch package from class file; disable \\( and \\) in pdf bookmarks to avoid warnings; adjust \\eqref in bookmarks; edit documentation.
v1.09: adjust nomenclature list; edit language support
v1.08: adjust penalties in nomenclature list; fix minor typos in template
v1.07: add commands for \\toprule, \\midrule, and \\bottomrule in ASME style; add advice on landscape material; minor edits to \\entry and for language support.
v1.06: allow standard \\date, \\maketitle, and \\title commands and abstract environment; make final column balancing a package option; remove \\normalfont from AMS equation tags to allow tags to match caption font; incorporate \\subfigure in example template; allow line numbers in AMS display math; provide comma between sequential footnote marks; adjust babel options; other minor edits; revise template text.
v1.05: automate list of figures/tables with option to omit; replace balance package with flushend package and automate; revise skips in nomenclature; address conflicts of lineno package with other elements; option to hyphenate typewriter font; new options for footer text; adjust \\emergencystretch and \\tolerance; additional documentation and references
v1.04: edit documentation; add language support via babel
v1.03: expand documentation; fix conflict between lineno and balance packages; more footer options; edit \\entry
v1.02: adjust formats of 2nd and 3rd level headings; add option for line numbers; eqn tags in blue
v1.01: edit documentation, remove development code
v1.00: initial release
---
####License####
Copyright (c) 2025 John H. Lienhard
Permission is hereby granted, free of charge, to any person obtaining a copy of this software and
associated documentation files (the "Software"), to deal in the Software without restriction,
including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense,
and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so,
subject to the following two conditions:
The above copyright notice and this permission notice shall be included in all copies or
substantial portions of the Software.
The software is provided "as is", without warranty of any kind, express or implied, including but
not limited to the warranties of merchantability, fitness for a particular purpose and noninfringement.
In no event shall the authors or copyright holders be liable for any claim, damages or other liability,
whether in an action of contract, tort or otherwise, arising from, out of or in connection with the
software or the use or other dealings in the software.

590
paper/asmejour/asmejour-sample.bib Normal file
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%% Sample bibliography file for asmejour.bst and asmejour.cls
%%
%% Revised: 2025-04-05
%% Copyright John H. Lienhard, MIT
%% Offered under the MIT license: https://ctan.org/license/mit
%% Titles should be in title case (first letters capitalized) according to ASME style
%% Allowable fields are listed after the first use of each entry type.
%%
@article{DKE1969,
author = {D. K. Edwards},
year = {1969},
title = {Radiative Transfer Characteristics of Materials},
journal = {{ASME} J. Heat Transfer-Trans. {ASME}},
volume = 91,
number = 1,
pages = {1--15},
doi = {10.1115/1.3580108},
month = feb,
}
%% article supports these fields: author, year, title, journal,
%% volume, number, pages OR eid,
%% doi OR url OR eprint with archive, note.
%% (The month field is not used in ASME style and will be ignored.)
@article{toohey2007,
author = {Kathleen S. Toohey and Nancy R. Sottos and Jennifer A. Lewis and Jeffrey S. Moore and Scott R. White},
year = {2007},
title = {Self-Healing Materials With Microvascular Networks},
journal = {Nature Materials},
volume = {6},
number = {8},
pages = {581--585},
doi = {10.1038/nmat1934},
}
@book{gibson2008,
author = {Tom A. Gibson and Matthew A. Tucker},
year = {2008},
title = {The Big Book of Cellular Studies},
publisher = {John Wiley and Sons},
address = {New York, NY},
}
%% book supports these fields: author OR editor, year, title, edition, version
%% series, volume OR number, publisher, address, type,
%% doi OR url OR eprint with archive, page, chapter, note.
%% type={} field can change "Chap." to something else.
@incollection{stevens1999,
author = {Thomas T. Stevens},
year = {1999},
title = {Stochastic Fields and Their Digital Simulation},
booktitle = {Stochastic Methods},
editor = {T. A. Sulle and M. Siiu},
publisher = {Martinius Publishers},
address = {Dordrecht, Germany},
pages = {22--36},
}
%% incollection supports these fields: author, year, title, booktitle, edition, editor,
%% series, volume OR number, publisher, address, type,
%% chapter, pages, doi OR url OR eprint with archive, note.
%% type={} field changes "Chap." to something else.
@inproceedings{wions2006,
author = {Thomas Wions and Christopher D. Mills},
year = {2006},
title = {Structural Dynamics in Parallel Manipulation},
booktitle = {Proceedings of the IDETC/CIE},
venue = {New Orleans, LA},
eventdate = {September 10--13},
type = {ASME Paper No.},
number = {DETC2005-99532},
pages = {777--798},
}
%% inproceedings supports these fields: author, year, title, booktitle, edition, editor, series, volume,
%% organization OR publisher, address OR venue, eventdate, [paper] number,
%% pages, doi, note, url, eprint with archive, url, type.
%% type = { } changes default "Paper No."
%% venue and eventdate are specific to the asmejour.bst style. The "series" field is rarely used.
%% If there are no pages as such, just omit the pages field and ignore the bibtex warning "missing pages".
@techreport{oligaria2011,
author = {Oligaria, T. T. and Fredy, C. W. and Popullo, A. Z. and Tucker, M. A.},
year = {2011},
title = {Characterization of {PKM} Dynamics},
type = {SAE Technical Paper},
number = {No. 2011-02-8345, 07ATC-96},
}
%% techreport supports these fields: author, year, title, institution, address, number, type, note
%% doi OR url OR eprint with archive.
%% ASME's online examples omit institution; however, the ASME journals will include it, e.g.:
%% institution = {Society of Automotive Engineers},
@phdthesis{mollen2014,
author = {T. P. Mollen},
year = {2014},
title = {Use of General Nonlinear Material in Articulated Systems},
type = {Ph.{D}. dissertation},
school = {University of Boston},
address = {Boston, MA},
}
%% phdthesis supports these fields: author, year, title, type, school, address, note.
%% Additional fields are also supported, but don't use them all: doi, eprint with archive, url, urldate, urltype
%% type = {} can optionally be added to change the style of thesis. Default is "Ph.D. thesis"
@book{smith2014,
author = {Smith, John},
year = {2014},
title = {A Dog's Life in Berlin},
publisher = {Oxford University Press},
address = {New York},
doi = {10.1115/1.888209},
note = {\doi{10.1115/1.888209}},
}
%% This example shows how to print a doi even though the doi field is hyperlinked to the title. An alternative is:
%% note = {\url{https://doi.org/10.1055/acprof.oso/97890.0394.000}},
@online{apple2019,
title = {Apple Privacy Policy},
url = {https://www.apple.com/legal/privacy/en-ww/},
urldate = {Apr. 5, 2020},
organization = {Apple Inc.},
address = {Cupertino, CA},
note = {last modified Dec. 31, 2019},
}
%% online supports these fields: author OR editor, year, title, version, versiontype, organization, address,
%% note, url, urldate, urltype
%% These additional fields are also supported, but are intended as alternatives to url: doi, eprint with archive
@online{kern,
author = {Uwe Kern},
year = {2024},
title = {Extending \LaTeX's color facilities: the \textsf{xcolor} package},
version = {3.02},
organization = {Comprehensive \TeX\ Archive Network},
url = {https://ctan.org/pkg/xcolor},
urldate = {Apr. 4, 2025},
}
@online{sharpe1,
author = {Michael Sharpe},
year = {2025},
title = {New {TX} Font Package},
version = {1.756},
organization = {Comprehensive \TeX\ Archive Network},
url = {https://ctan.org/pkg/newtx},
urldate = {Apr. 3, 2025},
}
@online{robertson2023,
author = {Will Robertson},
title = {Experimental Unicode mathematical typesetting: The \textsf{unicode-math} package},
version = {0.8r},
organization = {Comprehensive \TeX\ Archive Network},
year = {2023},
url = {https://ctan.org/pkg/unicode-math},
urldate = {March 9, 2025},
}
@article{lienhard2020,
author = {Lienhard, John H.},
title = {Heat Transfer in Flat-Plate Boundary Layers: A Correlation for Laminar, Transitional, and Turbulent Flow},
journal = jht,
volume = {142},
number = {6},
pages = {061805},
year = {2020},
month = jun,
doi = {10.1115/1.4046795},
}
% eid = {061805},
%% Note use of pages field rather than eid,to follow ASME style of putting "p." before the eid number.
%
%% May include numpages = {#} with eid to get "eid (# pages)"
%% Note use of jht macro for title (produces "ASME J. Heat Transfer"). All ASME journals have macros.
@article{lienhard2019,
author = {Lienhard, John H.},
title = {Linearization of Nongray Radiation Exchange: The Internal Fractional Function Reconsidered},
journal = jht,
volume = {141},
number = {5},
pages = {052701},
year = {2019},
month = mar,
doi = {10.1115/1.4042158},
}
%% note use of: pages to hold eid, and use of jhmt macro for the journal name
@online{sharpe2,
author = {Michael Sharpe},
title = {The \textsf{mathalpha}, {AKA} \textsf{mathalfa} Package},
version = {1.145},
organization = {Comprehensive \TeX\ Archive Network},
year = {2025},
url = {https://ctan.org/pkg/mathalpha},
urldate = {March 9, 2025},
}
@online{fairbairns,
author = {Robin Fairbairns and Sebastian Rahtz and Leonor Barroca},
year = {2016},
title = {A Package for Rotated Objects in \LaTeX},
version = {2.16d},
organization = {Comprehensive \TeX\ Archive Network},
url = {https://www.ctan.org/pkg/rotating},
urldate = {Oct. 2, 2019},
}
@online{fear,
author = {Simon Fear},
year = {2020},
title = {Publication Quality Tables in \LaTeX},
organization = {Comprehensive \TeX\ Archive Network},
version = {1.6180339},
url = {https://www.ctan.org/pkg/booktabs},
urldate = {Apr. 3, 2025},
}
@manual{GSL,
title = {{GNU} Scientific Library},
author = {Mark Galassi
and Jim Davies
and James Theiler
and Brian Gough
and Gerard Jungman
and Patrick Alken
and Michael Booth
and Fabrice Rossi
and Rhys Ulerich},
version = {2.7},
versiontype = {Release},
organization = {Free Software Foundation},
address = {Boston, MA},
year = 2021,
url = {https://www.gnu.org/software/gsl/},
}
%% manual supports these fields: author, year, title, edition, organization, address,
%% doi, eprint with archive, urldate, url, version, versiontype, note.
%% You can change "Accessed" with "urltype", e.g., urltype = {retrieved},
%% You can change "Version" with "versiontype, e.g., versiontype = {Release},
%% Next is an alternative approach to stating the version/release that doesn't use version and versiontype:
@online{dlmf,
title = {{NIST} {D}igital Library of Mathematical Functions, Release 1.0.17},
year = {2017},
editor = {F. W. J. Olver and A. B. {Olde Daalhuis} and D. W. Lozier and B. I. Schneider and
R. F. Boisvert and C. W. Clark and B. R. Miller and B. V. Saunders},
organization = {National Institute of Standards and Technology},
address = {Gaithersburg, MD},
url = {https://dlmf.nist.gov/},
urldate = {Dec. 22, 2018},
}
@online{texshop,
author = {Richard Koch},
title = {{\TeX}{S}hop, Version 5.49},
year = {2025},
url = {https://pages.uoregon.edu/koch/texshop/obtaining.html},
urldate = {Apr. 3, 2025},
organization = {University of Oregon},
address = {Eugene, OR},
}
@online{tolusis,
author = {Sigitas Tolu{\v{s}}is},
title = {The \textsf{flushend} Package},
version = {4.0},
organization = {Comprehensive \TeX\ Archive Network},
year = {2021},
url = {https://www.ctan.org/pkg/flushend},
urldate = {March 14, 2025},
}
@online{bottcher,
author = {Stephan I. B{\"o}ttcher and Uwe L{\"u}ck and Karl Wette},
title = {\textsf{lineno.sty}: A {\LaTeX} Package to Attach Line Numbers to Paragraphs},
version = {5.4},
organization = {Comprehensive \TeX\ Archive Network},
year = {2025},
url = {https://www.ctan.org/pkg/lineno},
urldate = {March 14, 2025},
}
@online{oostrum,
author = {Piet van Oostrum},
title = {The \textsf{fancyhdr} and \textsf{extramarks} Packages},
version = {5.2},
organization = {Comprehensive \TeX\ Archive Network},
year = {2025},
url = {https://www.ctan.org/pkg/fancyhdr},
urldate = {March 14, 2025},
}
@online{amsmath,
author = {{American Mathematical Society} and {LATEX3 Project}},
title = {User's Guide for the \textsf{amsmath} Package},
version = {2.17t},
organization = {Comprehensive \TeX\ Archive Network},
year = {2024},
url = {https://ctan.org/tex-archive/macros/latex/required/amsmath/amsldoc.pdf},
urldate = {March 14, 2025},
}
@online{lienhard2025,
author = {Lienhard, John H.},
title = {Wide Equations in {\texttt{asmejour.cls}}},
version = {1.04},
organization = {Comprehensive \TeX\ Archive Network},
year = {2025},
url = {https://www.ctan.org/pkg/asmejour},
urldate = {Apr. 5, 2025},
}
@book{ww1927,
author = {E. T. Whittaker and E. N. Watson},
year = {1920},
title = {A Course of Modern Analysis},
edition = {3},
publisher = {Cambridge University Press},
address = {Cambridge, UK},
url = {https://archive.org/details/courseofmodernan00whit},
chapter = {XIII},
pages = {265--280},
}
@article{euler1740,
author = {Leonard Euler},
year = 1740,
title = {De Summis Serierum Reciprocarum},
journal = {Commentarii Acad\-emiae Scientiarum Petropolitanae},
volume = 7,
pages = {123--134},
archive = arxiv,
eprint = {math/0506415},
note = {First communicated to Daniel Bernoulli in 1734 and read before the St.\ Petersburg Academy in December 1735},
}
@book{euler1748,
author = {Leonard Euler},
year = {1748},
title = {Introductio in Analysin Infinitorum},
volume = 1,
publisher = {Apud Marcum-Michaelem Bousquet \& Socios},
address = {Lausannae},
}
% note={English translation by I.\ Bruce available here at \url{http://www.17centurymaths.com/contents/introductiontoanalysisvol1.htm}},
@book{fourier1822,
author = {Jean Baptiste Joseph Fourier},
year = {1822},
title = {Th\'{e}orie Analytique de la Chaleur},
publisher = {Firmin Didot, P\`{e}re et Fils},
address = {Paris},
url = {https://archive.org/details/analyticaltheory00fourrich},
}
@article{pohlhausen1921,
author = {Pohlhausen, E.},
title = {Der {W}\"{a}rmeaustausch zwischen festen K\"{o}rpern und {F}l\"{u}ssigkeiten mit kleiner reibung und kleiner {W}\"{a}rmeleitung},
journal = {Zeitschrift f\"{u}r {A}ngewandte {M}athematik und {M}echanik},
volume = {1},
number = {2},
pages = {115--121},
doi = {10.1002/zamm.19210010205},
year = {1921},
}
%url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/zamm.19210010205},
@techreport{reynolds1958,
author = {W. C. Reynolds and W. M. Kays and S. J. Kline},
title = {Heat transfer in the Incompressible Turbulent Boundary Layer. {I}---Constant Wall Temperature},
type = {NASA Technical Memorandum No.\ },
number = {12-1-58W},
institution = {National Aeronautics and Space Administration},
address = {Washington, DC},
month = dec,
year = {1958},
archive = hndl,
eprint = {2060/19980228020},
}
%% Equivalent links for this case: url = {https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19980228020.pdf},
%% url = {https://hdl.handle.net/2060/19980228020}
@incollection{clauser56,
author = {Francis H. Clauser},
year = {1956},
title = {The Turbulent Boundary Layer},
booktitle = {Advances in Applied Mechanics},
editor = {H. L. Dryden and Th. von K\'arm\'an},
volume = {4},
publisher = {Elsevier},
address = {Amsterdam, The Netherlands},
pages = {1--51},
doi = {10.1016/S0065-2156(08)70370-3},
}
%% This common case is an article in series of edited books where the series title is the same for all volumes.
%% type = {..}, changes chapter to something else
%% url = {..}, can be added if it exists
%% edition = {..} can be added if relevant
@inserialcollection{DKE70,
author = {Donald K. Edwards},
title = {Thermal Radiation Measurements},
editor = {Ernst R. G. Eckert and Richard J. Goldstein},
booktitle = {Measurement Techniques in Heat Transfer},
chapter = {9},
pages = {353--396},
volume = {130},
series = {{AGARD}ograph},
month = nov,
publisher = {Advisory Group for Aerospace Research and Development of {NATO}, Technivision Services},
address = {Slough, England},
year = {1970},
}
%% This exotic variant of incollection cites an article in a book series where each volume has a different title.
%% In this case, the series field (title of the overall series of books) is used with a volume number to produce
%% ...Title (Series, Vol.#), ...
%% Series will not appear if the volume number is empty. If you don't have both, use incollection instead.
%%
%% inserialcollection supports these fields: author, year, title, booktitle, edition, editor, series,
%% volume OR number, publisher, address, chapter, pages,
%% doi OR url OR eprint with archive, note. type={} changes "Chap."
%% This entry type is defined by asmejour.bst
@book{EDM,
author = {D. K. Edwards and V. E. Denny and A. F. Mills},
title = {Transfer Processes},
publisher = {Hemisphere Publishing},
edition = {2},
year = 1979,
address = {Washington, DC},
}
@article{montijano2014,
title = {Numerical Methods With {\hologo{LuaLaTeX}}},
author = {Juan I. Montijano and Mario P{\'{e}}rez and Luis R{\'{a}}ndez and Juan Luis Varona},
year = 2014,
volume = 35,
month = jan,
number = {1},
pages = {51--56},
journal = {TUGboat},
url = {https://tug.org/TUGboat/tb35-1/tb109montijano.pdf},
}
@conference{Swaminathan2017IDABRO,
author = {Swaminathan, Jaichander and Stover, Richard L. and Tow, Emily W. and Warsinger, David M. and Lienhard, John H.},
booktitle = {Proceedings of IDA World Congress on Desalination and Water Reuse},
title = {Effect of Practical Losses on Optimal Design of Batch {RO} Systems},
year = {2017},
month = oct,
publisher = {International Desalination Association},
venue = {S{\~a}o Paulo, Brazil},
eventdate = {Oct. 15--20},
archive = hndl,
eprint = {1721.1/111971},
number = {IDA17WC-58334},
}
%% conference is the same as inproceedings
@misc{Fong2015,
title = {Analytical Methods for Squaring the Disc},
year = {2015},
author = {Chamberlain Fong},
howpublished = {{\itshape ArXiv e-prints}},
eprint = {1509.06344},
archive = arxiv,
month = sep,
}
@online{mpl,
title = {mpl Colormaps},
author = {St{\'e}fan {van der Walt} and Nathaniel Smith},
url = {https://bids.github.io/colormap/},
urldate = {Aug. 26, 2018},
year = 2015,
organization = {GitHub},
address = {San Francisco, CA},
month = sep,
}
@book{ahtt,
author = {Lienhard, V, John H. and Lienhard, IV, John H.},
title = {A Heat Transfer Textbook},
publisher = {Phlogiston Press},
year = 2024,
volume = {},
series = {},
address = {Cambridge, MA},
edition = {6},
month = aug,
version = {6.00},
url = {https://ahtt.mit.edu},
}
@misc{govindan2017,
author = {Prakash Narayan Govindan and Steven Lam and Maximus G. {St. John}},
year = {2017},
title = {Systems Including a Condensing Apparatus Such As a Bubble Column Condenser},
howpublished = {US Patent {\#}9700811},
url = {https://patents.google.com/patent/US9700811B2},
}
%% misc supports these fields: author, year, title, howpublished, note.
%% These fields are also supported, but don't use them all: doi, eprint with archive, url, urldate, urltype
@mastersthesis{smith1998,
author = {Robert Smith},
title = {Conformal Lubricated Contact of Cylindrical Surfaces Involved in a Steady Motion},
school = {Rochester Institute of Technology},
address = {Rochester, NY},
year = {1998},
}
%% mastersthesis supports these fields: author, year, title, type, school, address, note.
%% These fields are also supported, but don't use them all: doi, eprint with archive, url, urldate, urltype
%% type={} can optionally be used to change the type of thesis. Default is "Master's thesis"
%% The following example uses type to make an entry for a Bachelor's thesis.
