266 lines
12 KiB
TeX
266 lines
12 KiB
TeX
% Created 2025-03-19 Wed 19:08
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% Intended LaTeX compiler: pdflatex
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\documentclass[a4paper, 10pt, DIV=12, parskip=full, bibliography=totoc]{scrreprt}
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\input{preamble.tex}
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\input{preamble_extra.tex}
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\bibliography{nass-geometry.bib}
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\author{Dehaeze Thomas}
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\date{\today}
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\title{Nano Hexapod - Optimal Geometry}
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\hypersetup{
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pdfauthor={Dehaeze Thomas},
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pdftitle={Nano Hexapod - Optimal Geometry},
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pdfkeywords={},
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pdfsubject={},
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pdfcreator={Emacs 29.4 (Org mode 9.6)},
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pdflang={English}}
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\usepackage{biblatex}
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\begin{document}
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\maketitle
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\tableofcontents
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\clearpage
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\begin{itemize}
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\item In the conceptual design phase, the geometry of the Stewart platform was not optimized
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\item In the detail design phase, we want to see if the geometry can be optimized to improve the overall performances
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\item Optimization criteria: mobility, stiffness, dynamical decoupling, more performance / bandwidth
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\end{itemize}
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Outline:
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\begin{itemize}
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\item Review of Stewart platform: Section \ref{sec:detail_kinematics_stewart_review}
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Geometry, Actuators, Sensors, Joints
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\item Effect of geometry on the Stewart platform characteristics \ref{sec:detail_kinematics_geometry}
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\item Cubic configuration: benefits? \ref{sec:detail_kinematics_cubic}
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\end{itemize}
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\chapter{Review of Stewart platforms}
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\label{sec:detail_kinematics_stewart_review}
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\begin{itemize}
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\item as was explained in the conceptual phase, Stewart platform have the following key elements:
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\begin{itemize}
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\item two plates
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\item flexible joints
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\item actuators
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\item sensors
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\end{itemize}
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\item the geometry
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\item This results in various designs as shown in Table \ref{tab:detail_kinematics_stewart_review}
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\item The focus is here made on Stewart platforms for nano-positioning of vibration control.
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Not on long stroke stewart platforms.
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\item All presented Stewart platforms are using flexible joints, as it is a prerequisites for nano-positioning capabilities.
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\item Most of stewart platforms are using voice coil actuators or piezoelectric actuators.
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The actuators used for the Stewart platform will be chosen in the next section.
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\item Depending on the application, various sensors are integrated in the struts or on the plates.
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The choice of sensor for the nano-hexapod will be described in the next section.
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\item[{$\square$}] Only keep integrated sensor and not external metrology
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\item[{$\square$}] Check for missing information
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\end{itemize}
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\begin{figure}[htbp]
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\begin{subfigure}{0.48\textwidth}
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\begin{center}
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\includegraphics[scale=1,width=0.95\linewidth]{figs/detail_kinematics_jpl.jpg}
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\end{center}
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\subcaption{\label{fig:detail_kinematics_jpl}California Institute of Technology - USA}
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\end{subfigure}
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\begin{subfigure}{0.48\textwidth}
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\begin{center}
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\includegraphics[scale=1,width=0.95\linewidth]{figs/detail_kinematics_uw_gsp.jpg}
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\end{center}
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\subcaption{\label{fig:detail_kinematics_uw_gsp}University of Wyoming - USA}
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\end{subfigure}
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\bigskip
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\begin{subfigure}{0.53\textwidth}
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\begin{center}
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\includegraphics[scale=1,width=0.95\linewidth]{figs/detail_kinematics_ulb_pz.jpg}
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\end{center}
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\subcaption{\label{fig:detail_kinematics_ulb_pz}ULB - Belgium}
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\end{subfigure}
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\begin{subfigure}{0.43\textwidth}
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\begin{center}
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\includegraphics[scale=1,width=0.95\linewidth]{figs/detail_kinematics_uqp.jpg}
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\end{center}
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\subcaption{\label{fig:detail_kinematics_uqp}Naval Postgraduate School - USA}
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\end{subfigure}
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\caption{\label{fig:detail_kinematics_stewart_examples_cubic}Some examples of developped Stewart platform with Cubic geometry. (\subref{fig:detail_kinematics_jpl}), (\subref{fig:detail_kinematics_uw_gsp}), (\subref{fig:detail_kinematics_ulb_pz}), (\subref{fig:detail_kinematics_uqp})}
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\end{figure}
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\begin{figure}[htbp]