@mastersthesis{smith1996,
author = {Robert Smith},
title = {Cylindrical Surfaces Involved in a Steady Motion},
type = {Bachelor's thesis},
school = {Rochester Institute of Technology},
address = {Rochester, NY},
year = {1996},
}
@BOOK{johnson1980,
editor = {Howard Johnson},
year = {1980},
title = {Title of Edited Book},
publisher = {John Wiley and Sons, Inc.},
address = {New York, NY},
}
@proceedings{johnson2015,
editor = {Howard W. Johnson},
title = {The Title of the Proceedings},
year = 2015,
volume = 2,
organization = {Organization},
venue = {City, State},
eventdate = {April 27--28},
url = {https://news.mit.edu/2009/obit-johnson},
note = {Optional note},
}
%% proceedings supports these fields: author OR editor, year, title, edition, editor,
%% series, volume OR number, organization OR publisher,
%% address [of organization or publisher] OR venue, eventdate,
%% doi OR url OR eprint with archive.
%% The organization will appear as author/editor if those fields are empty.
%% If you opt to use the venue and eventdate fields, don't include the address field.
%% The very uncommon "series" field should be used with number, rather than volume.
@BOOK{kirk2288a,
author = {James Tiberius Kirk},
year = {2288},
title = {Decline and Fall of the Romulan Empire},
edition = 7,
series = {Humankind's Greatest Writings},
number = {23},
publisher = {Vulcan Free Press},
address = {T'Paal},
note = {To appear.},
}
%% One book in a series of books
@inbook{churchill1948,
author = {Winston S. Churchill},
year = {1948},
title = {The Gathering Storm},
edition = {1},
series = {The Second World War},
volume = {1},
chapter = {5},
pages = {66--89},
url = {https://www.worldcat.org/oclc/3025315},
publisher = {Houghton Mifflin Co.},
address = {Boston},
note = {{``The Locust Years''}},
}
%% inbook supports these fields: author OR editor, year, title, edition,
%% version, versiontype, series, volume OR number,
%% doi OR url OR eprint with archive, publisher, address, note.
%% type={} field can change "Chap." to something else.

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% !TEX encoding = UTF-8 Unicode
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%
%% This file is asmejour-template.tex, a template to format papers in the style of ASME journal papers.
%%
%% This file is version 1.26 dated 2024/04/18
%%
%% Author: John H. Lienhard V
%% Department of Mechanical Engineering
%% Massachusetts Institute of Technology
%% Cambridge, MA 02139-4307 USA
%%
%% Class options include:
%%
%% * Option to color the vertical bar in the title block [barcolor = colorname]
%% * where colorname is any name def'd by xcolor package; omit barcolor option to get black
%%
%% * Option to omit the list of figures and list of tables at the end [nolists]
%%
%% * Option to include line numbers [lineno]. You must run *twice* for proper placement of the
%% * line numbers. The lineno package does not number tables, footnotes, or captions.
%% * This option will disable balancing of the column heights on final page.
%%
%% * Option to balance column heights on final page [balance]. This option sometimes
%% * misbehaves, so use it with an awareness that it can create unexpected problems.
%% * This option is not compatible with line numbering.
%%
%% * Options for copyright notices:
%% * Omit the ASME copyright from the footer [nocopyright]
%% * Copyright footnote if all authors are government employees [govt]
%% * Copyright footnote if some authors are government employees [govtsome]
%% * Copyright footnote for government contractors [contractor]
%%
%% * Option to omit all ASME text fields from the footer [nofoot].
%%
%% * Option for single column formatting [singlecolumn].
%%
%% * Option for upright integrals [upint]
%%
%% * Additional math options from M. Sharpe's newtxmath package (pdfTeX only):
%% * [varvw] for v and w that are better distinguished from Greek nu; fine
%% * adjustments to subscripts [subscriptcorrection]; and various other options
%% * such as [smallerops, varg, slantedGreek, frenchmath, varbb, cmbraces].
%%
%% * Support for the unicode-math package and its math options (LuaLaTeX only)
%%
%% * Options for the typewriter font:
%% * [var0] replace default slashed zero by an unslashed zero
%% * [mono] force interword separation to be monospaced
%% * [hyphenate] allow hyphenation (pdfTeX only). Typewriter fonts usually are not hyphenated.
%%
%% * Options for the babel package to support passages in other languages (such as a translated
%% * abstract in an appendix), e.g. [german]. The main language will default to English
%% * unless a different main language is selected, e.g. [main=spanish]. See Appendix B for details.
%%
%% * PDF/A archivability compliance. Since 2022, LaTeX has included integrated support for PDF/A,
%% * through the \DocumentMetadata{..} command. This works with both pdfTeX and luaLaTeX.
%% * The legacy PDF/A class options have been dropped as of mid-2025.
%%
%% For details of the newtx package, refer to its documentation (available at CTAN: http://ctan.org).
%%
%% The use of commands defined or modified by the asmejour class is illustrated below. In particular, some care
%% is needed when using complicated math and macros in section headings, also illustrated below.
%%
%% ==> LaTeX distributions older than Oct. 2020 are not supported.
%%
%========================================================================
%%
%% LICENSE:
%%
%% Copyright (c) 2025 John H. Lienhard
%%
%% Offered under the MIT license: https://ctan.org/license/mit
%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% RECOMMENDED pdf management code.
%% This addition the LaTeX kernel was made by the LaTeX Project team in June 2022.
%% see https://www.latex-project.org/news/latex2e-news/ltnews35.pdf
%% If you have problems with these lines, your LaTeX format may be out of date. You can comment them out.
\DocumentMetadata{%
% testphase={phase-III,math,table,firstaid,title},% testphase for producing tagged pdf.
% pdfstandard = ua-2,
% pdfversion = 2.0,
pdfstandard=A-3u,% A-2b, A-2u, A-3b, or A-3u
pdfversion=1.7,
lang=en-US,
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Class options are described above. Use only the options you need.
%% Note: the [mathalfa=ccc=ddd] option was dropped in v1.25; load mathalpha in your preamble instead
\documentclass[balance,nocopyright,upint,varvw,hyphenate,barcolor=Goldenrod3,german]{asmejour}%
\allowdisplaybreaks % from amsmath package, allows multiline equations to break across pages (delete if not wanted)
% using \\* instead of \\ will prevent specific lines from being pagebreaks.
\usepackage{hologo} % access various latex logos if needed
%%%% pdf metadata %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\hypersetup{%
pdfauthor={John H. Lienhard}, % <=== change to YOUR name[s]!
pdftitle={ASME Journal Paper LaTeX Template}, % <=== change to YOUR pdf file title
pdfkeywords={ASME journal paper, LaTeX template, BibTeX style, asmejour class},% <=== change to YOUR pdf keywords
pdfsubject = {Describes the asmejour LaTeX template}, % <=== change to YOUR subject
% pdfurl={https://ctan.org/pkg/asmejour},% may delete
% pdflicenseurl={https://ctan.org/pkg/asmejour},% may delete
}
%%%% Journal name and optional copyright year %%%%%%%%%%%%%%
%% Omit "Journal of". If Journal Name is quite long, use \\ to insert a line break
\JourName{Heat and Mass Transfer}%<=== change to the name of your journal
%% The default copyright year is the current year
%% \PaperYear{2023} sets 2023; and \PaperYear{} omits the year entirely.
%%%% end of preamble %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{document}
% Change to your author name[s] and addresses, in the desired order of authors.
% First name, middle initial, last name
% Use title case (upper and lower case letters)
% Note usage below for corresponding author.
\SetAuthorBlock{John H.\ Lienhard\CorrespondingAuthor}{%
Fellow ASME\\
Rohsenow Kendall Heat Transfer Laboratory,\\
Department of Mechanical Engineering,\\
Massachusetts Institute of Technology,\\
Cambridge, MA 02139 USA\\
email: lienhard@mit.edu
}
% To label one or more corresponding authors put "Name\CorrespondingAuthor". No space after "Name".
% An optional argument can be added if email is not in address block as
% "Name\CorrespondingAuthor{write@to.me}"
% Can also include multiple emails and use the command more than once for multiple corresponding authors,
% "Name\CorrespondingAuthor{write@to.him, write@to.her}"
\SetAuthorBlock{Author Name[s]}{Department of Mechanical Engineering,\\
Institution or Company Name,\\
Street address,\\
City, State, Country\\
email: xxx@yyy.zzz
}
%%% Change to your paper title. Can insert line breaks if you wish (otherwise breaks are selected automatically).
\title{Preprint Template for ASME\\ Journal Papers: asmejour.cls}
%%% Change these to your keywords. Keywords are automatically printed at the end of the abstract.
%%% This command must come BEFORE the end of the abstract.
%%% If you don't want keywords, omit the \keyword{..} command.
\keywords{ASME, Paper, Template, {\upshape\LaTeX}, {\upshape\hologo{BibTeX}}, {\upshape\hologo{pdfLaTeX}}, {\upshape\hologo{LuaLaTeX}} }
%% Abstract should be no more than 250 words
\begin{abstract}
This paper is an example and a {\upshape\LaTeX} template for the {\upshape\texttt{asmejour}} class. Papers typeset in this class will follow ASME journal style for margins, fonts, headings, captions, and reference formats. The class will also lay out the author, title, and abstract in ASME style. The pdf file produced will include internal and external hyperlinks, bookmarks, and pdf metadata. The class is intended to be used with the {\upshape\texttt{asmejour.bst} \hologo{BibTeX}} style, which is part of this distribution. This style produces modern reference formats, including hyperlinked DOI and URL fields, and following current ASME practice. Options to the class include line numbering, final column balancing, various math options, government copyright notices, and archivability (PDF/A). In addition, section headers may contain mathematics, references, citations, and footnotes. The class is compatible with {\upshape\hologo{pdfLaTeX}} or {\upshape\hologo{LuaLaTeX}}.
\end{abstract}
\date{Version \versionno, \today}%% You can modify this information as desired.
%% Putting \date{} will suppress any date.
%% If this command is omitted, date defaults to \today
%% This command must come somewhere before \maketitle
\maketitle %% This command creates the author/title/abstract block. Essential!
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%% End of fields to be completed. Now write! %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Introduction}
The \texttt{asmejour} class typesets papers with margins, fonts, headings, captions, and reference formats that follow those used in journals published by the American Society of Mechanical Engineers (ASME). Internal and external hyperlinks will be set automatically, and the pdf file will contain bookmarks and metadata. Many other useful features are supported.
This class is not a publication of ASME, but the author has published in ASME journals since 1984. The intended use of this package is to enable authors to format their papers in ASME style prior to submission to an ASME journal for peer review.
The \texttt{.tex} file may be written using standard \LaTeX\ commands, although some specific initial commands are needed to format the block containing the author[s], title, and abstract. The class calls a number of packages, all of which are contained in up-to-date versions of \TeX~Live, Mac\TeX, and similar platforms. If you find that you are missing a package, you may obtain it at no cost from CTAN (\href{http://ctan.org}{ctan.org}).
Both \hologo{pdfLaTeX} and \hologo{LuaLaTeX} will load fonts that should be in your \LaTeX\ installation (all are in TeX Live). If fonts are missing from your installation, you can get them in CTAN (\href{http://ctan.org}{ctan.org}). For best results, use an up-to-date \LaTeX\ installation and update it every year or so.
\subsection{Essential Initial Commands}
To begin, fill in the fields to be completed at top of the \texttt{asmejour-template.tex} file. The first are pdf metadata in the preamble that will tag the pdf file itself. Next is the \verb|\JourName{..}| command, which should be changed as appropriate (omit ``Journal of'').
For each author, put author names and affiliation (with line breaks) into a separate \verb|\SetAuthorBlock{name}{affiliation}| command; follow the syntax illustrated \texttt{asmejour-template.tex} file. One author (or more) may be designated as the corresponding author by placing the command \verb|\CorrespondingAuthor| at the end of that name.
The title should be placed into \verb|\title{..}|, and line breaks may be specified if desired. Keywords may optionally be including using the \verb|\keywords{..}| command; this command \textit{must} be issued before the abstract. To omit keywords, just omit this command. Next, the abstract text must be placed into \verb|\begin{abstract}|\ldots\verb|\end{abstract}|. The abstract will automatically be italicized.
The date is automatically given as an unnumbered footnote, which defaults to \verb|\today|. Different text may be given using \verb|\date{..}|. Putting \verb|\date{}| will suppress the date footnote.
After setting up the authors, title, and abstract, issue the \verb|\maketitle| command. The introduction section comes next.
\subsection{Option to Color the Title Bar}
The vertical bar in the title block is black in all ASME journals. Since the \texttt{asmejour} class is only for preprints, we include the [fun] option to have the bar in color. Any color \texttt{name} recognized by the \texttt{xcolor} package~\cite{kern} may be invoked by including the option \texttt{[barcolor=name]} in the \verb|\documentclass[..]{asmejour}| command. The color for this example is \texttt{Goldenrod3}. To have a black bar, either omit \texttt{barcolor} entirely or use the name \texttt{black}.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{References to Figures, Equations, and Citations}
For ASME papers, the labels Figure and Equation should be abbreviated when they do not start a sentence, as in Fig.~\ref{fig:1} and Eq.~\eqref{eqn:1}. Figure~\ref{fig:1} is spelled out when it starts a sentence. Equation~\eqref{eqn:1} is spelled out when it starts a sentence.
Citations will be numbered automatically \cite{DKE1969}. They should be inserted at the appropriate point using a \verb|\cite{ref}| command~\cite{toohey2007,gibson2008}. The citations will be automatically sorted and compressed, as well, if they are given in a set \cite{stevens1999, DKE1969, wions2006, oligaria2011, mollen2014, smith2014, apple2019}. If naming a reference explicitly, put ``Ref.''\ in front of the number, as in Ref.~\cite{smith2014}. Reference~\cite{smith2014} is appropriate at the beginning of a sentence.
See the \texttt{asmeconf-sample.bib} file for examples of how to enter your references.
Equations are typeset in the usual way. The class file loads the \texttt{amsmath} and \texttt{mathtools} packages, which provide many macros to support sophisticated mathematics. Both work with either \hologo{pdfLaTeX} or \hologo{LuaLaTeX}.
\begin{equation}\label{eqn:1}
\mathbf{q} = -k\nabla T
\end{equation}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Section Headings and Captions}
ASME sets section headings and captions in bold face. In addition, the captions are in sans-serif type. The \texttt{asmejour} class chose appropriate fonts automatically. You can place \verb|\cite{..}|, \verb|\ref{..}|, \verb|\label{..}|, and into headings and captions directly, as you would in the main text. You can place \verb|\footnote{..}| into headings, but not into captions.\footnote{See \texttt{tex-stackexchange} for various approaches to footnotes in captions, if they seem necessary. For footnotes in tables, use the \texttt{tablefootnote} package.}
Sections may be numbered or left unnumbered. ASME publishes papers in either style.
Single-sentence captions should not end with a period. Multi-sentence captions do include periods.
Math can be used in captions or section headings, and an appropriate math font will be selected automatically. For a section heading that includes complicated math (and macros), you may use the optional argument of \verb|\section[..]{..}| to create a pdf bookmark without losing characters or producing warnings or errors. See the \texttt{asmejour-template.tex} source file for examples of this technique. These bookmarks should usually be text expressions, although some math is supported.
If you wish to override the default math format in a heading or caption, put \verb|\mathversion{normal}| in the heading or caption.
\subsection{More About Headings}
Section, subsection, and subsubsection headings should be in title case (first letter of primary words capitalized). ASME does not use \verb|\paragraph|, so the class file equates this command to \verb|\subsubsection|.
%%%%%%%%%%%%% begin figure %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% captions go below figures
\begin{figure}
\centering\includegraphics[width=\linewidth,alt={Linearization errors}]{sample-figure-1.pdf}
% best practice is to change \eqref to (\ref* ) in optional argument of caption, but it's usually not important
\caption[Caption with math, eqn.~(\ref*{eqn:1}): $\Delta T/T_m$ vs.\ $\Delta T/T_1$~\cite{lienhard2019}]{Caption with math, eqn.~\eqref{eqn:1}: $\Delta T/T_m$ vs.\ $\Delta T/T_1$~\cite{lienhard2019}\label{fig:1}}
\end{figure}
%%%%%%%%%%%%% end figure %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Tables and Figures}
Table \ref{tab:1} is an example of a simple table. Table captions should be placed above tables.
The class loads the \texttt{array} and \texttt{dcolumn} packages which provide extended capabilities for columns in the \texttt{tabular} environment (used in Tables \ref{tab:2} and \ref{tab:3}). Table~\ref{tab:3} is coded to have exactly the width of a text column.
The \texttt{booktabs} package \cite{fear} is loaded (and customized) to provide versions of \verb|\toprule|, \verb|\midrule|, and \verb|\bottomrule| appropriate to ASME-style tables.
Table~\ref{tab:4} spans both text columns using the \texttt{table*} environment. Figure~\ref{fig:2} spans both columns using the \texttt{figure*} environment. Two column tables and figures will always float to the top of a later page. Subcaptions in figures, such as Fig.~\ref{fig:isothermal-wall}, may be labeled and referenced individually.
Text in the figures should be checked for legibility at either single-column width (about 83~mm) or full-column width (about 170~mm). Figure captions should be placed below figures. Images in figures are handled by the standard \texttt{graphicx} package.
Landscape figures and tables may be produced at full-page size by putting \verb|\usepackage[figuresright]{rotating}| in your \texttt{.tex} file's preamble and using the \texttt{sidewaystable*} and \texttt{sidewaysfigure*} environments~\cite{fairbairns}.
%%%%%%%%%%%%%%%%% begin two column figure %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure*}[t]
\begin{subfigure}[t]{0.5\textwidth} % You will get same result using \begin{minipage}[t]{0.5\textwidth}
\centering{
\includegraphics[width=0.9\linewidth,alt={Nusselt number data for isothermal wall}]{sample-figure-2a.pdf}
\subcaption{}\label{fig:isothermal-wall}
}%
\end{subfigure}%
%%%%%%%% don't leave a break here
\begin{subfigure}[t]{0.5\textwidth} % You will get same result using \begin{minipage}[t]{0.5\textwidth}
\centering{
\includegraphics[width=0.927\linewidth,alt={Nusselt number data for constant heat flux wall}]{sample-figure-2b.pdf}
\subcaption{}\label{fig:uniform-flux-wall}
}\end{subfigure}%
\caption{A figure with two subfigures: \subref{fig:isothermal-wall} uniform wall temperature; and \subref{fig:uniform-flux-wall} uniform wall heat flux, unheated starting length \cite{lienhard2020}\label{fig:2}}
\end{figure*}
%%%%%%%%%%%%%%% end two column figure %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Reference Formatting with \texttt{asmejour.bst}}
The {\upshape\texttt{asmejour.bst}} \hologo{BibTeX} style follows the reference styles observed in ASME journals in 2025.\footnote{\texttt{asmejour.bst} is intended as a replacement for the older style \texttt{asmems4.bst}, which does not follow ASME's current reference formats or support DOI and URL.} The vast majority of published references are to journal papers and books. Examples for these and many other entry types are given in the \texttt{asmejour-sample.bib} file, which is part of this distribution. Citations and references are managed by the \texttt{natbib} package.
Nevertheless, a few comments are necessary.
\subsection{Capitalization of Titles} ASME's bibliography style requires that titles be in title case. The first letters of principal words are capitalized. This must be done when writing the \texttt{.bib} file.
ASME capitalizes ``With'', but not other prepositions.
\subsection{Hyperlinked Titles or Paper Numbers} When the entries \verb|@article{..|, \verb|@book{..|, \verb|@inbook{..|, \verb|@incollection{..|, \verb|@proceedings{..|, or \verb|@techreport{..| include \verb|doi={..}|, the document title, paper number, or report number will be hyperlinked to that doi number, and the doi number will not be printed. If no doi is included, but a url or eprint is included, then the title will be hyperlinked to that url or eprint. To display the doi (or the url or eprint when no doi is given), put it into the \verb|note={..}| field (using \verb|\doi{..}| or \verb|\url{..}| ) like this:
\begin{quote}
\verb|note = {\doi{10.1115/1.4042912}}|
\end{quote}
Include doi numbers in references whenever possible.
%%%%%%%%%%%%%%% begin simple table %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% captions go above tables
\begin{table}[t]
\caption{A simple table}\label{tab:1}
\centering{%
\begin{tabular}{l l r}
\toprule
Experiment & $u$ [m/s] & $T$ [\textdegree C] \\
\midrule
Run 11 & 12.5 & 103.4 \\
Run 12 & 24 & 68.3 \\
\bottomrule
\end{tabular}
}%
\end{table}
%% Note: location of tables and figures can be adjusted with the options [!tbhp]
%% see: https://latexref.xyz/dev/latex2e.html#Floats
%%%%%%%%%%%%%%%%% end table %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%% begin more complicated table %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{table}[t]
\caption{Table with more complicated columns}\label{tab:2}%
\centering{%
\begin{tabular}{!{\hspace*{0.5cm}} >{\raggedright\hangindent=1em} p{3cm} d{3} @{\hspace*{1cm}} d{3} !{\hspace*{0.5cm}}}
\toprule
Experiment & \multicolumn{1}{c@{\hspace*{1cm}}}{$u$ [m/s]} & \multicolumn{1}{c!{\hspace*{0.5cm}}}{$T$ [\textdegree C]} \\
\midrule
The first experiment we ran this morning & 124.3 & 68.3 \\
The second experiment we ran this morning & 82.50 & 103.46 \\
Our competitor's data & 72.321 & 141.384\\
\bottomrule
\end{tabular}
}%
\end{table}
%%%%%%%%%%%%%%%% end table %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{eprint Support} Elementary support for \texttt{eprint} numbers is included, either hyperlinking or generating a url at the end of the citation. The \texttt{archive} type may be specified using the macros \texttt{arxiv, googlebooks, hndl, jstore, oclc}, or \texttt{pubmed} (e.g., \texttt{archive=hndl}, \textit{without} braces). Both \texttt{eprint} and \texttt{archive} fields \textit{must} be given. Other root urls may be invoked using \verb|archive = {http://another.url.org/}|.
\subsection{Online Sources} A bibliography field \verb|@online{..| is included for citation of online sources, such as web pages. A \texttt{url}, \texttt{doi}, or \texttt{eprint} with \texttt{archive} should be included. See the examples of use in the \texttt{asmejour-sample.bib} file.
\subsection{Date Accessed} The \verb|urldate={..}| field may be used to provide the date on which a given url was accessed. By default, the text printed will be \texttt{accessed `date',}. The word ``accessed'' may be changed using the \verb|urltype={..}| field.
\subsection{Conference Location and Date} For the entry types \verb|@inproceeedings{..| and \verb|@proceeedings{..|, you may include \verb|venue={..}| and \verb|eventdate={..}| to specify the city and the date of a conference. Omit \verb|address={..}| if \verb|venue={..}| is used.
\subsection{Version Number\footnote{Footnotes can appear in \texttt{\string\section} commands.\label{ftnt:3}}}
The \verb|version={..}| field may be used with \verb|@book|, \verb|@online|, and \verb|@manual|. By default, the text will read \texttt{Version `number'} as in Refs.~\cite{sharpe1,sharpe2}, but different wording may be selected using the \verb|versiontype={..}| field, e.g., to say ``Revision'' or something similar, as in Ref.~\cite{GSL}. ASME often puts the version in the title, as in Refs.~\cite{dlmf, texshop}, so I've left the final decision for discussion between the authors and the copy editor.
\subsection{Articles in Collections} In addition to the standard entry, \verb|@incollection{..|, an entry \verb|@inserialcollection{..| is defined for serials in which each volume has a different title. See the \texttt{asmejour-sample.bib} file for discussion and compare Ref.~\cite{clauser56} to Ref.~\cite{DKE70}.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{More on Math}
In most cases, long equations can be kept below the column width by using one of the multiline equation environments defined by \texttt{amsmath},
such as \texttt{align}, \texttt{split}, or \texttt{multline}~\cite{amsmath}. The following equation is set with the \texttt{multline} environment:
\begin{multline}
\frac{\partial}{\partial t}\left[\rho\Bigl(e + \lVert\mathbf{u}\rVert^2\mspace{-3mu}\big/2\Bigr)\right] + \nabla\cdot\left[\rho\Bigl(h + \lVert\mathbf{u}\rVert^2\mspace{-3mu}\big/2 \Bigr)\mathbf{u}\right]\\
={}-\nabla \cdot \mathbf{q} + \rho \mathbf{u}\cdot\mathbf{g}+ \frac{\partial}{\partial x_j}\bigl(d_{ji}u_i\bigr) + \dot{Q}_v\label{eqn:energy}
\end{multline}
An example using \texttt{align} appears in Appendix~\ref{app:zetafunction}.
For equations that seem impossible to break over several lines, two options are available. First,
an experimental package for setting equations that span two columns, \texttt{asmewide.sty}, can be loaded, although that code may require hand-fitting around floats and page breaks (see the examples in~\cite{lienhard2025}). Second, a new page can be started in one-column mode, then returning to two-column mode:
\begin{verbatim}
\twocolumn[A passage of single column text.
\[ F = \textrm{wide and unbreakable expression} \]
]
\end{verbatim}
That approach also involves finding a break point, to avoid leaving a lot of white space on the previous pages.
Math italics are used for Roman and lower-case Greek letters by default. If you want an upright letter in math, you can use the relevant math alphabet, e.g., \verb|\mathrm, \mathbf, \mathsf|:
\begin{equation}\label{eqn:newton2}
\vec{F} = m \vec{a} \quad\textrm{or}\quad \vec{\mathrm{F}} = m \vec{\mathrm{a}} \quad\textrm{or}\quad \mathbf{F} = m \mathbf{a} \quad\textrm{or}\quad \vec{\mathsf{F}} = m \vec{\mathsf{a}}
\end{equation}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% The next passage needs to run with either lualatex or pdftex, which call bold-italic math differently. So we define the following to work with either:
\newcommand*\MyMathbfit[1]{\ifPDFtex\bm{#1}\else\symbfit{#1}\fi}
ASME typesets vectors in upright bold, like the third instance in Eq.~\eqref{eqn:newton2}, and sets matrices in bold italic. In the next equation, $\mathbf{w}$ is a vector and $\MyMathbfit{J}_1$ is a matrix:
\begin{equation}\label{eqn:dw}
d\mathbf{w} =
\begin{pmatrix}
du \\ dv
\end{pmatrix} =
\underbrace{\begin{pmatrix}
\partial u/\partial x & \partial u/\partial y \\
\partial v/\partial x & \partial v/\partial y
\end{pmatrix}}_{=\,\MyMathbfit{J}_1} \begin{pmatrix} %% see 12 lines above for \MyMathbfit !
dx \\ dy
\end{pmatrix}
\end{equation}
Note that selecting bold-face italic depends on the engine: with \hologo{pdfTeX}, do \verb|\bm{..}|; with \hologo{LuaLaTeX}, do \verb|\symbfit{..}|. But for both engines, you can get upright letters, as used in the text font, using \verb|\mathbf{..}| or with \verb|\textbf{..}|
\begin{equation}
\mathbf{u}_r = u_r\,\hat{\textbf{\i}}+v_r\,\hat{\textbf{\j}}+w_r\,\hat{\textbf{k}}
\end{equation}
or, \textit{very} rarely (perhaps never?), \verb|\mathversion{bold}| for an entire equation\footnote{For sans-serif math expressions, \texttt{asmejour.cls} provides \texttt{\string\mathversion \{sans\}} and \texttt{\string\mathversion \{sansbold\}}. These fonts can act as engineering gothic for figures.}:
\mathversion{bold}\begin{equation}
S = k \ln w = k \ln \biggl(\frac{N!}{\prod_i N_i!}\biggr)
\end{equation}
\mathversion{normal}% avoiding an extra line break with %
Note that the math version must be changed \textit{before} starting math mode. To end bold, do \verb|\mathversion{normal}|.
Slanted lower-case greek letters are available in the usual way, e.g., \verb|\alpha|. The class file also provides \textit{upright} sans-serif Greek letters with \verb|\sfalpha| and similar expressions: $\sfalpha, \sfbeta, \sfgamma, \sfdelta,$ etc. Bold upright sans-serif greek can be obtained in \hologo{pdfTeX} as \verb|\bm{\sfalpha}| or in \hologo{LuaLaTeX} as \verb|\sfbfalpha|.
Also note that \texttt{newtxmath} (\hologo{pdfTeX}) provides upright, serif Greek letters as, e.g., \verb|\upomega| (vs.\ \verb|\omega|).
\subsection{The \texttt{newtxmath} and \texttt{unicode-math} Packages~\cite{sharpe1,robertson2023}} The \texttt{newtxmath} package, loaded by default with \hologo{pdfLaTeX}, includes many options for mathematics, most of which can be called as options to \verb|\documentclass|. For example, the \texttt{upint} option selects upright integral signs (rather than slanted integral signs):
\begin{quote}
\verb|\documentclass[upint]{asmeconf}|.
\end{quote}
The option \verb|subscriptcorrection| improves the spacing of math subscripts. Math options are discussed further in the \texttt{asmeconf-template.tex} file.
If using \hologo{LuaLaTeX}, the math features of \texttt{unicode-math} are available. These include commands to select a boldface, upright symbol, \verb|\symbfup{..}| or \verb|\mathbfup{..}|, to select boldface fraktur symbol, \verb|\symbffrak{..}| or \verb|\mathbffrak{..}|, and so on. See the documentation of \texttt{unicode-math} for details~\cite{robertson2023}.
The \texttt{[upint]} option also works under \hologo{LuaLaTeX}.
\subsection{Controlling Calligraphic, Script, Fraktur, or BB Fonts}
With \hologo{pdfLaTeX}, the \texttt{[mathalpha]} package may be loaded in the preamble~\cite{sharpe2}.\footnote{As of v1.25, the \texttt{[mathalfa=ccc=ddd]} class option has been dropped.} This package supports variety of font for calligraphic, fraktur, script, and blackboard bold fonts. For example,
\begin{center}
\verb|\usepackage[cal=euler,frak=boondox]{mathalpha}|
\end{center}
selects the Euler font for \verb|\mathcal| and the Boondox font for \verb|\mathfrak|. See the \texttt{mathalpha} documentation for details~\cite{sharpe2}.
Under \hologo{LuaLaTeX}, the \texttt{unicode-math} \texttt{range} function can be used to select such fonts~\cite{robertson2023}. For example, the following command in the preamble would select the Euler Math font for calligraphic, script, fraktur, and blackboard bold fonts:
\begin{quote}\raggedright
\verb|\setmathfont{Euler-Math}[|
\verb| range={cal,scr,frak,bb},|
\verb| Extension=.otf,Scale=MatchUppercase]|
\end{quote}
%% Dealing with complicated math in a section heading: optional argument of \section provides the pdf bookmark
%% without losing characters or producing warnings/errors. Note that bookmark can include simple math.
%% The command \mathbf{U} takes the U the character from the bold text font
\subsection[Math in a Section Heading: \omega\cdot U=0]{Math in a Section Heading: $\dot{\omega}\cdot\mathbf{U}=0$}
To include complicated math in a section heading without producing bookmark-related errors, use the optional argument of \verb|\section| to create the pdf bookmark. The heading above was set with the following command:
\begin{quote}\raggedright
\verb|\subsection[Math in a Section Heading:|
\hspace*{1em}\verb|\omega\cdot U=0]{Math in a Section Heading:|
\hspace*{1em}\verb|$\dot{\omega}\cdot\mathbf{U}}=0$}|
\end{quote}
Note that bookmarks can include simple math.
\subsection{Units and Nomenclature} ASME requires SI units. U.~S.\ style units may follow in parentheses. Be sure to put your symbols into the nomenclature list, including the SI units.
%%%%%%%%%%%%%%%%%%% begin linewidth table %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{table}[t]
\caption{Table at full column width with columns in math mode}\label{tab:3}
\newcolumntype{C}{>{$}c<{$}} % math-mode version of "c" column type, from array package
\begin{tabular*}{\linewidth}{@{\extracolsep{\fill}}CCCC@{\extracolsep{\fill}}}
\toprule
X_{z} & X_{c} & X_{c,m} & X_{c,2}\rule{0pt}{8pt}\\
3.92069 & 5.70943 & 6.32429 & 7.08757\\[2pt]
\varepsilon (T_1) & \varepsilon^i (T_1) & \varepsilon^i (T_m) & \alpha (T_1, T_2)\\
0.7258 & 0.6237 & 0.6807 & 0.7964 \\[2pt]
q_\textrm{gray} & q_\textrm{int, $T_1$} & q_\textrm{int, $T_m$} & q_\textrm{exact}\\
400.2 & 462.1 & 371.0 & 371.8 \\
\bottomrule
\end{tabular*}
\end{table}
%%%%%%%%%%%%%%%%%%%% end linewidth table %%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Additional Options for \texttt{asmejour.cls}}
\subsection{Lists of Figures and Tables} A list of figures and a list of tables are generated automatically as the last page. To omit these lists, use the option \texttt{[nolists]}.
\subsection{Final Column Balancing} The option \texttt{[balance]} invokes the the \texttt{flushend} package~\cite{tolusis}.
This package will attempt to give equal height to the two columns on the last page. The performance of this package is sometimes inconsistent (with odd page layout or, very rarely, errors), so use this option with caution.
\subsection{Line Numbers} The option \texttt{[lineno]} invokes the the \texttt{lineno} package~\cite{bottcher}, which produces line numbers in the margins. You must run \LaTeX\ \textit{twice} for proper placement of the numbers. The \texttt{lineno} package is not compatible with the \texttt{flushend} package that makes final short columns the same height. Balancing is disabled when this option is called. See the documentation of the \texttt{lineno} package for further commands to control line numbering. The abstract, tables, captions, and footnotes will not be numbered.
\subsection{Changing the Footer Text}\label{sec:footer} The option \texttt{[nofoot]} will omit everything other than a page number from the page footer. The option \texttt{nocopyright} will omit the ASME copyright from the first page footer. The command \verb|\PreprintString{..}| replaces the words \textsf{PREPRINT FOR REVIEW}. The left and right preprint strings can be changed separately using an optional argument: \verb|\PreprintString{..}[L]| and \verb|\PreprintString{..}[R]|.
The final paper number may be added to the page number using \verb|\PaperNumber{..}|.
The footers are generated with the \texttt{fancyhdr} package~\cite{oostrum}.
\subsection{Vertical Space on Title Page} The space between the author/title/abstract block and the main text defaults to 12.5~mm. Infrequently, a different value may be desirable. The space can be changed using \verb|\AbstractSep{..}|, where the argument is a \LaTeX\ dimension with units (e.g., 5mm).
\subsection{Federal Copyright Notices} Several types of copyright statement can be placed in an unnumbered footnote on the first page. Use the option \texttt{[govt]} when all authors are federal employees, \texttt{[govtsome]} when some authors are federal employees, and \texttt{[contractor]} when the authors are federal contractors.
\subsection{Archivability:~PDF/A} In June 2022, the \LaTeX{}3 team added support for PDF/A to the \LaTeX\ kernel through the command \verb|\DocumentMetadata{..}|. This approach works with \textit{both} \hologo{pdfLaTeX} and \hologo{LuaLaTeX}. Note that accessible conformance~(\texttt{a} or \texttt{UA-2} level, a.k.a.\ ``well-tagged PDF'') is still under development by the \LaTeX3 team.
As of \texttt{asmejour} v1.25, the legacy PDF/A options \texttt{[pdf-a]}, \texttt{[pdfapart=]}, and \texttt{[pdfaconformance=]} have been dropped.
\subsection{Typewriter Font Options} This font is the sans-serif, monospaced font \texttt{inconsolata}. By default, the word spacing is variable, but option \texttt{[mono]} ends this behavior. A slashed zero is the default; option \texttt{[var0]} removes the slash. Option \texttt{[hyphenate]} enables hyphenation of the typewriter font when running \hologo{pdfTeX}.
\subsection{Single column layout} The class option \texttt{[singlecolumn]} switches from two-column to one-column layout.
%%%%%%%%%%%%%%% begin two column table %%%%%%%%%%%%%%%%%%
%
% note: the fourth column could be a dcolumn instead of using \makebox, with d{1.4} replacing c column.
%
\begin{table*}[t]
\caption{A table spanning two columns}\label{tab:4}%
\centering{%
\begin{tabular*}{0.8\textwidth}{@{\hspace*{1.5em}}@{\extracolsep{\fill}}ccc!{\hspace*{3.em}}ccc@{\hspace*{1.5em}}}
\toprule
\multicolumn{1}{@{\hspace*{1.5em}}c}{$x$\rule{0pt}{8pt}} &
\multicolumn{1}{c}{$\textrm{erf}(x)$} &
\multicolumn{1}{c!{\hspace*{3.em}}}{$\textrm{erfc}(x)$} &
\multicolumn{1}{c}{$x$} &
\multicolumn{1}{c}{$\textrm{erf}(x)$} &
\multicolumn{1}{c@{\hspace*{1.5em}}}{$\textrm{erfc}(x)$} \\
\midrule
0.00 & 0.00000 & 1.00000 & 1.10 & 0.88021 & 0.11980 \\
0.05 & 0.05637 & 0.94363 & 1.20 & 0.91031 & 0.08969 \\
0.10 & 0.11246 & 0.88754 & 1.30 & 0.93401 & 0.06599 \\
0.15 & 0.16800 & 0.83200 & 1.40 & 0.95229 & 0.04771 \\
0.20 & 0.22270 & 0.77730 & 1.50 & 0.96611 & 0.03389 \\
0.30 & 0.32863 & 0.67137 & 1.60 & 0.97635 & 0.02365 \\
0.40 & 0.42839 & 0.57161 & 1.70 & 0.98379 & 0.01621 \\
0.50 & 0.52050 & 0.47950 & 1.80 & 0.98909 & 0.01091 \\
0.60 & 0.60386 & 0.39614 & 1.82\makebox[0pt][l]{14} & 0.99000 & 0.01000 \\
0.70 & 0.67780 & 0.32220 & 1.90 & 0.99279 & 0.00721 \\
0.80 & 0.74210 & 0.25790 & 2.00 & 0.99532 & 0.00468 \\
0.90 & 0.79691 & 0.20309 & 2.50 & 0.99959 & 0.00041 \\
1.00 & 0.84270 & 0.15730 & 3.00 & 0.99998 & 0.00002 \\
\bottomrule
\end{tabular*}
}%
\end{table*}
%%%%%%%%%%%%%%%% end two column table %%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Conclusions}
The class \texttt{asmejour} and associated files are for typesetting preprints in the style of ASME journals.
Documentation is provided in this file and by comments in the \texttt{.tex} source code. Examples of references are shown in the \texttt{asmejour-sample.bib} file. The \texttt{asemjour.bst} file produces references following ASME's current formats. The code is compatible with both {\hologo{pdfLaTeX}} and \hologo{LuaLaTeX}. This package is not a publication of ASME and is offered at no cost under the terms of the \hrefurl{https://ctan.org/license/mit}{MIT license}.
\begin{enumerate}
\item First conclusion
\item Second conclusion
\item Third conclusion
\end{enumerate}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section*{Acknowledgment} %% ASME requests this exact spelling, singular.
Acknowledge individuals, institutions, or companies that supported the authors in preparing the work. Those mentioned might have provided technical support, insightful comments or conversations, materials used in the work, or access to facilities.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section*{Funding Data}
\begin{itemize}
\item U.S.\ Department of Heat Transfer, Office of Important Ideas (DOHT-OII Award No.\ 3.14159265)
\end{itemize}
%%%%%%%%% NOMENCLATURE %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%
%% The width of labels is set after two latex runs. If you don't like the result, an optional
%% argument to the environment can be given with the desired width, e.g., [20pt].
%% The name "nomenclature" can be changed using an optional second argument to the environment.
%% e.g., \begin{nomenclature}[40pt][List of Symbols]
%%
%% Entries may be given as shown below:
%%
%% \EntryHeading{Greek Letters}
%% \entry{symbol}{definition}
%%
\begin{nomenclature}
% capital letter comes first, lower case second
% don't capitalize first word of the definition
\entry{$\overline{h}$}{average heat transfer coefficient (W m$\cramped{^{-2}}$ K$\cramped{^{-1}}$)}% \cramped{} lowers superscripts; see documentation of mathtools package!
\entry{$k$}{thermal conductivity (W m$^{-1}$ K$^{-1}$)}
\entry{$\mathbf{q}$}{heat flux vector (W m$^{-2}$)}
\EntryHeading{Greek Letters}
\entry{$\alpha$}{thermal diffusivity (m$^2$ s$^{-1}$)}
\entry{$\nu$}{kinematic viscosity (m$^2$ s$^{-1}$)}
\EntryHeading{Dimensionless Groups}
\entry{Pr}{Prandtl number, $\nu/\alpha$}
\entry{Sc}{Schmidt number, $\nu/\mathcal{D}_{1,2}$}
\EntryHeading{Superscripts and Subscripts}
\entry{b}{bulk value}
\entry{$\infty$}{free stream value}
\end{nomenclature}
%%%%%%%%%%%%%%% APPENDICES %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Note that appendices will be "numbered" A, B, C, ... etc. Use \section, not \section*
%% The equation counter is automatically reset for each appendix
%% Figures will be numbered consecutively with the paper.