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\begin{subfigure}{0.48\textwidth}
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\begin{center}
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\includegraphics[scale=1,height=5cm]{figs/detail_kinematics_pph.jpg}
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\end{center}
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\subcaption{\label{fig:detail_kinematics_pph}Naval Postgraduate School - USA}
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\end{subfigure}
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\begin{subfigure}{0.48\textwidth}
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\begin{center}
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\includegraphics[scale=1,height=5cm]{figs/detail_kinematics_zhang11.jpg}
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\end{center}
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\subcaption{\label{fig:detail_kinematics_zhang11}Beihang University - China}
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\end{subfigure}
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\bigskip
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\begin{subfigure}{0.43\textwidth}
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\begin{center}
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\includegraphics[scale=1,height=5cm]{figs/detail_kinematics_yang19.jpg}
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\end{center}
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\subcaption{\label{fig:detail_kinematics_yang19}Nanjing University - China}
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\end{subfigure}
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\begin{subfigure}{0.53\textwidth}
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\begin{center}
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\includegraphics[scale=1,height=5cm]{figs/detail_kinematics_naves.jpg}
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\end{center}
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\subcaption{\label{fig:detail_kinematics_naves}University of Twente - Netherlands}
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\end{subfigure}
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\caption{\label{fig:detail_kinematics_stewart_examples_non_cubic}Some examples of developped Stewart platform with non-cubic geometry. (\subref{fig:detail_kinematics_pph}), (\subref{fig:detail_kinematics_zhang11}), (\subref{fig:detail_kinematics_yang19}), (\subref{fig:detail_kinematics_naves})}
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\end{figure}
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\begin{table}[htbp]
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\caption{\label{tab:detail_kinematics_stewart_review}Examples of Stewart platform developed. When not specifically indicated, sensors are included in the struts. All presented Stewart platforms are using flexible joints. The table is sorted by ``date''}
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\centering
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\scriptsize
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\begin{tabularx}{\linewidth}{llllX}
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\toprule
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& \textbf{Geometry} & \textbf{Actuators} & \textbf{Sensors} & \textbf{Reference}\\
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\midrule
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& Cubic (6-UPU) & Magnetostrictive & Force (collocated), Accelerometers & \cite{geng93_six_degree_of_freed_activ,geng94_six_degree_of_freed_activ,geng95_intel_contr_system_multip_degree}\\
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Figure \ref{fig:detail_kinematics_jpl} & Cubic & Voice Coil (0.5 mm) & Force (collocated) & \cite{spanos95_soft_activ_vibrat_isolat,rahman98_multiax}\\
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& Cubic & Voice Coil (10 mm) & Force, LVDT, Geophones & \cite{thayer98_stewar,thayer02_six_axis_vibrat_isolat_system,hauge04_sensor_contr_space_based_six}\\
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Figure \ref{fig:detail_kinematics_uw_gsp} & Cubic (CoM=CoK) & Voice Coil & Force & \cite{mcinroy99_dynam,mcinroy99_precis_fault_toler_point_using_stewar_platf,mcinroy00_desig_contr_flexur_joint_hexap,li01_simul_vibrat_isolat_point_contr,jafari03_orthog_gough_stewar_platf_microm}\\
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& Cubic & Piezoelectric (\(25\,\mu m\)) & Piezo force sensors & \cite{defendini00_techn}\\
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Figure \ref{fig:detail_kinematics_ulb_pz} & Cubic & APA (\(50\,\mu m\)) & Force sensor & \cite{abu02_stiff_soft_stewar_platf_activ}\\
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Figure \ref{fig:detail_kinematics_pph} & Non-Cubic & Voice Coil & Accelerometers & \cite{chen03_payload_point_activ_vibrat_isolat}\\
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& Cubic & Voice Coil & Force & \cite{hanieh03_activ_stewar,preumont07_six_axis_singl_stage_activ}\\
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Figure \ref{fig:detail_kinematics_uqp} & Cubic & Piezoelectric (\(50\,\mu m\)) & Geophone aligned with the strut & \cite{agrawal04_algor_activ_vibrat_isolat_spacec}\\
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& Non-Cubic & Piezoelectric (\(16\,\mu m\)) & Eddy Current & \cite{furutani04_nanom_cuttin_machin_using_stewar}\\
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& Cubic & Piezoelectric (\(120\,\mu m\)) & External capacitive & \cite{ting06_desig_stewar_nanos_platf,ting13_compos_contr_desig_stewar_nanos_platf}\\
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& Non-Cubic & Piezoelectric (\(160\,\mu m\)) & External capacitive (LION) & \cite{ting07_measur_calib_stewar_microm_system}\\
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Figure \ref{fig:detail_kinematics_zhang11} & Non-cubic & Magnetostrictive & Inertial & \cite{zhang11_six_dof}\\
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& 6-SPS (Optimized) & Piezoelectric & Strain Gauge & \cite{du14_piezo_actuat_high_precis_flexib}\\
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& Cubic & Voice Coil & Accelerometer in each leg & \cite{chi15_desig_exper_study_vcm_based,tang18_decen_vibrat_contr_voice_coil,jiao18_dynam_model_exper_analy_stewar}\\
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& Cubic & Piezoelectric & Force Sensor + Accelerometer & \cite{wang16_inves_activ_vibrat_isolat_stewar}\\
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& Almost cubic & Voice Coil & Force Sensor + Accelerometer & \cite{beijen18_self_tunin_mimo_distur_feedf,tjepkema12_activ_ph}\\
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Figure \ref{fig:detail_kinematics_yang19} & 6-UPS (Cubic?) & Piezoelectric & Force, Position & \cite{yang19_dynam_model_decoup_contr_flexib}\\
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Figure \ref{fig:detail_kinematics_naves} & Non-Cubic & 3-phase rotary motor & Rotary Encoders & \cite{naves20_desig,naves20_t_flex}\\
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\bottomrule
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\end{tabularx}
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\end{table}
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\begin{itemize}
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\item[{$\square$}] \url{https://research.tdehaeze.xyz/stewart-simscape/docs/bibliography.html}
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\item[{$\square$}] Joints and actuators are optimized in the next section
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\end{itemize}
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\chapter{Effect of geometry on Stewart platform properties}
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\label{sec:detail_kinematics_geometry}
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\begin{itemize}