\appendix % starts appendices
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Incomplete Zeta Function~\cite{lienhard2019}\label{app:zetafunction}}
This text is just for illustration. The radiation fractional function may be written in terms of the incomplete zeta function for convenience:
\begin{align}
f(\lambda T) &= \frac{1}{\sigma T^4} \int_0^\lambda\frac{2\pi h c_o^2}{\lambda^5 \left[ \exp (h c_o/k_B T \lambda) - 1\right] } \, d\lambda \\
&= \frac{1}{\sigma T^4}\frac{2\pi k_B^4 T^4}{h^3c_o^2}\int^\infty_{c_2/\lambda T}\frac{t^3}{e^t -1}\, dt\label{eqn:zeta}
\end{align}
When $\lambda T \rightarrow \infty$, $f = 1$ and the last equation yields the well-known result
\begin{equation}
\sigma T^4 =\frac{2\pi k_B^4 T^4}{h^3c_o^2} \underbrace{\int_0^\infty \frac{t^3}{e^t - 1} \, dt}_{\equiv\mspace{2mu} \zeta(4)\Gamma(4)}
\end{equation}
where the Gamma function $\Gamma(4) = 3!$ and the Riemann zeta function, $\zeta(4)$, has the indicated integral representation \cite[\S13.12]{ww1927}. A classical result due to Euler \cite{euler1740} gives $\zeta(4) = \pi^4/90$ (see also \cite[\S167]{euler1748}), from which we recover the usual definition of the Stefan-Boltzmann constant, $\sigma$.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Language Support\label{app:language}}
ASME publishes in English, but the \texttt{babel} package is loaded for users who may wish to include other languages.
For example, an author might wish to include an appendix that provides the abstract in another language. As an example,
a passage in German is shown in \selectlanguage{german}\appendixname~\ref{app:pohlhausen}\selectlanguage{english}.
When more than one language option is included in \verb|\documentclass[..]{asmejour}|, English will be
assumed to be the main language of the document. (To choose a different main language, set the class option \texttt{[main=..]}).
The standard caption and section names will follow \texttt{babel}'s dictionary for primary languages other than English. Users may additionally change ``Keywords'', ``Nomenclature'', and ``Corresponding author'' by renewing the commands \verb|\keywordname|, \verb|\nomname|, and \verb|\CAwords|. Changes to the page footer were described in Sec.~\ref{sec:footer}.
The font encoding is set to T1 (\hologo{pdfLaTeX}) or TU (\hologo{LuaLaTeX}), and utf-8 input is supported:
%% If you have trouble with the next line, your file may not be saved in utf-8 format. You can delete these lines to resolve the issue.
\typeout{If you have trouble with the next line, your file may not be saved in utf-8 format. You can delete that line to resolve the issue.}
\ifluatex\typeout{Under LuaLaTeX, some of these accents must be obtained as escaped characters, with \=a, \c{e}, \l, \.o, \oe, \v{z}, \'z, etc.}\fi
àáâäæãåā èéęëêēė îïíīįì ôöòóœøōõ ûüùúū çćč ł ñń ßśš ÿ žźż.
Note that some languages make characters ``active.'' For example, the \texttt{[spanish]} option of \texttt{babel} makes the period character active. This change conflicts with the default behavior of \texttt{dcolumn} in this class, which aligns table columns of type \verb|d{m.n}| on the decimal point (see comments in the \texttt{.cls} file).
No effort has been made to support customization of language-specific fonts.\footnote{For English, you \textit{must} have these OpenType fonts (\texttt{.otf}) installed (all are in TeX Live and will be present if your installation is complete and up-to-date): TeX Gyre Termes, TeX Gyre Termes Math, TeX Gyre Heros, Inconsolatazi4, XITSMath-Bold, LeteSansMath, LeteSansMath-Bold, and STIX Two Math.} Such fonts can be implemented using \texttt{babel} commands with \texttt{fontspec} under \hologo{LuaLaTeX}. The bibliography style, \texttt{asmejour.bst}, is designed in English and aimed at \texttt{BibTeX}.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\selectlanguage{german}
\section{Der Wärmeaustausch zwischen festen Körpern und Flüssigkeiten mit kleiner reibung und kleiner Wärmeleitung (von E. Pohlhausen)\label{app:pohlhausen}}
In einer strömenden Flussigkeit sind Wärmeleitung und Wärmekonvektion Vorgänge, die mit der inneren Reibung (oder Impulsleitung) und mit der Impulskonvektion große Aehnlichkeit besitzen. Mathematisch findet dies seinen Ausdruck in dem gleichartigen Bau der Differentialgleichungen, die einerseits für die Temperatur und anderseits für den Geschwindigkeitsvektor in der Flüssigkeit bestehen. Man kann daraus auf eine Beziehung
zwischen dem Wärmeaustanch und dem Reibungswiderstand schließen, die eine strömende Flüssigkeit an einem festen Körper hervorrufen. Dies ist zuerst von Prandtl ausgesprochen und durchgeführt worden, und zwar für turbulente Vorgänge, unter der vereinfachenden Annahme von Wärmequellen und -senken im Innern der Flüssigkeit~\cite{pohlhausen1921}.
\selectlanguage{english}% don't forget to return to your main language
%%%%%%%%%%%%% BIBLIOGRAPHY %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\nocite{*} %% <=== Delete this line - unless you wish to typeset the entire contents of your .bib file.
\bibliographystyle{asmejour} %% .bst file that follows ASME journal format. Do not change.
\bibliography{asmejour-sample} %% <=== change this to name of your bib file
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% To omit final list of figures and tables, use the class option [nolists]
\end{document}

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%% Examples of a widetext macro for setting wide equations in the asmejour class.
%%
%% Copyright (c) 2025 John H. Lienhard. Use under the MIT license: https://ctan.org/license/mit
%%
%%
%% USAGE: * \begin{widetext} ...wide material here... \end{widetext}
%% OPTIONAL ARGUMENTS:
%% * \begin{widetext[N] .. changes upper/lower separation of wide material from default 10pt to Npt
%% * \begin{widetext}[][tbn]: t = top line only; b = bottom line only; n = no lines. BOTH arguments are REQUIRED, even if first is left empty.
%%
%% The widetext environment can only appear once per page. It clashes with floats and footnotes, as discussed herein.
%%
%% NB: the strip environment from cuted is incompatible with the [lineno] option to asmejour!
%%
\DocumentMetadata{%
pdfstandard=A-3u,% A-2b, A-2u, A-3b, or A-3u (don't use u options with LuaLaTeX)
pdfversion=1.7,
lang=en-US,
}
\documentclass[nocopyright,nolists]{asmejour}
%% This file's version and date are:
\def\AJwidetextversion{1.04}
\def\AJverdate{April 5, 2025}
%
\usepackage{asmewide}
\usepackage{lipsum}% Latin filler text (lipsum generates a message about 'unused global options' - this can be ignored)
%
%%%% asmejour template inputs %%%%
\JourName{Applied Mechanics}
\date{Version~\AJwidetextversion. Revised \AJverdate}
%
\makeatletter
\definecolor{JAMBlue}{rgb}{0.090, 0.574, 0.637} % 23, 147, 163 - similar to JAM masthead color
\renewcommand\asmejour@barcolor{JAMBlue!80!white}
\makeatother
%
%%%%
%
\begin{filecontents}{asme-wide-equations.bib}
@online{lienhard2021,
author = {Lienhard, V, John H.},
title = {Preprint Template for {ASME} Journal Papers: \texttt{asmejour.cls}},
organization = {Comprehensive \TeX\ Archive Network},
version = {{\versionno}},
year = {2021},
url = {https://ctan.org/pkg/asmejour},
urldate = {{\today}},
}
@online{tolucsis1,
author = {Sigitas Tolu\v{s}is},
year = {2021},
title = {The \texttt{cuted} package},
version = {2.0},
organization = {Comprehensive \TeX\ Archive Network},
url = {https://ctan.org/pkg/cuted},
urldate = {Dec. 30, 2021},
}
@online{tolucsis2,
author = {Sigitas Tolu\v{s}is},
year = {2021},
title = {The \texttt{sttools} collection},
version = {3.0},
organization = {Comprehensive \TeX\ Archive Network},
url = {https://ctan.org/pkg/sttools},
urldate = {Dec. 30, 2021},
}
@book{stakgold,
author = {Ivar Stakgold},
title = {Boundary Value Problems of Mathematical Physics},
year = {1967},
publisher = {Macmillan},
address = {New York},
}
\end{filecontents}
%
\hypersetup{%
pdfauthor={John H. Lienhard},
pdftitle={Wide Equations in asmejour.cls},
pdfkeywords={ASME journal paper, LaTeX template, wide equations, widetext},
pdfsubject = {Examples of setting wide equations in the asmejour LaTeX template},
pdfurl={https://ctan.org/pkg/asmejour},
pdflicenseurl={https://ctan.org/pkg/asmejour},
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{document}
\PreprintString{PREPRINT}
\SetAuthorBlock{John H.\ Lienhard V}{%
Fellow of ASME \\
Rohsenow Kendall Heat Transfer Laboratory, \\
Department of Mechanical Engineering,\\
Massachusetts Institute of Technology, \\
Cambridge, MA 02139 USA \\
email: lienhard@mit.edu
}
\title{Wide Equations in asmejour.cls}
\keywords{ASME journal, paper, {\upshape\LaTeX} template, wide equations, asmejour}
\begin{abstract}
This paper gives several examples of typesetting very wide equations with {\upshape\LaTeX} in the {\upshape\texttt{asmejour}} class~{\upshape\cite{lienhard2021}} using
{\upshape\texttt{asmewide.sty}}. The style defines is a version of the {\upshape\texttt{widetext}} enviroment built on the 2021 release of
{\upshape\texttt{cuted.sty}}~{\upshape\cite{tolucsis1}} from the
{\upshape\texttt{sttools}} bundle~{\upshape\cite{tolucsis2}}, which is available from CTAN, \href{http://ctan.org}{ctan.org}.
Significant hand-fitting around page breaks, floats, and footnotes is required to obtain good results. \textcolor{red}{Only the text
in \textbf{red} in this document meant to be read---the rest is simply filler to aid in layout.}
\end{abstract}
\maketitle
\section{Introduction}
\lipsum[1-3]
\section{Section}
\lipsum[4]
%%%%%%%%%%%%%%%%% begin two column figure %%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure*}[t]
\begin{subfigure}[c]{0.495\textwidth}
\centering{\includegraphics{zonal-harmonic2.pdf}}%
\subcaption{\label{fig:zonal}}
\end{subfigure}
%%%%%%%% don't leave a break here
\begin{subfigure}[c]{0.495\textwidth}
\centering{\includegraphics{tesseral-harmonic.pdf}}%
\subcaption{\label{fig:tesseral}}%
\end{subfigure}%
\caption{A figure with two subfigures: (a) Zonal harmonic $n=1, m=0$, (b) Tesseral harmonic $n=2, m=3$. See Appendix~\ref{sec:sph-har}.\label{fig:1}}
\end{figure*}
%%%%%%%%%%%%%%%%%%% end two column figure %%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\lipsum[5-8]
\section{Section}
\lipsum[9-12]
%%%%%%%%%%%%%%%%%%%% Example WT1 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Single Wide Equation on the Page}
\textcolor{red}{Equation~\eqref{eqn:WT1} is an equation with a matrix that is too large to fit into one column. A multiline math environment will not help because the equation cannot be broken into parts that each fit into a column.}
\textcolor{red}{A two-column wide figure, Fig.~\ref{fig:1}, has floated from a previous page to the top of this page, but this figure does not interfere with the \texttt{widetext} environment (a single column figure would cause problems).}
% let's have this work with either pdftex or luatex
\newcommand*\MyBoldPhi{\ifPDFtex\bm{\Phi}\else\symbfup{\Phi}\fi}
\begin{widetext}
\begin{equation}\label{eqn:WT1}
\mathbf{WT1:}\quad
\mathfrak{W}(\MyBoldPhi)= \begin{Vmatrix}
\dfrac\varphi{(\varphi_1,\varepsilon_1)} & 0 & \hdotsfor{4} & 0 & \\[\jot]
\dfrac{\varphi k_{21}}{(\varphi_2,\varepsilon_1)} & \dfrac\varphi{(\varphi_2,\varepsilon_2)} & 0 & \hdotsfor{3} & 0 \\[\jot]
\dfrac{\varphi k_{31}}{(\varphi_3,\varepsilon_1)} &\dfrac{\varphi k_{32}}{(\varphi_3,\varepsilon_2)} & \dfrac\varphi{(\varphi_3,\varepsilon_3)}& 0 & \hdotsfor{2} & 0 \\[\jot]
\vdots & & & \smash{\rotatebox{15}{$\ddots$}} & & & \vdots \\[\jot]
\dfrac{\varphi k_{n-2\, 1}}{(\varphi_{n-2},\varepsilon_1)} &
\dfrac{\varphi k_{n-2\, 2}}{(\varphi_{n-2},\varepsilon_2)} &\hdotsfor{1} & \dfrac{\varphi k_{n-2\,n-3}}{(\varphi_{n-2},\varepsilon_{n-3})} & \dfrac\varphi{(\varphi_{n-2},\varepsilon_{n-2})}& 0& 0 \\[\jot]
\dfrac{\varphi k_{n-1\, 1}}{(\varphi_{n-1},\varepsilon_1)} & \dfrac{\varphi k_{n-1\, 2}}{(\varphi_{n-1},\varepsilon_2)} &\hdotsfor{2} &
\dfrac{\varphi k_{n-1\,n-2}}{(\varphi_{n-1},\varepsilon_{n-2})}& \dfrac{\varphi}{(\varphi_{n-1},\varepsilon_{n-1})} & 0 \\[\jot]
\dfrac{\varphi k_{n1}}{(\varphi_n,\varepsilon_1)} & \dfrac{\varphi k_{n2}}{(\varphi_n,\varepsilon_2)} & \hdotsfor{3} &
\dfrac{\varphi k_{n\,n-1}}{(\varphi_n,\varepsilon_{n-1})} & \dfrac{\varphi}{(\varphi_n,\varepsilon_n)}
\end{Vmatrix}
\end{equation}
\end{widetext}
\lipsum[12-13]
%%%%%%%%%%%%%%%%%%%% Examples WT2 & WT3 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Two Wide Equations on the Page}
\lipsum[14-16]
\begin{widetext}%
\begin{equation}\mathbf{WT2:}
\int_a^b\biggl\{\int_a^b[f(x)^2g(y)^2+f(y)^2g(x)^2]
-2f(x)g(x)f(y)g(y)\,dx\biggr\}\,dy
\ne \frac{1}{\sqrt{\int_a^b\biggl\{g(y)^2\int_a^bf^2+f(y)^2
\int_a^b g^2-2f(y)g(y)\int_a^b fg\biggr\}\,dy}}
\end{equation}
\textcolor{red}{In this case, we have a pair of wide equations on the same page. The \texttt{widetext} environment cannot be used twice on the same page! To resolve the conflict, we remain in single column mode between the two equations.}
\textcolor{red}{This page also includes a single column float, Table~\ref{tab:2}. This float must come after the \texttt{widetext} environment. We use the \texttt{\textbackslash begin\{table\}[b]} option to force the table to the bottom of the column. The two column table, Table~\ref{tab:4}, floats to the top of the next page and creates no problems.}
\begin{equation}\mathbf{WT3:}
\int_a^b\biggl\{\int_a^b[f(x)^2g(y)^2+f(y)^2g(x)^2]
-2f(x)g(x)f(y)g(y)\,dx\biggr\}\,dy
\ne \frac{1}{\sqrt{\int_a^b\biggl\{g(y)^2\int_a^bf^2+f(y)^2
\int_a^b g^2-2f(y)g(y)\int_a^b fg\biggr\}\,dy}}
\end{equation}
\end{widetext}
\lipsum[17]
%%%%%%%%%%%%%%% begin single column table %%%%%%%%%%%%%%%%%%%%%%
\begin{table}[b]
\caption{Table with more complicated columns}\label{tab:2}%
\centering{%
\begin{tabular}{!{\hspace*{0.5cm}} >{\raggedright\hangindent=1em} p{3cm} d{3} @{\hspace*{1cm}} d{3} !{\hspace*{0.5cm}}}
\hline\hline
\rule{0pt}{10pt} Experiment & \multicolumn{1}{c@{\hspace*{1cm}}}{$u$ [m/s]} & \multicolumn{1}{c!{\hspace*{0.5cm}}}{$T$ [\textdegree C]} \\[1pt]
\hline
The first experiment we ran this morning & 124.3 & 68.3 \rule{0pt}{10pt} \\
The second experiment we ran this morning & 82.50 & 103.46 \\
Our competitor's data & 72.321 & 141.384 \\[1pt]
\hline\hline
\end{tabular}
}
\end{table}
%%%%%%%%%%%%%%%% end table %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%% begin two column table %%%%%%%%%%%%%%%%%%%%%%%%%
\begin{table*}[t]
\caption{A table spanning two columns}\label{tab:4}%
\centering{%
\begin{tabular*}{0.8\textwidth}{@{\hspace*{1.5em}}@{\extracolsep{\fill}}ccc!{\hspace*{3.em}}ccc@{\hspace*{1.5em}}}
\hline\hline
\multicolumn{1}{@{\hspace*{1.5em}}c}{$x$\rule{0pt}{11pt}} &
\multicolumn{1}{c}{$\textrm{erf}(x)$} &
\multicolumn{1}{c!{\hspace*{3.em}}}{$\textrm{erfc}(x)$} &
\multicolumn{1}{c}{$x$} &
\multicolumn{1}{c}{$\textrm{erf}(x)$} &
\multicolumn{1}{c@{\hspace*{1.5em}}}{$\textrm{erfc}(x)$} \\ \hline
0.00 & 0.00000 & 1.00000 & 1.10 & 0.88021 & 0.11980\rule{0pt}{11pt} \\
0.05 & 0.05637 & 0.94363 & 1.20 & 0.91031 & 0.08969 \\
0.10 & 0.11246 & 0.88754 & 1.30 & 0.93401 & 0.06599 \\
0.15 & 0.16800 & 0.83200 & 1.40 & 0.95229 & 0.04771 \\
0.20 & 0.22270 & 0.77730 & 1.50 & 0.96611 & 0.03389 \\
0.30 & 0.32863 & 0.67137 & 1.60 & 0.97635 & 0.02365 \\
0.40 & 0.42839 & 0.57161 & 1.70 & 0.98379 & 0.01621 \\
0.50 & 0.52050 & 0.47950 & 1.80 & 0.98909 & 0.01091 \\
0.60 & 0.60386 & 0.39614 & 1.82\makebox[0pt][l]{14} & 0.99000 & 0.01000 \\
0.70 & 0.67780 & 0.32220 & 1.90 & 0.99279 & 0.00721 \\
0.80 & 0.74210 & 0.25790 & 2.00 & 0.99532 & 0.00468 \\
0.90 & 0.79691 & 0.20309 & 2.50 & 0.99959 & 0.00041 \\
1.00 & 0.84270 & 0.15730 & 3.00 & 0.99998 & 0.00002 \\[2pt]
\hline\hline
\end{tabular*}
}
\end{table*}
%%%%%%%%%%%%%%%% end table %%%%%%%%%%%%%%%%%%%
\lipsum[18-25]
\lipsum[27]
%%%%%%%%%%%%%%%%%%%% Examples WT4 & WT5 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Wide Equation Pair Split Across Page Break and Followed by Wide Equation}
\textcolor{red}{Note that the upper rule is cleared after the first use in a \texttt{widetext} environment. This means that it will not show up at the top of the next page.}
\textcolor{red}{The \texttt{\textbackslash newpage} command may be used between the equations to force the second one onto the next page, e.g., try removing the source code line \texttt{\textbackslash lipsum[27]} with and without \texttt{\textbackslash newpage}.}
\lipsum[26-28]
\begin{widetext}[5]% reducing \stripsep from the default 10pt to 5pt with the option [5], to make more room below the equation number
\begin{equation}\mathbf{WT4:}
\int_a^b\Biggl\{\int_a^b[f(x)^2g(y)^2+f(y)^2g(x)^2] -2f(x)g(x)f(y)g(y)\,dx\Biggr\}\,dy
\ne \frac{1}{\sqrt{\displaystyle\int_a^b\biggl\{g(y)^2\int_a^bf^2+f(y)^2 \int_a^b g^2-2f(y)g(y)\int_a^b fg\biggr\}\,dy}}
\end{equation}
\newpage % note some differences in the size between pdftex and luatex; luatex needs this forced page break
\begin{equation}\mathbf{WT5:}
\int_a^b\Biggl\{\int_a^b[f(x)^2g(y)^2+f(y)^2g(x)^2]
-2f(x)g(x)f(y)g(y)\,dx\Biggr\}\,dy
\ne \frac{1}{\sqrt{\displaystyle\int_a^b\biggl\{g(y)^2\int_a^bf^2+f(y)^2
\int_a^b g^2-2f(y)g(y)\int_a^b fg\biggr\}\,dy}}
\end{equation}
\vskip 3pt % some extra space for cramped equation number
\textcolor{red}{In this case, we again have a pair of wide equations on the same page, so we stay in single column mode
until both are done\footnotemark. The single column table, Table~\ref{tab:3}, is forced to the bottom of the page with the \texttt{[b]} option.}
\lipsum[32-33]
\begin{equation}\mathbf{WT6:}
\int_a^b\biggl\{\int_a^b[f(x)^2g(y)^2+f(y)^2g(x)^2]
-2f(x)g(x)f(y)g(y)\,dx\biggr\}\,dy
\ne \frac{1}{\sqrt{\displaystyle\int_a^b\biggl\{g^2\int_a^bf^2+f^2
\int_a^b g^2-2fg\int_a^b fg\biggr\}\,dy}}
\end{equation}
\end{widetext}
\footnotetext{\textcolor{red}{The code from \texttt{cuted.sty} doesn't play well with footnotes, so we put a \texttt{\textbackslash footnotemark} command inside the wide environment and place a separate \texttt{\textbackslash footnotetext\{..\}} command outside the wide environment.}}%
\lipsum[34-37]
%%%%%%%%%%%%%%%%%%% begin linewidth table %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{table}[b]
\newcolumntype{C}{>{$}c<{$}} % math-mode version of "c" column type, from array package
\caption{\label{tab:3}Table at full column width with columns in math mode}
\centering{%
\begin{tabular*}{\linewidth}{@{\extracolsep{\fill}}CCCC@{\extracolsep{\fill}}}
\hline\hline
X_{z} & X_{c} & X_{c,m} & X_{c,2}\rule{0pt}{11pt}\\
3.92069 & 5.70943 & 6.32429 & 7.08757\\[2pt]
\varepsilon (T_1) & \varepsilon^i (T_1) & \varepsilon^i (T_m) & \alpha (T_1, T_2)\\
0.7258 & 0.6237 & 0.6807 & 0.7964 \\[2pt]
q_\textrm{gray} & q_\textrm{int, $T_1$} & q_\textrm{int, $T_m$} & q_\textrm{exact}\\
400.2 & 462.1 & 371.0 & 371.8 \\[1pt]
\hline\hline
\end{tabular*}
}
\end{table}
%%%%%%%%%%%%%%%%%%%% end linewidth table %%%%%%%%%%%%%%%%%%%%%%%
\lipsum[40-54]
\textcolor{red}{For eqn.~\eqref{eqn:WT7}, we drop the bottom line, keeping the top line and removing the vertical space: \texttt{\textbackslash begin\{widetext\}[0][t]}.}
\begin{widetext}[0][t]
\begin{equation}\label{eqn:WT7}%
\mathbf{WT7:}\quad
\cfrac{1}{1+ \cfrac{1}{abcxyz+(ax^2-by^3+cz^4)(\alpha\chi^2-\beta\upsilon^3+\kappa\zeta^4)(ax^4-by^3+cz^2)(a^2x^2-by^3+c^2z^2)}}
\end{equation}
\end{widetext}
\lipsum[50-63]
\textcolor{red}{In this case, we drop the top line: \texttt{\textbackslash begin\{widetext\}[][b]}.}
\vskip 80pt% <== an extra skip to push this widetext over the edge
\begin{widetext}[][b]
\begin{equation}\label{eqn:WT8}
\mathbf{WT8:}\quad
\mathfrak{W}(\MyBoldPhi)= \begin{Vmatrix}
\dfrac\varphi{(\varphi_1,\varepsilon_1)} & 0 & \hdotsfor{4} & 0 & \\[\jot]
\dfrac{\varphi k_{21}}{(\varphi_2,\varepsilon_1)} & \dfrac\varphi{(\varphi_2,\varepsilon_2)} & 0 & \hdotsfor{3} & 0 \\[\jot]
\dfrac{\varphi k_{31}}{(\varphi_3,\varepsilon_1)} &\dfrac{\varphi k_{32}}{(\varphi_3,\varepsilon_2)} & \dfrac\varphi{(\varphi_3,\varepsilon_3)}& 0 & \hdotsfor{2} & 0 \\[\jot]
\vdots & & & \smash{\rotatebox{15}{$\ddots$}} & & & \vdots \\[\jot]
\dfrac{\varphi k_{n-2\, 1}}{(\varphi_{n-2},\varepsilon_1)} &
\dfrac{\varphi k_{n-2\, 2}}{(\varphi_{n-2},\varepsilon_2)} &\hdotsfor{1} & \dfrac{\varphi k_{n-2\,n-3}}{(\varphi_{n-2},\varepsilon_{n-3})} & \dfrac\varphi{(\varphi_{n-2},\varepsilon_{n-2})}& 0& 0 \\[\jot]
\dfrac{\varphi k_{n-1\, 1}}{(\varphi_{n-1},\varepsilon_1)} & \dfrac{\varphi k_{n-1\, 2}}{(\varphi_{n-1},\varepsilon_2)} &\hdotsfor{2} &
\dfrac{\varphi k_{n-1\,n-2}}{(\varphi_{n-1},\varepsilon_{n-2})}& \dfrac{\varphi}{(\varphi_{n-1},\varepsilon_{n-1})} & 0 \\[\jot]
\dfrac{\varphi k_{n1}}{(\varphi_n,\varepsilon_1)} & \dfrac{\varphi k_{n2}}{(\varphi_n,\varepsilon_2)} & \hdotsfor{3} &
\dfrac{\varphi k_{n\,n-1}}{(\varphi_n,\varepsilon_{n-1})} & \dfrac{\varphi}{(\varphi_n,\varepsilon_n)}
\end{Vmatrix}
\end{equation}
\end{widetext}
\lipsum[55-56]
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\appendix
\section{Spherical harmonics\label{sec:sph-har}}
Without getting into the details, a regular function $f(\theta,\phi)$ on the surface of the unit sphere may be written
\begin{equation}
f(\theta,\phi) = \sum_{n=0}^\infty \sum_{m=-n}^n f_{m,n} Y_n^m(\theta,\phi)
\end{equation}
for $Y_n^m(\theta,\phi) = e^{i m\phi}P^{|m|}_n(\cos\theta)$, for $|m|<n$. The case $n=3$, $m=2$ (a \textit{tesseral harmonic}) is shown in Fig.~\ref{fig:tesseral}.
These functions are orthogonal, with the normalization constant~\cite[App.~A]{stakgold}:
\begin{equation}
N_{m,n}=\int_0^{2\pi}\!\!d\phi\int_0^{\pi}\!\!d\theta \sin\theta\, \big|Y^m_n(\theta,\phi)\big|^2 = \frac{4\pi (n+|m|)!}{(2n+1)(n-|m|)!}
\end{equation}
If $f$ is independent of the azimuthal angle $\phi$, the solution appears in ordinary Legendre polynomials, $P_n$, rather than associated Legendre polynomials, $P^m_n$ ($P^0_n = P_n$):
\begin{equation}
f(\theta) = \sum_{n=0}^\infty f_n\, P_n(\cos\theta)
\end{equation}
The terms in this series are called \textit{zonal harmonics}.
%%%%%%%%%%%%%%%%%%%% bibliography %%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\bibliographystyle{asmejour}
\bibliography{asme-wide-equations}
\end{document}

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%%
%% This file is `asmewide.sty'.
%%
%% Copyright (c) 2025 John H. Lienhard. Use under the MIT license: https://ctan.org/license/mit
%%
%% Defines a widetext environment within ASME dimensions
%% Use for material spanning both columns (i.e., for wide equations)
%%
%% The original widetext environment was developed in revtex; elements of the present code have been modified revtex4-2.dtx, under LPPL1.3c.
%% The unmodified code is available at: https://ctan.org/pkg/revtex
%% This code also adopts concepts from the widetext.sty package by Anjishnu Sarkar, https://blog.pnas.org/widetext.sty.
%% The modifications made were: follow ASME dimensions; remove revtex-specific macros; update/rework commands; adapt to most recent cuted.sty
%% (Leaders don't vanish at pagebreaks, as in revtex, evidently related to how cuted.sty handles strip construction. Have coded around this.)
%%
%% Required packages: cuted.sty v2.0 and flushend.sty v4.0 [2021/10/04] or later;
%% asmeconf.cls or asmejour.cls w/their required packages, esp. etoolbox, xparse
%%
%% The widetext environment can only appear once per page. It clashes with floats and footnotes,
%% and often requires some hand-fitting of page layouts.
%%
%% USAGE: \begin{widetext} ...wide material here... \end{widetext}
%% OPTIONAL ARGUMENTS:
%% \begin{widetext[N] ...change upper/lower separation of wide material from default Xpt to Npt (X = 5pt asmeconf.cls; X = 10pt asmejour.cls)
%% \begin{widetext}[][tbn]: t = top line only; b = bottom line only; n = no lines. BOTH arguments are REQUIRED, even if first is left empty.
%%
%% asmewide,sty supports one option, [raggedend], which suppresses final page column balancing: \usepackage[raggedend]{asmewide}
%%
%% NB: the strip environment from cuted is incompatible with the [lineno] option to asmeconf and asmejour!
%%
\NeedsTeXFormat{LaTeX2e}
\def\AW@versionno{1.11}
\def\AW@versiondate{2025/01/22\space}
\ProvidesPackage{asmewide}[\AW@versiondate\space v\AW@versionno\space ASME wide equation environment (JHL)]
\DeclareOption{raggedend}{% Added 2022/05/08, to suppressed flushend on last page, if desired
\AfterEndPreamble{\raggedend}
}
\DeclareOption*{}
\ProcessOptions \relax
\ifdefined\NewDocumentCommand\else
\RequirePackage{xparse}
\fi
\RequirePackage{etoolbox}
\RequirePackage{cuted}[2021/10/04]%features used here were first added in the [2021/10/04] version of cuted.sty!
\@ifpackagelater{cuted}{2021/10/04}{%
\relax
}{%
\PackageError{asmewide}{Your version of cuted.sty is too old. You can get an update at https://ctan.org/pkg/cuted}{You need an up-to-date version of cuted.sty to run asmewide.sty.}%
}
\RequirePackage{flushend}[2021/10/04]
%
% https://tex.stackexchange.com/a/43541/119566
\def\@getcl@ss#1.cls#2\relax{\def\@currentclass{#1}}
\def\@getclass{\expandafter\@getcl@ss\@filelist\relax}
\@getclass
\typeout{Running asmewide.sty with the \@currentclass\space class.}
%
\newbox\@TopLeader
\newbox\@BottomLeader
\newlength\savparskip \setlength\savparskip{\parskip}
\newlength\@RuleWidth
\appto\maketitle{\setlength\@RuleWidth{\dimexpr(\columnwidth+0.5\columnsep-1pt)}}% do this after entering twocolumn, in \maketitle. 2025/01/22
\newlength\@TopSpace \setlength\@TopSpace{0ex}
\newlength\@TopCorr \setlength\@TopCorr{-5pt}
\def\@asmeindent{3.5mm}
\def\@TopRuleWeight{0.5pt}
\def\@BottomRuleWeight{0.5pt}
\def\@DSS{5}% default stripsep
%
\@ifclassloaded{asmeconf}{%
\setlength\@TopCorr{-1ex}% keep \abovedisplayskip since text could start the page
\setlength\@TopSpace{1ex}% provide space apparently lost with cuted.sty in asmeconf.cls
\def\@asmeindent{0.25in}% asmeconf
}{\relax}
\@ifclassloaded{asmejour}{%
\AtBeginDocument{\setlength\@RuleWidth{\columnwidth}}
\setlength\@TopCorr{-9pt}% asmejour
\def\@BottomRuleWeight{1pt}% asmejour
\def\@DSS{10}% default stripsep, asmejour
}{\relax}
%
% Set ascenders and descenders 1.2 times greater than \baselineskip
\NewDocumentCommand\@SetTopLeader{}{% NB: boxes are cleared after they are used; this command is issued once with each widetext environment
\setbox\@TopLeader\vbox{%
\hbox to \@RuleWidth{%
\leaders\hrule height\@TopRuleWeight \hfil
\vrule height 1.2\baselineskip width\@TopRuleWeight}
}
}
\NewDocumentCommand\@TopLine{}{%
\vskip\@TopSpace
\dimen@\ht\@TopLeader\advance\dimen@\dp\@TopLeader
\cleaders\box\@TopLeader\vskip\dimen@
}
\NewDocumentCommand\@SetBottomLeader{}{%
\setbox\@BottomLeader\hbox to \@RuleWidth{%
\vrule depth 1.2\baselineskip width\@BottomRuleWeight
\leaders\hrule height\@BottomRuleWeight \hfil
}
}
\NewDocumentCommand\@BottomLine{}{%
\par
\vskip 3pt% provide some space between low equation numbers and rule
\setbox\@BottomLeader\vbox{%
\hbox to \textwidth{\hfil\box\@BottomLeader}%
}%
\dimen@\ht\@BottomLeader\advance\dimen@\dp\@BottomLeader
\cleaders\box\@BottomLeader\vskip\dimen@
\vskip -1.5pt% reduce trailing separation w.r.t. baseline when \stripsep = 0
}
\preCutedStrip={\@TopLine}
\postCutedStrip={\@BottomLine}
\DeclareDocumentEnvironment{widetext}{O{\@DSS}o}{%
\@SetTopLeader
\@SetBottomLeader
\notblank{#1}{%
\setlength{\stripsep}{#1pt plus 5pt minus 5pt}
}{
\setlength{\stripsep}{\@DSS pt plus 5pt minus 5pt}
}
\ifstrequal{#2}{t}{\setbox\@BottomLeader\vbox{}}{%
\ifstrequal{#2}{b}{\setbox\@TopLeader\vbox{\vskip \@TopCorr}}{%cuted inserts some additional space, we remove here
\ifstrequal{#2}{n}{\setbox\@TopLeader\vbox{\vskip \@TopCorr}\setbox\@BottomLeader\vbox{}}{\relax}
}
}
\begin{strip}
\setlength\parindent{\@asmeindent}% strip makes parindent zero; enlarge for ASME
\setlength\parskip{\savparskip}% strip makes \parskip zero w/o glue; set to match main text
}{%
\end{strip}\ignorespacesafterend
}
%%
\endinput
%%
%% End of file `asmewide.sty'.

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@@ -1,32 +1,26 @@
#+TITLE: Decoupling Properties of the Cubic Architecture
:DRAWER:
#+LANGUAGE: en
#+EMAIL: dehaeze.thomas@gmail.com
#+AUTHOR: Dehaeze Thomas
#+BIND: org-latex-image-default-option "scale=1"
#+BIND: org-latex-image-default-width ""
#+LaTeX_CLASS: scrreprt
#+LaTeX_CLASS_OPTIONS: [a4paper, 10pt, DIV=12, parskip=full, bibliography=totoc]
#+OPTIONS: toc:nil date:nil
#+LaTeX_CLASS: asmejour
#+LaTeX_CLASS_OPTIONS: [balance,nocopyright,nolists]
#+LATEX_HEADER: \input{preamble.tex}
#+LATEX_HEADER_EXTRA: \input{preamble_extra.tex}
#+LATEX_HEADER_EXTRA: \bibliography{dehaeze26_cubic_architecture.bib}
#+BIND: org-latex-bib-compiler "biber"
#+LATEX_HEADER_EXTRA: \usepackage[square,numbers]{natbib}
#+LATEX_HEADER_EXTRA: \JourName{Journal of Mechanical Design}
:END:
#+latex: \clearpage
* Build :noexport:
#+NAME: startblock
#+BEGIN_SRC emacs-lisp :results none :tangle no
(add-to-list 'org-latex-classes
'("scrreprt"
"\\documentclass{scrreprt}"
("\\chapter{%s}" . "\\chapter*{%s}")
'("asmejour"
"\\documentclass{asmejour}"
("\\section{%s}" . "\\section*{%s}")
("\\subsection{%s}" . "\\subsection*{%s}")
("\\subsubsection{%s}" . "\\subsubsection*{%s}")
("\\paragraph{%s}" . "\\paragraph*{%s}")
))
@@ -52,12 +46,27 @@
(setq org-latex-packages-alist nil)
(setq org-latex-default-packages-alist nil)
;; Do not include the subtitle inside the title
(setq org-latex-subtitle-separate t)
(setq org-latex-subtitle-format "\\subtitle{%s}")
;; Remove empty title as it is manually placed after "/begin{document}"
(defun my-org-latex-remove-title (str)
(replace-regexp-in-string "^\\\\title{}$" "" str))
(setq org-export-before-parsing-hook '(org-ref-glossary-before-parsing
org-ref-acronyms-before-parsing))
(advice-add 'org-latex-template :filter-return 'my-org-latex-remove-title)
;; Remove empty date
(defun my-org-latex-remove-date (str)
(replace-regexp-in-string "^\\\\date{}$" "" str))
(advice-add 'org-latex-template :filter-return 'my-org-latex-remove-date)
;; Remove Automatic add of \usepackage{biblatex}
(defun my-org-remove-biblatex-final (output backend info)
"Remove any \\usepackage[...]{biblatex} line from final LaTeX output."
(when (eq backend 'latex)
(replace-regexp-in-string
"\\\\usepackage\\(\\[[^]]*\\]\\)?{biblatex}[ \t]*\\(\n\\|$\\)" "" output)))
(add-hook 'org-export-filter-final-output-functions
#'my-org-remove-biblatex-final)
#+END_SRC
* Notes :noexport:
@@ -70,13 +79,105 @@ Guide: https://www.asme.org/publications-submissions/journals/information-for-au
Research papers undergo full peer review. Authors are encouraged to prepare concise manuscripts that convey clearly the significance of the work. Research Papers do not have a specified length but are usually 8,000 to 12,000 words with 5-8 figures or tables.
#+end_quote
12000 words should be equivalent to 25 pages.
** LaTeX Template
%% * Option to color the vertical bar in the title block [barcolor = colorname]
%% * where colorname is any name def'd by xcolor package; omit barcolor option to get black
%%
%% * Option to omit the list of figures and list of tables at the end [nolists]
%%
%% * Option to include line numbers [lineno]. You must run *twice* for proper placement of the
%% * line numbers. The lineno package does not number tables, footnotes, or captions.
%% * This option will disable balancing of the column heights on final page.
%%
%% * Option to balance column heights on final page [balance]. This option sometimes
%% * misbehaves, so use it with an awareness that it can create unexpected problems.
%% * This option is not compatible with line numbering.
%%
%% * Options for copyright notices:
%% * Omit the ASME copyright from the footer [nocopyright]
%% * Copyright footnote if all authors are government employees [govt]
%% * Copyright footnote if some authors are government employees [govtsome]
%% * Copyright footnote for government contractors [contractor]
%%
%% * Option to omit all ASME text fields from the footer [nofoot].
%%
%% * Option for single column formatting [singlecolumn].
%%
%% * Option for upright integrals [upint]
%%
%% * Additional math options from M. Sharpe's newtxmath package (pdfTeX only):
%% * [varvw] for v and w that are better distinguished from Greek nu; fine
%% * adjustments to subscripts [subscriptcorrection]; and various other options
%% * such as [smallerops, varg, slantedGreek, frenchmath, varbb, cmbraces].
%%
%% * Support for the unicode-math package and its math options (LuaLaTeX only)
%%
%% * Options for the typewriter font:
%% * [var0] replace default slashed zero by an unslashed zero
%% * [mono] force interword separation to be monospaced
%% * [hyphenate] allow hyphenation (pdfTeX only). Typewriter fonts usually are not hyphenated.
%%
%% * Options for the babel package to support passages in other languages (such as a translated
%% * abstract in an appendix), e.g. [german]. The main language will default to English
%% * unless a different main language is selected, e.g. [main=spanish]. See Appendix B for details.
%%
%% * PDF/A archivability compliance. Since 2022, LaTeX has included integrated support for PDF/A,
%% * through the \DocumentMetadata{..} command. This works with both pdfTeX and luaLaTeX.
%% * The legacy PDF/A class options have been dropped as of mid-2025.
** DONE [#B] Setup the template for the journal
CLOSED: [2025-11-27 Thu 17:30] SCHEDULED: <2025-11-26 Wed>
** TODO [#B] Add more content from the PhD thesis?
Maybe add:
- [[file:~/Cloud/work-projects/ID31-NASS/phd-thesis-chapters/B1-nass-geometry/nass-geometry.org::*Review of Stewart platforms][Review of Stewart platforms]]
- [[file:~/Cloud/work-projects/ID31-NASS/phd-thesis-chapters/B1-nass-geometry/nass-geometry.org::*Effect of geometry on Stewart platform properties][Effect of geometry on Stewart platform properties]]
- [ ] [[file:~/Cloud/work-projects/ID31-NASS/phd-thesis-chapters/A5-simscape-nano-hexapod/simscape-nano-hexapod.org::*The Stewart platform][The Stewart platform]]
For the equations of motion, definition of the geometry, Jacobian matrix, etc...
- [ ] [[file:~/Cloud/work-projects/ID31-NASS/phd-thesis-chapters/B1-nass-geometry/nass-geometry.org::*Review of Stewart platforms][Review of Stewart platforms]]
- [ ] [[file:~/Cloud/work-projects/ID31-NASS/phd-thesis-chapters/B1-nass-geometry/nass-geometry.org::*Effect of geometry on Stewart platform properties][Effect of geometry on Stewart platform properties]]
* Introduction :ignore:
* Title and Abstract :ignore:
#+begin_export latex
\SetAuthorBlock{Thomas Dehaeze\CorrespondingAuthor}{%
ESRF, The European Synchrotron\\
Grenoble, France\\
email: thomas.dehaeze@esrf.fr
}
\SetAuthorBlock{Christophe Collette}{%
Precision Mechatronics Laboratory\\
University of Li\`{e}ge, Belgium\\
email: christophe.collette@uliege.be
}
%%% Change to your paper title. Can insert line breaks if you wish (otherwise breaks are selected automatically).