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\item Remind that the choice of frames (independently of the physical geometry) impacts the obtained stiffness matrix (as it is defined as forces/motion evaluated at the chosen frame)
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\item Important: bi (join position w.r.t top platform) and si (orientation of struts)
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\end{itemize}
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For the nano-hexapod:
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\begin{itemize}
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\item Size requirements: Maximum height, maximum radius
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\end{itemize}
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\section{Stiffness}
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\begin{itemize}
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\item Give some examples:
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\begin{itemize}
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\item struts further apart: higher angular stiffness, same linear stiffness
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\item orientation: more vertical => increase vertical stiffness, decrease horizontal stiffness
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\end{itemize}
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\end{itemize}
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\section{Mobility and required joint and actuator stroke}
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\begin{itemize}
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\item Comparison of the XYZ mobility (fixed orientation) for two geometry (or maybe only in the XY or YZ plane to see more clearly the differences)
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\item[{$\square$}] \href{file:///home/thomas/Cloud/work-projects/ID31-NASS/matlab/stewart-simscape/org/kinematic-study.org}{Estimated required actuator stroke from specified platform mobility}
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Will be useful to choose the actuators
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\item[{$\square$}] \href{file:///home/thomas/Cloud/work-projects/ID31-NASS/matlab/stewart-simscape/org/kinematic-study.org}{Estimation of the Joint required Stroke}
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Will be useful to design the flexible joints
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\end{itemize}
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\section*{Conclusion}
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\begin{itemize}
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\item[{$\square$}] Table that summarize the findings
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\href{file:///home/thomas/Cloud/work-projects/ID31-NASS/documents/state-of-thesis-2020/index.org}{Optimal Nano-Hexapod Geometry}
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\end{itemize}
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\chapter{The Cubic Architecture}
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\label{sec:detail_kinematics_cubic}
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Cubic configuration \url{file:///home/thomas/Cloud/work-projects/ID31-NASS/matlab/stewart-simscape/org/cubic-configuration.org}
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\section{The Cubic Architecture}
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From \cite{geng94_six_degree_of_freed_activ}, 7 properties of cubic configuration:
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\begin{enumerate}
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\item Uniformity in control capability in all directions
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\item Uniformity in stiffness in all directions
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\item Minimum cross coupling force effect among actuators
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\item Facilitate collocated sensor-actuator control system design
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\item Simple kinematics relationships
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\item Simple dynamic analysis
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\item Simple mechanical design
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\end{enumerate}
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\begin{itemize}
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\item Principle
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\item Examples of Stewart platform with Cubic architecture
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\item Different options?
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Center of the cube above the top platform?
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Where to mention that ? With examples
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\end{itemize}
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\section{Static Properties}
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Explain that we get diagonal K matrix => static decoupling in the cartesian frame.
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Uniform mobility in X,Y,Z directions
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\section{Dynamical Properties?}
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\cite{mcinroy00_desig_contr_flexur_joint_hexap}
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\cite{afzali-far16_vibrat_dynam_isotr_hexap_analy_studies}:
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\begin{itemize}
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\item proposes an architecture where the CoM can be above the top platform
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\item ``\textbf{Dynamic isotropy}, leading to equal eigenfrequencies, is a powerful optimization measure.''
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\end{itemize}
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\begin{itemize}
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\item Show examples where the dynamics can indeed be decoupled in the cartesian frame (i.e. decoupled K and M matrices)
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\item Better decoupling between the struts? not sure\ldots{}
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Compute the coupling between the struts for a cubic and non-cubic architecture
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\item Same resonance frequencies for suspension modes?
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Maybe in one case: sphere at the CoM?
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Could be nice to show that.
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Say that this can be nice for optimal damping for instance (link to paper explaining that)
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\end{itemize}
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\chapter{Conclusion}
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\label{sec:detail_kinematics_conclusion}
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Inertia used for experiments will be very broad => difficult to optimize the dynamics
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Specific geometry is not found to have a huge impact on performances.
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Practical implementation is important.
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Geometry impacts the static and dynamical characteristics of the Stewart platform.
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Considering the design constrains, the slight change of geometry will not significantly impact the obtained results.
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\printbibliography[heading=bibintoc,title={Bibliography}]
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\end{document}
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