\title{Decoupling Properties of the Cubic Architecture}
#+end_export
# less than 150 words and is normally in italics
#+begin_export latex
\begin{abstract}
{\it This is the abstract.
This article illustrates preparation of ASME paper using
Please use this template to test how your figures will look on the printed journal page of the Journal of Mechanical Design. The Journal will no longer publish papers that contain errors in figure resolution. These usually consist of unreadable or fuzzy text, and pixilation or rasterization of lines. This template identifies the specifications used by JMD some of which may not be easily duplicated; for example, ASME actually uses Helvetica Condensed Bold, but this is not generally available so for the purpose of this exercise Helvetica is adequate. However, reproduction of the journal page is not the goal, instead this exercise is to verify the quality of your figures. Notice that this abstract is to be set in 9pt Times Italic, single spaced and right justified.
}
\end{abstract}
#+end_export
#+begin_export latex
\date{Version \versionno, \today}%% You can modify this information as desired.
%% Putting \date{} will suppress any date.
%% If this command is omitted, date defaults to \today
%% This command must come somewhere before \maketitle
\maketitle %% This command creates the author/title/abstract block. Essential!
#+end_export
* Introduction
The Cubic configuration for the Stewart platform was first proposed by Dr. Gough in a comment to the original paper by Dr. Stewart [[cite:&stewart65_platf_with_six_degrees_freed]].
This configuration is characterized by active struts arranged in a mutually orthogonal configuration connecting the corners of a cube, as shown in Figure ref:fig:detail_kinematics_cubic_architecture_example.
@@ -90,15 +191,15 @@ It is also possible to implement designs with strut lengths smaller than the cub
#+attr_latex: :options [htbp]
#+begin_figure
#+attr_latex: :caption \subcaption{\label{fig:detail_kinematics_cubic_architecture_example}Classical Cubic architecture}
#+attr_latex: :options {0.49\textwidth}
#+attr_latex: :options {\linewidth}
#+begin_subfigure
#+attr_latex: :scale 1
#+attr_latex: :scale 0.7
[[file:figs/detail_kinematics_cubic_architecture_example.png]]
#+end_subfigure
#+attr_latex: :caption \subcaption{\label{fig:detail_kinematics_cubic_architecture_example_small}Alternative configuration}
#+attr_latex: :options {0.49\textwidth}
#+attr_latex: :options {\linewidth}
#+begin_subfigure
#+attr_latex: :scale 1
#+attr_latex: :scale 0.7
[[file:figs/detail_kinematics_cubic_architecture_example_small.png]]
#+end_subfigure
#+end_figure
@@ -121,12 +222,14 @@ Consider the cubic architecture shown in Figure ref:fig:detail_kinematics_cubic_
The unit vectors corresponding to the edges of the cube are described by equation eqref:eq:detail_kinematics_cubic_s.
\begin{equation}\label{eq:detail_kinematics_cubic_s}
\hat{\bm{s}}_1 = \begin{bmatrix} \frac{\sqrt{2}}{\sqrt{3}} \\ 0 \\ \frac{1}{\sqrt{3}} \end{bmatrix} \quad
\hat{\bm{s}}_2 = \begin{bmatrix} \frac{-1}{\sqrt{6}} \\ \frac{-1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} \end{bmatrix} \quad
\hat{\bm{s}}_3 = \begin{bmatrix} \frac{-1}{\sqrt{6}} \\ \frac{ 1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} \end{bmatrix} \quad
\hat{\bm{s}}_4 = \begin{bmatrix} \frac{\sqrt{2}}{\sqrt{3}} \\ 0 \\ \frac{1}{\sqrt{3}} \end{bmatrix} \quad
\hat{\bm{s}}_5 = \begin{bmatrix} \frac{-1}{\sqrt{6}} \\ \frac{-1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} \end{bmatrix} \quad
\hat{\bm{s}}_6 = \begin{bmatrix} \frac{-1}{\sqrt{6}} \\ \frac{ 1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} \end{bmatrix}
\begin{align*}
\hat{\bm{s}}_1 = \begin{bmatrix} \frac{\sqrt{2}}{\sqrt{3}} \\ 0 \\ \frac{1}{\sqrt{3}} \end{bmatrix} \quad
\hat{\bm{s}}_2 = \begin{bmatrix} \frac{-1}{\sqrt{6}} \\ \frac{-1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} \end{bmatrix} \quad
\hat{\bm{s}}_3 = \begin{bmatrix} \frac{-1}{\sqrt{6}} \\ \frac{ 1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} \end{bmatrix} \\
\hat{\bm{s}}_4 = \begin{bmatrix} \frac{\sqrt{2}}{\sqrt{3}} \\ 0 \\ \frac{1}{\sqrt{3}} \end{bmatrix} \quad
\hat{\bm{s}}_5 = \begin{bmatrix} \frac{-1}{\sqrt{6}} \\ \frac{-1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} \end{bmatrix} \quad
\hat{\bm{s}}_6 = \begin{bmatrix} \frac{-1}{\sqrt{6}} \\ \frac{ 1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} \end{bmatrix}
\end{align*}
\end{equation}
#+name: fig:detail_kinematics_cubic_schematic_cases
@@ -134,15 +237,15 @@ The unit vectors corresponding to the edges of the cube are described by equatio
#+attr_latex: :options [htbp]
#+begin_figure
#+attr_latex: :caption \subcaption{\label{fig:detail_kinematics_cubic_schematic_full}Full cube}
#+attr_latex: :options {0.48\textwidth}
#+attr_latex: :options {\linewidth}
#+begin_subfigure
#+attr_latex: :scale 0.9
#+attr_latex: :scale 0.8
[[file:figs/detail_kinematics_cubic_schematic_full.png]]
#+end_subfigure
#+attr_latex: :caption \subcaption{\label{fig:detail_kinematics_cubic_schematic}Cube's portion}
#+attr_latex: :options {0.48\textwidth}
#+attr_latex: :options {\linewidth}
#+begin_subfigure
#+attr_latex: :scale 0.9
#+attr_latex: :scale 0.8
[[file:figs/detail_kinematics_cubic_schematic.png]]
#+end_subfigure
#+end_figure
@@ -150,16 +253,18 @@ The unit vectors corresponding to the edges of the cube are described by equatio
Coordinates of the cube's vertices relevant for the top joints, expressed with respect to the cube's center, are shown in equation eqref:eq:detail_kinematics_cubic_vertices.
\begin{equation}\label{eq:detail_kinematics_cubic_vertices}
\tilde{\bm{b}}_1 = \tilde{\bm{b}}_2 = H_c \begin{bmatrix} \frac{1}{\sqrt{2}} \\ \frac{-\sqrt{3}}{\sqrt{2}} \\ \frac{1}{2} \end{bmatrix}, \quad
\tilde{\bm{b}}_3 = \tilde{\bm{b}}_4 = H_c \begin{bmatrix} \frac{1}{\sqrt{2}} \\ \frac{ \sqrt{3}}{\sqrt{2}} \\ \frac{1}{2} \end{bmatrix}, \quad
\tilde{\bm{b}}_5 = \tilde{\bm{b}}_6 = H_c \begin{bmatrix} \frac{-2}{\sqrt{2}} \\ 0 \\ \frac{1}{2} \end{bmatrix}
\begin{align*}
\tilde{\bm{b}}_1 &= \tilde{\bm{b}}_2 = H_c \begin{bmatrix} \frac{1}{\sqrt{2}} \\ \frac{-\sqrt{3}}{\sqrt{2}} \\ \frac{1}{2} \end{bmatrix}, \quad
\tilde{\bm{b}}_3 = \tilde{\bm{b}}_4 = H_c \begin{bmatrix} \frac{1}{\sqrt{2}} \\ \frac{ \sqrt{3}}{\sqrt{2}} \\ \frac{1}{2} \end{bmatrix}, \\
\tilde{\bm{b}}_5 &= \tilde{\bm{b}}_6 = H_c \begin{bmatrix} \frac{-2}{\sqrt{2}} \\ 0 \\ \frac{1}{2} \end{bmatrix}
\end{align*}
\end{equation}
In the case where top joints are positioned at the cube's vertices, a diagonal stiffness matrix is obtained as shown in equation eqref:eq:detail_kinematics_cubic_stiffness.
Translation stiffness is twice the stiffness of the struts, and rotational stiffness is proportional to the square of the cube's size $H_c$.
\begin{equation}\label{eq:detail_kinematics_cubic_stiffness}
\bm{K}_{\{B\} = \{C\}} = k \begin{bmatrix}
\bm{K} = k \begin{bmatrix}
2 & 0 & 0 & 0 & 0 & 0 \\
0 & 2 & 0 & 0 & 0 & 0 \\
0 & 0 & 2 & 0 & 0 & 0 \\
@@ -189,14 +294,15 @@ Considering a vertical shift as shown in Figure ref:fig:detail_kinematics_cubic_
Off-diagonal elements increase proportionally with the height difference between the cube's center and the considered $\{B\}$ frame.
\begin{equation}\label{eq:detail_kinematics_cubic_stiffness_off_centered}
\bm{K}_{\{B\} \neq \{C\}} = k \begin{bmatrix}
\bm{K} = k \\
{\footnotesize \begin{bmatrix}
2 & 0 & 0 & 0 & -2 H & 0 \\
0 & 2 & 0 & 2 H & 0 & 0 \\
0 & 0 & 2 & 0 & 0 & 0 \\
0 & 2 H & 0 & \frac{3}{2} H_c^2 + 2 H^2 & 0 & 0 \\
-2 H & 0 & 0 & 0 & \frac{3}{2} H_c^2 + 2 H^2 & 0 \\
0 & 0 & 0 & 0 & 0 & 6 H_c^2 \\
\end{bmatrix}
\end{bmatrix}}
\end{equation}
This stiffness matrix structure is characteristic of Stewart platforms exhibiting symmetry, and is not an exclusive property of cubic architectures.
@@ -224,15 +330,15 @@ Furthermore, an inverse relationship exists between the cube's dimension and rot
#+attr_latex: :options [htbp]
#+begin_figure
#+attr_latex: :caption \subcaption{\label{fig:detail_kinematics_cubic_mobility_translations}Mobility in translation}
#+attr_latex: :options {0.48\textwidth}
#+attr_latex: :options {\linewidth}
#+begin_subfigure
#+attr_latex: :scale 1
#+attr_latex: :scale 0.8
[[file:figs/detail_kinematics_cubic_mobility_translations.png]]
#+end_subfigure
#+attr_latex: :caption \subcaption{\label{fig:detail_kinematics_cubic_mobility_rotations}Mobility in rotation}
#+attr_latex: :options {0.48\textwidth}
#+attr_latex: :options {\linewidth}
#+begin_subfigure
#+attr_latex: :scale 1
#+attr_latex: :scale 0.8
[[file:figs/detail_kinematics_cubic_mobility_rotations.png]]
#+end_subfigure
#+end_figure
@@ -269,7 +375,7 @@ To achieve a diagonal mass matrix, the center of mass of the mobile components m
#+name: fig:detail_kinematics_cubic_payload
#+caption: Cubic stewart platform with top cylindrical payload
#+attr_latex: :width 0.6\linewidth
#+attr_latex: :width 0.7\linewidth
[[file:figs/detail_kinematics_cubic_payload.png]]
To verify these properties, a cubic Stewart platform with a cylindrical payload was analyzed (Figure ref:fig:detail_kinematics_cubic_payload).
@@ -282,15 +388,15 @@ Conversely, when positioned at the center of stiffness, coupling occurred at hig
#+attr_latex: :options [htbp]
#+begin_figure
#+attr_latex: :caption \subcaption{\label{fig:detail_kinematics_cubic_cart_coupling_com}$\{B\}$ at the center of mass}
#+attr_latex: :options {0.48\textwidth}
#+attr_latex: :options {\linewidth}
#+begin_subfigure
#+attr_latex: :width 0.95\linewidth
#+attr_latex: :scale 0.8
[[file:figs/detail_kinematics_cubic_cart_coupling_com.png]]
#+end_subfigure
#+attr_latex: :caption \subcaption{\label{fig:detail_kinematics_cubic_cart_coupling_cok}$\{B\}$ at the cube's center}
#+attr_latex: :options {0.48\textwidth}
#+attr_latex: :options {\linewidth}
#+begin_subfigure
#+attr_latex: :width 0.95\linewidth
#+attr_latex: :scale 0.8
[[file:figs/detail_kinematics_cubic_cart_coupling_cok.png]]
#+end_subfigure
#+end_figure
@@ -299,7 +405,7 @@ Conversely, when positioned at the center of stiffness, coupling occurred at hig
An effective strategy for improving dynamical performances involves aligning the cube's center (center of stiffness) with the center of mass of the moving components [[cite:&li01_simul_fault_vibrat_isolat_point]].
This can be achieved by positioning the payload below the top platform, such that the center of mass of the moving body coincides with the cube's center (Figure ref:fig:detail_kinematics_cubic_centered_payload).
This approach was physically implemented in several studies [[cite:&mcinroy99_dynam;&jafari03_orthog_gough_stewar_platf_microm]], as shown in Figure ref:fig:detail_kinematics_uw_gsp.
This approach was physically implemented in several studies [[cite:&mcinroy99_dynam;&jafari03_orthog_gough_stewar_platf_microm]].
The resulting dynamics are indeed well-decoupled (Figure ref:fig:detail_kinematics_cubic_cart_coupling_com_cok), taking advantage from diagonal stiffness and mass matrices.
The primary limitation of this approach is that, for many applications including the nano-hexapod, the payload must be positioned above the top platform.
If a design similar to Figure ref:fig:detail_kinematics_cubic_centered_payload were employed for the nano-hexapod, the X-ray beam would intersect with the struts during spindle rotation.
@@ -309,15 +415,15 @@ If a design similar to Figure ref:fig:detail_kinematics_cubic_centered_payload w
#+attr_latex: :options [htbp]
#+begin_figure
#+attr_latex: :caption \subcaption{\label{fig:detail_kinematics_cubic_centered_payload}Payload at the cube's center}
#+attr_latex: :options {0.49\textwidth}
#+attr_latex: :options {\linewidth}
#+begin_subfigure
#+attr_latex: :width 0.95\linewidth
#+attr_latex: :width 0.7\linewidth
[[file:figs/detail_kinematics_cubic_centered_payload.png]]
#+end_subfigure
#+attr_latex: :caption \subcaption{\label{fig:detail_kinematics_cubic_cart_coupling_com_cok}Fully decoupled cartesian plant}
#+attr_latex: :options {0.49\textwidth}
#+attr_latex: :options {\linewidth}
#+begin_subfigure
#+attr_latex: :width 0.95\linewidth
#+attr_latex: :scale 0.8
[[file:figs/detail_kinematics_cubic_cart_coupling_com_cok.png]]
#+end_subfigure
#+end_figure
@@ -348,7 +454,7 @@ The second uses a non-cubic Stewart platform shown in Figure ref:fig:detail_kine
#+name: fig:detail_kinematics_non_cubic_payload
#+caption: Stewart platform with non-cubic architecture
#+attr_latex: :width 0.6\linewidth
#+attr_latex: :width 0.7\linewidth
[[file:figs/detail_kinematics_non_cubic_payload.png]]
** Relative Displacement Sensors
@@ -365,15 +471,15 @@ The resonance frequencies differ between the two cases because the more vertical
#+attr_latex: :options [htbp]
#+begin_figure
#+attr_latex: :caption \subcaption{\label{fig:detail_kinematics_non_cubic_decentralized_dL}Non cubic architecture}
#+attr_latex: :options {0.48\textwidth}
#+attr_latex: :options {\linewidth}
#+begin_subfigure
#+attr_latex: :width 0.95\linewidth
#+attr_latex: :scale 0.8
[[file:figs/detail_kinematics_non_cubic_decentralized_dL.png]]
#+end_subfigure
#+attr_latex: :caption \subcaption{\label{fig:detail_kinematics_cubic_decentralized_dL}Cubic architecture}
#+attr_latex: :options {0.48\textwidth}
#+attr_latex: :options {\linewidth}
#+begin_subfigure
#+attr_latex: :width 0.95\linewidth
#+attr_latex: :scale 0.8
[[file:figs/detail_kinematics_cubic_decentralized_dL.png]]
#+end_subfigure
#+end_figure
@@ -389,15 +495,15 @@ The system demonstrates good decoupling at high frequency in both cases, with no
#+attr_latex: :options [htbp]
#+begin_figure
#+attr_latex: :caption \subcaption{\label{fig:detail_kinematics_non_cubic_decentralized_fn}Non cubic architecture}
#+attr_latex: :options {0.48\textwidth}
#+attr_latex: :options {\linewidth}
#+begin_subfigure
#+attr_latex: :width 0.95\linewidth
#+attr_latex: :scale 0.8
[[file:figs/detail_kinematics_non_cubic_decentralized_fn.png]]
#+end_subfigure
#+attr_latex: :caption \subcaption{\label{fig:detail_kinematics_cubic_decentralized_fn}Cubic architecture}
#+attr_latex: :options {0.48\textwidth}
#+attr_latex: :options {\linewidth}
#+begin_subfigure
#+attr_latex: :width 0.95\linewidth
#+attr_latex: :scale 0.8
[[file:figs/detail_kinematics_cubic_decentralized_fn.png]]
#+end_subfigure
#+end_figure
@@ -441,21 +547,21 @@ This approach yields a compact architecture, but the small cube size may result
#+attr_latex: :options [htbp]
#+begin_figure
#+attr_latex: :caption \subcaption{\label{fig:detail_kinematics_cubic_above_small_iso}Isometric view}
#+attr_latex: :options {0.36\textwidth}
#+attr_latex: :options {\linewidth}
#+begin_subfigure
#+attr_latex: :width 0.9\linewidth
#+attr_latex: :scale 0.7
[[file:figs/detail_kinematics_cubic_above_small_iso.png]]
#+end_subfigure
#+attr_latex: :caption \subcaption{\label{fig:detail_kinematics_cubic_above_small_side}Side view}
#+attr_latex: :options {0.30\textwidth}
#+attr_latex: :options {\linewidth}
#+begin_subfigure
#+attr_latex: :width 0.9\linewidth
#+attr_latex: :scale 0.7
[[file:figs/detail_kinematics_cubic_above_small_side.png]]
#+end_subfigure
#+attr_latex: :caption \subcaption{\label{fig:detail_kinematics_cubic_above_small_top}Top view}
#+attr_latex: :options {0.30\textwidth}
#+attr_latex: :options {\linewidth}
#+begin_subfigure
#+attr_latex: :width 0.9\linewidth
#+attr_latex: :scale 0.7
[[file:figs/detail_kinematics_cubic_above_small_top.png]]
#+end_subfigure
#+end_figure
@@ -468,28 +574,28 @@ Increasing the cube's size such that eqref:eq:detail_kinematics_cube_medium is v
2 H_{CoM} < H_c < 2 (H_{CoM} + H)
\end{equation}
This configuration resembles the design proposed in [[cite:&yang19_dynam_model_decoup_contr_flexib]] (Figure ref:fig:detail_kinematics_yang19), although their design is not strictly cubic.
This configuration resembles the design proposed in [[cite:&yang19_dynam_model_decoup_contr_flexib]], although their design is not strictly cubic.
#+name: fig:detail_kinematics_cubic_above_medium
#+caption: Cubic architecture with cube's center above the top platform. A cube height of 140mm is used.
#+attr_latex: :options [htbp]
#+begin_figure
#+attr_latex: :caption \subcaption{\label{fig:detail_kinematics_cubic_above_medium_iso}Isometric view}
#+attr_latex: :options {0.36\textwidth}
#+attr_latex: :options {\linewidth}
#+begin_subfigure
#+attr_latex: :width 0.9\linewidth
#+attr_latex: :scale 0.7
[[file:figs/detail_kinematics_cubic_above_medium_iso.png]]
#+end_subfigure
#+attr_latex: :caption \subcaption{\label{fig:detail_kinematics_cubic_above_medium_side}Side view}
#+attr_latex: :options {0.30\textwidth}
#+attr_latex: :options {\linewidth}
#+begin_subfigure
#+attr_latex: :width 0.9\linewidth
#+attr_latex: :scale 0.7
[[file:figs/detail_kinematics_cubic_above_medium_side.png]]
#+end_subfigure
#+attr_latex: :caption \subcaption{\label{fig:detail_kinematics_cubic_above_medium_top}Top view}
#+attr_latex: :options {0.30\textwidth}
#+attr_latex: :options {\linewidth}
#+begin_subfigure
#+attr_latex: :width 0.9\linewidth
#+attr_latex: :scale 0.7
[[file:figs/detail_kinematics_cubic_above_medium_top.png]]
#+end_subfigure
#+end_figure
@@ -507,21 +613,21 @@ When the cube's height exceeds twice the sum of the platform height and CoM heig
#+attr_latex: :options [htbp]
#+begin_figure
#+attr_latex: :caption \subcaption{\label{fig:detail_kinematics_cubic_above_large_iso}Isometric view}
#+attr_latex: :options {0.36\textwidth}
#+attr_latex: :options {\linewidth}
#+begin_subfigure
#+attr_latex: :width 0.9\linewidth
#+attr_latex: :scale 0.7
[[file:figs/detail_kinematics_cubic_above_large_iso.png]]
#+end_subfigure
#+attr_latex: :caption \subcaption{\label{fig:detail_kinematics_cubic_above_large_side}Side view}
#+attr_latex: :options {0.30\textwidth}
#+attr_latex: :options {\linewidth}
#+begin_subfigure
#+attr_latex: :width 0.9\linewidth
#+attr_latex: :scale 0.7
[[file:figs/detail_kinematics_cubic_above_large_side.png]]
#+end_subfigure
#+attr_latex: :caption \subcaption{\label{fig:detail_kinematics_cubic_above_large_top}Top view}
#+attr_latex: :options {0.30\textwidth}
#+attr_latex: :options {\linewidth}
#+begin_subfigure
#+attr_latex: :width 0.9\linewidth
#+attr_latex: :scale 0.7
[[file:figs/detail_kinematics_cubic_above_large_top.png]]
#+end_subfigure
#+end_figure
@@ -563,5 +669,23 @@ To address this limitation, modified cubic architectures have been proposed with
Three distinct configurations have been identified, each with different geometric arrangements but sharing the common characteristic that the cube's center is positioned above the top platform.
This structural modification enables the alignment of the moving body's center of mass with the center of stiffness, resulting in beneficial decoupling properties in the Cartesian frame.
* Acknowledgment :ignore:
#+begin_export latex
\begin{acknowledgment}
ASME Technical Publications provided the format specifications for the Journal of Mechanical Design, though they are not easy to reproduce. It is their commitment to ensuring quality figures in every issue of JMD that motivates this effort to have authors review the presentation of their figures.
Thanks go to D. E. Knuth and L. Lamport for developing the wonderful word processing software packages \TeX\ and \LaTeX. We would like to thank Ken Sprott, Kirk van Katwyk, and Matt Campbell for fixing bugs in the ASME style file \verb+asme2ej.cls+, and Geoff Shiflett for creating
ASME bibliography stype file \verb+asmems4.bst+.
\end{acknowledgment}
#+end_export
* Bibliography :ignore:
#+latex: \printbibliography[heading=bibintoc,title={Bibliography}]
#+begin_export latex
\bibliographystyle{asmems4}
% Here's where you specify the bibliography database file.
% The full file name of the bibliography database for this
% article is asme2e.bib. The name for your database is up
% to you.
\bibliography{dehaeze26_cubic_architecture}
#+end_export

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@@ -1,28 +1,53 @@
% Created 2025-11-26 Wed 09:39
% Created 2025-11-27 Thu 17:52
% Intended LaTeX compiler: pdflatex
\documentclass[a4paper, 10pt, DIV=12, parskip=full, bibliography=totoc]{scrreprt}
\documentclass[balance,nocopyright,nolists]{asmejour}
\input{preamble.tex}
\input{preamble_extra.tex}
\bibliography{dehaeze26_cubic_architecture.bib}
\usepackage[square,numbers]{natbib}
\JourName{Journal of Mechanical Design}
\author{Dehaeze Thomas}
\date{\today}
\title{Decoupling Properties of the Cubic Architecture}
\hypersetup{
pdfauthor={Dehaeze Thomas},
pdftitle={Decoupling Properties of the Cubic Architecture},
pdftitle={},
pdfkeywords={},
pdfsubject={},
pdfcreator={Emacs 30.2 (Org mode 9.7.34)},
pdflang={English}}
\usepackage{biblatex}
\begin{document}
\maketitle
\tableofcontents
\SetAuthorBlock{Thomas Dehaeze\CorrespondingAuthor}{%
ESRF, The European Synchrotron\\
Grenoble, France\\
email: thomas.dehaeze@esrf.fr
}
\SetAuthorBlock{Christophe Collette}{%
Precision Mechatronics Laboratory\\
University of Li\`{e}ge, Belgium\\
email: christophe.collette@uliege.be
}
%%% Change to your paper title. Can insert line breaks if you wish (otherwise breaks are selected automatically).
\title{Decoupling Properties of the Cubic Architecture}
\begin{abstract}
{\it This is the abstract.
This article illustrates preparation of ASME paper using
Please use this template to test how your figures will look on the printed journal page of the Journal of Mechanical Design. The Journal will no longer publish papers that contain errors in figure resolution. These usually consist of unreadable or fuzzy text, and pixilation or rasterization of lines. This template identifies the specifications used by JMD some of which may not be easily duplicated; for example, ASME actually uses Helvetica Condensed Bold, but this is not generally available so for the purpose of this exercise Helvetica is adequate. However, reproduction of the journal page is not the goal, instead this exercise is to verify the quality of your figures. Notice that this abstract is to be set in 9pt Times Italic, single spaced and right justified.
}
\end{abstract}
\date{Version \versionno, \today}%% You can modify this information as desired.
%% Putting \date{} will suppress any date.
%% If this command is omitted, date defaults to \today
%% This command must come somewhere before \maketitle
\maketitle %% This command creates the author/title/abstract block. Essential!
\section{Introduction}
\clearpage
The Cubic configuration for the Stewart platform was first proposed by Dr. Gough in a comment to the original paper by Dr. Stewart \cite{stewart65_platf_with_six_degrees_freed}.
This configuration is characterized by active struts arranged in a mutually orthogonal configuration connecting the corners of a cube, as shown in Figure \ref{fig:detail_kinematics_cubic_architecture_example}.
@@ -31,15 +56,15 @@ Practical implementations of such configurations can be observed in Figures \ref
It is also possible to implement designs with strut lengths smaller than the cube's edges (Figure \ref{fig:detail_kinematics_cubic_architecture_example_small}), as exemplified in Figure \ref{fig:detail_kinematics_ulb_pz}.
\begin{figure}[htbp]
\begin{subfigure}{0.49\textwidth}
\begin{subfigure}{\linewidth}
\begin{center}
\includegraphics[scale=1,scale=1]{figs/detail_kinematics_cubic_architecture_example.png}
\includegraphics[scale=1,scale=0.7]{figs/detail_kinematics_cubic_architecture_example.png}
\end{center}
\subcaption{\label{fig:detail_kinematics_cubic_architecture_example}Classical Cubic architecture}
\end{subfigure}
\begin{subfigure}{0.49\textwidth}
\begin{subfigure}{\linewidth}
\begin{center}
\includegraphics[scale=1,scale=1]{figs/detail_kinematics_cubic_architecture_example_small.png}
\includegraphics[scale=1,scale=0.7]{figs/detail_kinematics_cubic_architecture_example_small.png}
\end{center}
\subcaption{\label{fig:detail_kinematics_cubic_architecture_example_small}Alternative configuration}
\end{subfigure}
@@ -55,32 +80,34 @@ The mobility and stiffness properties of the cubic configuration are analyzed in
Dynamical decoupling is investigated in Section \ref{ssec:detail_kinematics_cubic_dynamic}, while decentralized control, crucial for the NASS, is examined in Section \ref{ssec:detail_kinematics_decentralized_control}.
Given that the cubic architecture imposes strict geometric constraints, alternative designs are proposed in Section \ref{ssec:detail_kinematics_cubic_design}.
The ultimate objective is to determine the suitability of the cubic architecture for the nano-hexapod.
\chapter{Static Properties}
\section{Static Properties}
\label{ssec:detail_kinematics_cubic_static}
\section{Stiffness matrix for the Cubic architecture}
\subsection{Stiffness matrix for the Cubic architecture}
Consider the cubic architecture shown in Figure \ref{fig:detail_kinematics_cubic_schematic_full}.
The unit vectors corresponding to the edges of the cube are described by equation \eqref{eq:detail_kinematics_cubic_s}.
\begin{equation}\label{eq:detail_kinematics_cubic_s}
\hat{\bm{s}}_1 = \begin{bmatrix} \frac{\sqrt{2}}{\sqrt{3}} \\ 0 \\ \frac{1}{\sqrt{3}} \end{bmatrix} \quad
\hat{\bm{s}}_2 = \begin{bmatrix} \frac{-1}{\sqrt{6}} \\ \frac{-1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} \end{bmatrix} \quad
\hat{\bm{s}}_3 = \begin{bmatrix} \frac{-1}{\sqrt{6}} \\ \frac{ 1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} \end{bmatrix} \quad
\hat{\bm{s}}_4 = \begin{bmatrix} \frac{\sqrt{2}}{\sqrt{3}} \\ 0 \\ \frac{1}{\sqrt{3}} \end{bmatrix} \quad
\hat{\bm{s}}_5 = \begin{bmatrix} \frac{-1}{\sqrt{6}} \\ \frac{-1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} \end{bmatrix} \quad
\hat{\bm{s}}_6 = \begin{bmatrix} \frac{-1}{\sqrt{6}} \\ \frac{ 1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} \end{bmatrix}
\begin{align*}
\hat{\bm{s}}_1 = \begin{bmatrix} \frac{\sqrt{2}}{\sqrt{3}} \\ 0 \\ \frac{1}{\sqrt{3}} \end{bmatrix} \quad
\hat{\bm{s}}_2 = \begin{bmatrix} \frac{-1}{\sqrt{6}} \\ \frac{-1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} \end{bmatrix} \quad
\hat{\bm{s}}_3 = \begin{bmatrix} \frac{-1}{\sqrt{6}} \\ \frac{ 1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} \end{bmatrix} \\
\hat{\bm{s}}_4 = \begin{bmatrix} \frac{\sqrt{2}}{\sqrt{3}} \\ 0 \\ \frac{1}{\sqrt{3}} \end{bmatrix} \quad
\hat{\bm{s}}_5 = \begin{bmatrix} \frac{-1}{\sqrt{6}} \\ \frac{-1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} \end{bmatrix} \quad
\hat{\bm{s}}_6 = \begin{bmatrix} \frac{-1}{\sqrt{6}} \\ \frac{ 1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} \end{bmatrix}
\end{align*}
\end{equation}
\begin{figure}[htbp]
\begin{subfigure}{0.48\textwidth}
\begin{subfigure}{\linewidth}
\begin{center}
\includegraphics[scale=1,scale=0.9]{figs/detail_kinematics_cubic_schematic_full.png}
\includegraphics[scale=1,scale=0.8]{figs/detail_kinematics_cubic_schematic_full.png}
\end{center}
\subcaption{\label{fig:detail_kinematics_cubic_schematic_full}Full cube}
\end{subfigure}
\begin{subfigure}{0.48\textwidth}
\begin{subfigure}{\linewidth}
\begin{center}
\includegraphics[scale=1,scale=0.9]{figs/detail_kinematics_cubic_schematic.png}
\includegraphics[scale=1,scale=0.8]{figs/detail_kinematics_cubic_schematic.png}
\end{center}
\subcaption{\label{fig:detail_kinematics_cubic_schematic}Cube's portion}
\end{subfigure}
@@ -90,16 +117,18 @@ The unit vectors corresponding to the edges of the cube are described by equatio
Coordinates of the cube's vertices relevant for the top joints, expressed with respect to the cube's center, are shown in equation \eqref{eq:detail_kinematics_cubic_vertices}.
\begin{equation}\label{eq:detail_kinematics_cubic_vertices}
\tilde{\bm{b}}_1 = \tilde{\bm{b}}_2 = H_c \begin{bmatrix} \frac{1}{\sqrt{2}} \\ \frac{-\sqrt{3}}{\sqrt{2}} \\ \frac{1}{2} \end{bmatrix}, \quad
\tilde{\bm{b}}_3 = \tilde{\bm{b}}_4 = H_c \begin{bmatrix} \frac{1}{\sqrt{2}} \\ \frac{ \sqrt{3}}{\sqrt{2}} \\ \frac{1}{2} \end{bmatrix}, \quad
\tilde{\bm{b}}_5 = \tilde{\bm{b}}_6 = H_c \begin{bmatrix} \frac{-2}{\sqrt{2}} \\ 0 \\ \frac{1}{2} \end{bmatrix}
\begin{align*}
\tilde{\bm{b}}_1 &= \tilde{\bm{b}}_2 = H_c \begin{bmatrix} \frac{1}{\sqrt{2}} \\ \frac{-\sqrt{3}}{\sqrt{2}} \\ \frac{1}{2} \end{bmatrix}, \quad
\tilde{\bm{b}}_3 = \tilde{\bm{b}}_4 = H_c \begin{bmatrix} \frac{1}{\sqrt{2}} \\ \frac{ \sqrt{3}}{\sqrt{2}} \\ \frac{1}{2} \end{bmatrix}, \\
\tilde{\bm{b}}_5 &= \tilde{\bm{b}}_6 = H_c \begin{bmatrix} \frac{-2}{\sqrt{2}} \\ 0 \\ \frac{1}{2} \end{bmatrix}
\end{align*}
\end{equation}
In the case where top joints are positioned at the cube's vertices, a diagonal stiffness matrix is obtained as shown in equation \eqref{eq:detail_kinematics_cubic_stiffness}.
Translation stiffness is twice the stiffness of the struts, and rotational stiffness is proportional to the square of the cube's size \(H_c\).
\begin{equation}\label{eq:detail_kinematics_cubic_stiffness}
\bm{K}_{\{B\} = \{C\}} = k \begin{bmatrix}
\bm{K} = k \begin{bmatrix}
2 & 0 & 0 & 0 & 0 & 0 \\
0 & 2 & 0 & 0 & 0 & 0 \\
0 & 0 & 2 & 0 & 0 & 0 \\
@@ -120,7 +149,7 @@ In that case, the location of the top joints can be expressed by equation \eqref
The stiffness matrix is therefore diagonal when the considered \(\{B\}\) frame is located at the center of the cube (shown by frame \(\{C\}\)).
This means that static forces (resp torques) applied at the cube's center will induce pure translations (resp rotations around the cube's center).
This specific location where the stiffness matrix is diagonal is referred to as the ``Center of Stiffness'' (analogous to the ``Center of Mass'' where the mass matrix is diagonal).
\section{Effect of having frame \(\{B\}\) off-centered}
\subsection{Effect of having frame \(\{B\}\) off-centered}
When the reference frames \(\{A\}\) and \(\{B\}\) are shifted from the cube's center, off-diagonal elements emerge in the stiffness matrix.
@@ -128,14 +157,15 @@ Considering a vertical shift as shown in Figure \ref{fig:detail_kinematics_cubic
Off-diagonal elements increase proportionally with the height difference between the cube's center and the considered \(\{B\}\) frame.
\begin{equation}\label{eq:detail_kinematics_cubic_stiffness_off_centered}
\bm{K}_{\{B\} \neq \{C\}} = k \begin{bmatrix}
\bm{K} = k \\
{\footnotesize \begin{bmatrix}
2 & 0 & 0 & 0 & -2 H & 0 \\
0 & 2 & 0 & 2 H & 0 & 0 \\
0 & 0 & 2 & 0 & 0 & 0 \\
0 & 2 H & 0 & \frac{3}{2} H_c^2 + 2 H^2 & 0 & 0 \\
-2 H & 0 & 0 & 0 & \frac{3}{2} H_c^2 + 2 H^2 & 0 \\
0 & 0 & 0 & 0 & 0 & 6 H_c^2 \\
\end{bmatrix}
\end{bmatrix}}
\end{equation}
This stiffness matrix structure is characteristic of Stewart platforms exhibiting symmetry, and is not an exclusive property of cubic architectures.
@@ -144,7 +174,7 @@ This poses a practical limitation, as in most applications, the relevant frame (
It should be noted that for the stiffness matrix to be diagonal, the cube's center doesn't need to coincide with the geometric center of the Stewart platform.
This observation leads to the interesting alternative architectures presented in Section \ref{ssec:detail_kinematics_cubic_design}.
\section{Uniform Mobility}
\subsection{Uniform Mobility}
The translational mobility of the Stewart platform with constant orientation was analyzed.
Considering limited actuator stroke (elongation of each strut), the maximum achievable positions in XYZ space were estimated.
@@ -158,21 +188,21 @@ The rotational mobility, illustrated in Figure \ref{fig:detail_kinematics_cubic_
Furthermore, an inverse relationship exists between the cube's dimension and rotational mobility, with larger cube sizes corresponding to more limited angular displacement capabilities.
\begin{figure}[htbp]
\begin{subfigure}{0.48\textwidth}
\begin{subfigure}{\linewidth}
\begin{center}
\includegraphics[scale=1,scale=1]{figs/detail_kinematics_cubic_mobility_translations.png}
\includegraphics[scale=1,scale=0.8]{figs/detail_kinematics_cubic_mobility_translations.png}
\end{center}
\subcaption{\label{fig:detail_kinematics_cubic_mobility_translations}Mobility in translation}
\end{subfigure}
\begin{subfigure}{0.48\textwidth}
\begin{subfigure}{\linewidth}
\begin{center}
\includegraphics[scale=1,scale=1]{figs/detail_kinematics_cubic_mobility_rotations.png}
\includegraphics[scale=1,scale=0.8]{figs/detail_kinematics_cubic_mobility_rotations.png}
\end{center}
\subcaption{\label{fig:detail_kinematics_cubic_mobility_rotations}Mobility in rotation}
\end{subfigure}
\caption{\label{fig:detail_kinematics_cubic_mobility}Mobility of a Stewart platform with Cubic architecture. Both for translations (\subref{fig:detail_kinematics_cubic_mobility_translations}) and rotations (\subref{fig:detail_kinematics_cubic_mobility_rotations})}
\end{figure}
\chapter{Dynamical Decoupling}
\section{Dynamical Decoupling}
\label{ssec:detail_kinematics_cubic_dynamic}
This section examines the dynamics of the cubic architecture in the Cartesian frame which corresponds to the transfer function from forces and torques \(\bm{\mathcal{F}}\) to translations and rotations \(\bm{\mathcal{X}}\) of the top platform.
When relative motion sensors are integrated in each strut (measuring \(\bm{\mathcal{L}}\)), the pose \(\bm{\mathcal{X}}\) is computed using the Jacobian matrix as shown in Figure \ref{fig:detail_kinematics_centralized_control}.
@@ -182,7 +212,7 @@ When relative motion sensors are integrated in each strut (measuring \(\bm{\math
\includegraphics[scale=1]{figs/detail_kinematics_centralized_control.png}
\caption{\label{fig:detail_kinematics_centralized_control}Typical control architecture in the cartesian frame}
\end{figure}
\section{Low frequency and High frequency coupling}
\subsection{Low frequency and High frequency coupling}
As derived during the conceptual design phase, the dynamics from \(\bm{\mathcal{F}}\) to \(\bm{\mathcal{X}}\) is described by Equation \eqref{eq:detail_kinematics_transfer_function_cart}.
At low frequency, the behavior of the platform depends on the stiffness matrix \eqref{eq:detail_kinematics_transfer_function_cart_low_freq}.
@@ -203,7 +233,7 @@ To achieve a diagonal mass matrix, the center of mass of the mobile components m
\begin{figure}[htbp]
\centering
\includegraphics[scale=1,width=0.6\linewidth]{figs/detail_kinematics_cubic_payload.png}
\includegraphics[scale=1,width=0.7\linewidth]{figs/detail_kinematics_cubic_payload.png}
\caption{\label{fig:detail_kinematics_cubic_payload}Cubic stewart platform with top cylindrical payload}
\end{figure}
@@ -213,52 +243,52 @@ When the \(\{B\}\) frame was positioned at the center of mass, coupling at low f
Conversely, when positioned at the center of stiffness, coupling occurred at high frequency due to the non-diagonal mass matrix (Figure \ref{fig:detail_kinematics_cubic_cart_coupling_cok}).
\begin{figure}[htbp]
\begin{subfigure}{0.48\textwidth}
\begin{subfigure}{\linewidth}
\begin{center}
\includegraphics[scale=1,width=0.95\linewidth]{figs/detail_kinematics_cubic_cart_coupling_com.png}
\includegraphics[scale=1,scale=0.8]{figs/detail_kinematics_cubic_cart_coupling_com.png}
\end{center}
\subcaption{\label{fig:detail_kinematics_cubic_cart_coupling_com}$\{B\}$ at the center of mass}
\end{subfigure}
\begin{subfigure}{0.48\textwidth}
\begin{subfigure}{\linewidth}
\begin{center}
\includegraphics[scale=1,width=0.95\linewidth]{figs/detail_kinematics_cubic_cart_coupling_cok.png}
\includegraphics[scale=1,scale=0.8]{figs/detail_kinematics_cubic_cart_coupling_cok.png}
\end{center}
\subcaption{\label{fig:detail_kinematics_cubic_cart_coupling_cok}$\{B\}$ at the cube's center}
\end{subfigure}
\caption{\label{fig:detail_kinematics_cubic_cart_coupling}Transfer functions for a Cubic Stewart platform expressed in the Cartesian frame. Two locations of the \(\{B\}\) frame are considered: at the center of mass of the moving body (\subref{fig:detail_kinematics_cubic_cart_coupling_com}) and at the cube's center (\subref{fig:detail_kinematics_cubic_cart_coupling_cok}).}
\end{figure}
\section{Payload's CoM at the cube's center}
\subsection{Payload's CoM at the cube's center}
An effective strategy for improving dynamical performances involves aligning the cube's center (center of stiffness) with the center of mass of the moving components \cite{li01_simul_fault_vibrat_isolat_point}.
This can be achieved by positioning the payload below the top platform, such that the center of mass of the moving body coincides with the cube's center (Figure \ref{fig:detail_kinematics_cubic_centered_payload}).
This approach was physically implemented in several studies \cite{mcinroy99_dynam,jafari03_orthog_gough_stewar_platf_microm}, as shown in Figure \ref{fig:detail_kinematics_uw_gsp}.
This approach was physically implemented in several studies \cite{mcinroy99_dynam,jafari03_orthog_gough_stewar_platf_microm}.
The resulting dynamics are indeed well-decoupled (Figure \ref{fig:detail_kinematics_cubic_cart_coupling_com_cok}), taking advantage from diagonal stiffness and mass matrices.
The primary limitation of this approach is that, for many applications including the nano-hexapod, the payload must be positioned above the top platform.
If a design similar to Figure \ref{fig:detail_kinematics_cubic_centered_payload} were employed for the nano-hexapod, the X-ray beam would intersect with the struts during spindle rotation.
\begin{figure}[htbp]
\begin{subfigure}{0.49\textwidth}
\begin{subfigure}{\linewidth}
\begin{center}
\includegraphics[scale=1,width=0.95\linewidth]{figs/detail_kinematics_cubic_centered_payload.png}
\includegraphics[scale=1,width=0.7\linewidth]{figs/detail_kinematics_cubic_centered_payload.png}
\end{center}
\subcaption{\label{fig:detail_kinematics_cubic_centered_payload}Payload at the cube's center}
\end{subfigure}
\begin{subfigure}{0.49\textwidth}
\begin{subfigure}{\linewidth}
\begin{center}
\includegraphics[scale=1,width=0.95\linewidth]{figs/detail_kinematics_cubic_cart_coupling_com_cok.png}
\includegraphics[scale=1,scale=0.8]{figs/detail_kinematics_cubic_cart_coupling_com_cok.png}
\end{center}
\subcaption{\label{fig:detail_kinematics_cubic_cart_coupling_com_cok}Fully decoupled cartesian plant}
\end{subfigure}
\caption{\label{fig:detail_kinematics_cubic_com_cok}Cubic Stewart platform with payload at the cube's center (\subref{fig:detail_kinematics_cubic_centered_payload}). Obtained cartesian plant is fully decoupled (\subref{fig:detail_kinematics_cubic_cart_coupling_com_cok})}
\end{figure}
\section{Conclusion}
\subsection{Conclusion}
The analysis of dynamical properties of the cubic architecture yields several important conclusions.
Static decoupling, characterized by a diagonal stiffness matrix, is achieved when reference frames \(\{A\}\) and \(\{B\}\) are positioned at the cube's center.
Note that this property can also be obtained with non-cubic architectures that exhibit symmetrical strut arrangements.
Dynamic decoupling requires both static decoupling and coincidence of the mobile platform's center of mass with reference frame \(\{B\}\).
While this configuration offers powerful control advantages, it requires positioning the payload at the cube's center, which is highly restrictive and often impractical.
\chapter{Decentralized Control}
\section{Decentralized Control}
\label{ssec:detail_kinematics_decentralized_control}
The orthogonal arrangement of struts in the cubic architecture suggests a potential minimization of inter-strut coupling, which could theoretically create favorable conditions for decentralized control.
Two sensor types integrated in the struts are considered: displacement sensors and force sensors.
@@ -276,10 +306,10 @@ The second uses a non-cubic Stewart platform shown in Figure \ref{fig:detail_kin
\begin{figure}[htbp]
\centering
\includegraphics[scale=1,width=0.6\linewidth]{figs/detail_kinematics_non_cubic_payload.png}
\includegraphics[scale=1,width=0.7\linewidth]{figs/detail_kinematics_non_cubic_payload.png}
\caption{\label{fig:detail_kinematics_non_cubic_payload}Stewart platform with non-cubic architecture}
\end{figure}
\section{Relative Displacement Sensors}
\subsection{Relative Displacement Sensors}
The transfer functions from actuator force in each strut to the relative motion of the struts are presented in Figure \ref{fig:detail_kinematics_decentralized_dL}.
As anticipated from the equations of motion from \(\bm{f}\) to \(\bm{\mathcal{L}}\) \eqref{eq:detail_kinematics_transfer_function_struts}, the \(6 \times 6\) plant is decoupled at low frequency.
@@ -289,46 +319,46 @@ No significant advantage is evident for the cubic architecture (Figure \ref{fig:
The resonance frequencies differ between the two cases because the more vertical strut orientation in the non-cubic architecture alters the stiffness properties of the Stewart platform, consequently shifting the frequencies of various modes.
\begin{figure}[htbp]
\begin{subfigure}{0.48\textwidth}
\begin{subfigure}{\linewidth}
\begin{center}
\includegraphics[scale=1,width=0.95\linewidth]{figs/detail_kinematics_non_cubic_decentralized_dL.png}
\includegraphics[scale=1,scale=0.8]{figs/detail_kinematics_non_cubic_decentralized_dL.png}
\end{center}
\subcaption{\label{fig:detail_kinematics_non_cubic_decentralized_dL}Non cubic architecture}
\end{subfigure}
\begin{subfigure}{0.48\textwidth}
\begin{subfigure}{\linewidth}
\begin{center}
\includegraphics[scale=1,width=0.95\linewidth]{figs/detail_kinematics_cubic_decentralized_dL.png}
\includegraphics[scale=1,scale=0.8]{figs/detail_kinematics_cubic_decentralized_dL.png}
\end{center}
\subcaption{\label{fig:detail_kinematics_cubic_decentralized_dL}Cubic architecture}
\end{subfigure}
\caption{\label{fig:detail_kinematics_decentralized_dL}Bode plot of the transfer functions from actuator force to relative displacement sensor in each strut. Both for a non-cubic architecture (\subref{fig:detail_kinematics_non_cubic_decentralized_dL}) and for a cubic architecture (\subref{fig:detail_kinematics_cubic_decentralized_dL})}
\end{figure}
\section{Force Sensors}
\subsection{Force Sensors}
Similarly, the transfer functions from actuator force to force sensors in each strut were analyzed for both cubic and non-cubic Stewart platforms.
The results are presented in Figure \ref{fig:detail_kinematics_decentralized_fn}.
The system demonstrates good decoupling at high frequency in both cases, with no clear advantage for the cubic architecture.
\begin{figure}[htbp]
\begin{subfigure}{0.48\textwidth}
\begin{subfigure}{\linewidth}
\begin{center}
\includegraphics[scale=1,width=0.95\linewidth]{figs/detail_kinematics_non_cubic_decentralized_fn.png}
\includegraphics[scale=1,scale=0.8]{figs/detail_kinematics_non_cubic_decentralized_fn.png}
\end{center}
\subcaption{\label{fig:detail_kinematics_non_cubic_decentralized_fn}Non cubic architecture}
\end{subfigure}
\begin{subfigure}{0.48\textwidth}
\begin{subfigure}{\linewidth}
\begin{center}
\includegraphics[scale=1,width=0.95\linewidth]{figs/detail_kinematics_cubic_decentralized_fn.png}
\includegraphics[scale=1,scale=0.8]{figs/detail_kinematics_cubic_decentralized_fn.png}
\end{center}
\subcaption{\label{fig:detail_kinematics_cubic_decentralized_fn}Cubic architecture}
\end{subfigure}
\caption{\label{fig:detail_kinematics_decentralized_fn}Bode plot of the transfer functions from actuator force to force sensor in each strut. Both for a non-cubic architecture (\subref{fig:detail_kinematics_non_cubic_decentralized_fn}) and for a cubic architecture (\subref{fig:detail_kinematics_cubic_decentralized_fn})}
\end{figure}
\section{Conclusion}
\subsection{Conclusion}
The presented results do not demonstrate the pronounced decoupling advantages often associated with cubic architectures in the literature.
Both the cubic and non-cubic configurations exhibited similar coupling characteristics, suggesting that the benefits of orthogonal strut arrangement for decentralized control is less obvious than often reported in the literature.
\chapter{Cubic architecture with Cube's center above the top platform}
\section{Cubic architecture with Cube's center above the top platform}
\label{ssec:detail_kinematics_cubic_design}
As demonstrated in Section \ref{ssec:detail_kinematics_cubic_dynamic}, the cubic architecture can exhibit advantageous dynamical properties when the center of mass of the moving body coincides with the cube's center, resulting in diagonal mass and stiffness matrices.
As shown in Section \ref{ssec:detail_kinematics_cubic_static}, the stiffness matrix is diagonal when the considered \(\{B\}\) frame is located at the cube's center.
@@ -340,7 +370,7 @@ Three key parameters define the geometry of the cubic Stewart platform: \(H\), t
Depending on the cube's size \(H_c\) in relation to \(H\) and \(H_{CoM}\), different designs emerge.
In the following examples, \(H = 100\,mm\) and \(H_{CoM} = 20\,mm\).
\section{Small cube}
\subsection{Small cube}
When the cube size \(H_c\) is smaller than twice the height of the CoM \(H_{CoM}\) \eqref{eq:detail_kinematics_cube_small}, the resulting design is shown in Figure \ref{fig:detail_kinematics_cubic_above_small}.
@@ -354,27 +384,27 @@ Adjacent struts are parallel to each other, differing from the typical architect
This approach yields a compact architecture, but the small cube size may result in insufficient rotational stiffness.
\begin{figure}[htbp]
\begin{subfigure}{0.36\textwidth}
\begin{subfigure}{\linewidth}
\begin{center}
\includegraphics[scale=1,width=0.9\linewidth]{figs/detail_kinematics_cubic_above_small_iso.png}
\includegraphics[scale=1,scale=0.7]{figs/detail_kinematics_cubic_above_small_iso.png}
\end{center}
\subcaption{\label{fig:detail_kinematics_cubic_above_small_iso}Isometric view}
\end{subfigure}
\begin{subfigure}{0.30\textwidth}
\begin{subfigure}{\linewidth}
\begin{center}
\includegraphics[scale=1,width=0.9\linewidth]{figs/detail_kinematics_cubic_above_small_side.png}
\includegraphics[scale=1,scale=0.7]{figs/detail_kinematics_cubic_above_small_side.png}
\end{center}
\subcaption{\label{fig:detail_kinematics_cubic_above_small_side}Side view}
\end{subfigure}
\begin{subfigure}{0.30\textwidth}
\begin{subfigure}{\linewidth}
\begin{center}
\includegraphics[scale=1,width=0.9\linewidth]{figs/detail_kinematics_cubic_above_small_top.png}
\includegraphics[scale=1,scale=0.7]{figs/detail_kinematics_cubic_above_small_top.png}
\end{center}
\subcaption{\label{fig:detail_kinematics_cubic_above_small_top}Top view}
\end{subfigure}
\caption{\label{fig:detail_kinematics_cubic_above_small}Cubic architecture with cube's center above the top platform. A cube height of 40mm is used.}
\end{figure}
\section{Medium sized cube}
\subsection{Medium sized cube}
Increasing the cube's size such that \eqref{eq:detail_kinematics_cube_medium} is verified produces an architecture with intersecting struts (Figure \ref{fig:detail_kinematics_cubic_above_medium}).
@@ -382,30 +412,30 @@ Increasing the cube's size such that \eqref{eq:detail_kinematics_cube_medium} is
2 H_{CoM} < H_c < 2 (H_{CoM} + H)
\end{equation}
This configuration resembles the design proposed in \cite{yang19_dynam_model_decoup_contr_flexib} (Figure \ref{fig:detail_kinematics_yang19}), although their design is not strictly cubic.
This configuration resembles the design proposed in \cite{yang19_dynam_model_decoup_contr_flexib}, although their design is not strictly cubic.
\begin{figure}[htbp]
\begin{subfigure}{0.36\textwidth}
\begin{subfigure}{\linewidth}
\begin{center}
\includegraphics[scale=1,width=0.9\linewidth]{figs/detail_kinematics_cubic_above_medium_iso.png}
\includegraphics[scale=1,scale=0.7]{figs/detail_kinematics_cubic_above_medium_iso.png}
\end{center}
\subcaption{\label{fig:detail_kinematics_cubic_above_medium_iso}Isometric view}
\end{subfigure}
\begin{subfigure}{0.30\textwidth}
\begin{subfigure}{\linewidth}
\begin{center}
\includegraphics[scale=1,width=0.9\linewidth]{figs/detail_kinematics_cubic_above_medium_side.png}
\includegraphics[scale=1,scale=0.7]{figs/detail_kinematics_cubic_above_medium_side.png}
\end{center}
\subcaption{\label{fig:detail_kinematics_cubic_above_medium_side}Side view}
\end{subfigure}
\begin{subfigure}{0.30\textwidth}
\begin{subfigure}{\linewidth}
\begin{center}
\includegraphics[scale=1,width=0.9\linewidth]{figs/detail_kinematics_cubic_above_medium_top.png}
\includegraphics[scale=1,scale=0.7]{figs/detail_kinematics_cubic_above_medium_top.png}
\end{center}
\subcaption{\label{fig:detail_kinematics_cubic_above_medium_top}Top view}
\end{subfigure}
\caption{\label{fig:detail_kinematics_cubic_above_medium}Cubic architecture with cube's center above the top platform. A cube height of 140mm is used.}
\end{figure}
\section{Large cube}
\subsection{Large cube}
When the cube's height exceeds twice the sum of the platform height and CoM height \eqref{eq:detail_kinematics_cube_large}, the architecture shown in Figure \ref{fig:detail_kinematics_cubic_above_large} is obtained.
@@ -414,27 +444,27 @@ When the cube's height exceeds twice the sum of the platform height and CoM heig
\end{equation}
\begin{figure}[htbp]
\begin{subfigure}{0.36\textwidth}
\begin{subfigure}{\linewidth}
\begin{center}
\includegraphics[scale=1,width=0.9\linewidth]{figs/detail_kinematics_cubic_above_large_iso.png}
\includegraphics[scale=1,scale=0.7]{figs/detail_kinematics_cubic_above_large_iso.png}
\end{center}
\subcaption{\label{fig:detail_kinematics_cubic_above_large_iso}Isometric view}
\end{subfigure}
\begin{subfigure}{0.30\textwidth}
\begin{subfigure}{\linewidth}
\begin{center}
\includegraphics[scale=1,width=0.9\linewidth]{figs/detail_kinematics_cubic_above_large_side.png}
\includegraphics[scale=1,scale=0.7]{figs/detail_kinematics_cubic_above_large_side.png}
\end{center}
\subcaption{\label{fig:detail_kinematics_cubic_above_large_side}Side view}
\end{subfigure}
\begin{subfigure}{0.30\textwidth}
\begin{subfigure}{\linewidth}
\begin{center}
\includegraphics[scale=1,width=0.9\linewidth]{figs/detail_kinematics_cubic_above_large_top.png}
\includegraphics[scale=1,scale=0.7]{figs/detail_kinematics_cubic_above_large_top.png}
\end{center}
\subcaption{\label{fig:detail_kinematics_cubic_above_large_top}Top view}
\end{subfigure}
\caption{\label{fig:detail_kinematics_cubic_above_large}Cubic architecture with cube's center above the top platform. A cube height of 240mm is used.}
\end{figure}
\section{Platform size}
\subsection{Platform size}
For the proposed configuration, the top joints \(\bm{b}_i\) (resp. the bottom joints \(\bm{a}_i\)) and are positioned on a circle with radius \(R_{b_i}\) (resp. \(R_{a_i}\)) described by Equation \eqref{eq:detail_kinematics_cube_joints}.
@@ -447,7 +477,7 @@ For the proposed configuration, the top joints \(\bm{b}_i\) (resp. the bottom jo
Since the rotational stiffness for the cubic architecture scales with the square of the cube's height \eqref{eq:detail_kinematics_cubic_stiffness}, the cube's size can be determined based on rotational stiffness requirements.
Subsequently, using Equation \eqref{eq:detail_kinematics_cube_joints}, the dimensions of the top and bottom platforms can be calculated.
\chapter*{Conclusion}
\section*{Conclusion}
The analysis of the cubic architecture for Stewart platforms yielded several important findings.
While the cubic configuration provides uniform stiffness in the XYZ directions, it stiffness property becomes particularly advantageous when forces and torques are applied at the cube's center.
Under these conditions, the stiffness matrix becomes diagonal, resulting in a decoupled Cartesian plant at low frequencies.
@@ -465,5 +495,17 @@ However, this arrangement presents practical challenges, as the cube's center is
To address this limitation, modified cubic architectures have been proposed with the cube's center positioned above the top platform.
Three distinct configurations have been identified, each with different geometric arrangements but sharing the common characteristic that the cube's center is positioned above the top platform.
This structural modification enables the alignment of the moving body's center of mass with the center of stiffness, resulting in beneficial decoupling properties in the Cartesian frame.
\printbibliography[heading=bibintoc,title={Bibliography}]
\begin{acknowledgment}
ASME Technical Publications provided the format specifications for the Journal of Mechanical Design, though they are not easy to reproduce. It is their commitment to ensuring quality figures in every issue of JMD that motivates this effort to have authors review the presentation of their figures.
Thanks go to D. E. Knuth and L. Lamport for developing the wonderful word processing software packages \TeX\ and \LaTeX. We would like to thank Ken Sprott, Kirk van Katwyk, and Matt Campbell for fixing bugs in the ASME style file \verb+asme2ej.cls+, and Geoff Shiflett for creating
ASME bibliography stype file \verb+asmems4.bst+.
\end{acknowledgment}
\bibliographystyle{asmems4}
% Here's where you specify the bibliography database file.
% The full file name of the bibliography database for this
% article is asme2e.bib. The name for your database is up
% to you.
\bibliography{dehaeze26_cubic_architecture}
\end{document}

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paper/preamble.tex
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@@ -1,35 +1,22 @@
\usepackage[ %
acronym, % Separate acronyms and glossary
toc, % appear in ToC
automake, % auto-use the makeglossaries command (requires shell-escape)
nonumberlist, % don't back reference pages
nogroupskip, % don't group by letter
nopostdot % don't add a dot at the end of each element
]{glossaries}
\usepackage[stylemods=longextra]{glossaries-extra}
\setabbreviationstyle[acronym]{long-short}
\setglossarystyle{long-name-desc}
\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{cases}
\usepackage{empheq}
\usepackage[binary-units=true]{siunitx}
\sisetup{%
detect-all = true,
detect-family = true,
detect-mode = true,
detect-shape = true,
detect-weight = true,
detect-inline-weight = math,
\usepackage{graphicx} % for loading jpg figures
\usepackage{hyperref} % to set up hyperlinks
\hypersetup{
colorlinks=true,
linkcolor=blue,
citecolor=blue,
urlcolor=blue,
}
\DeclareSIUnit\px{px}
\DeclareSIUnit\rms{rms}
\usepackage{bm}
\makeindex
\makeglossaries
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\DeclareGraphicsRule{.gif}{png}{.png}{\noexpand\Gin@base.png}
\makeatother
\usepackage{caption}
\usepackage{subcaption}

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paper/preamble_extra.tex
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@@ -1,134 +0,0 @@
\usepackage{float}
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\usepackage{caption,tabularx,booktabs}
\usepackage{bm}
\usepackage{xpatch} % Recommanded for biblatex
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style=ieee, % bib style
hyperref=true, % activate hyperref support
backref=true, % activate backrefs
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url=false, % don't show url tags
doi=false, % don't show doi tags
urldate=long, % display type for dates
maxnames=3, %
minnames=1, %
maxbibnames=5, %
minbibnames=3, %
maxcitenames=2, %
mincitenames=1 %
]{biblatex}
\setlength\bibitemsep{1.1\itemsep}
\usepackage{caption}
\usepackage{subcaption}
\captionsetup[figure]{labelfont=bf}
\captionsetup[subfigure]{labelfont=bf}
\captionsetup[listing]{labelfont=bf}
\captionsetup[table]{labelfont=bf}
\usepackage{xcolor}
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