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\input{preamble.tex}
\input{preamble_extra.tex}
\bibliography{nass-geometry.bib}
\author{Dehaeze Thomas}
\date{\today}
\title{Nano Hexapod - Optimal Geometry}
\hypersetup{
 pdfauthor={Dehaeze Thomas},
 pdftitle={Nano Hexapod - Optimal Geometry},
 pdfkeywords={},
 pdfsubject={},
 pdfcreator={Emacs 29.4 (Org mode 9.6)}, 
 pdflang={English}}
\usepackage{biblatex}

\begin{document}

\maketitle
\tableofcontents

\clearpage

\begin{itemize}
\item In the conceptual design phase, the geometry of the Stewart platform was not optimized
\item In the detail design phase, we want to see if the geometry can be optimized to improve the overall performances
\item Optimization criteria: mobility, stiffness, dynamical decoupling, more performance / bandwidth
\end{itemize}

Outline:
\begin{itemize}
\item Review of Stewart platform: Section \ref{sec:detail_kinematics_stewart_review}
Geometry, Actuators, Sensors, Joints
\item Effect of geometry on the Stewart platform characteristics \ref{sec:detail_kinematics_geometry}
\item Cubic configuration: benefits? \ref{sec:detail_kinematics_cubic}
\end{itemize}

\chapter{Review of Stewart platforms}
\label{sec:detail_kinematics_stewart_review}
\begin{itemize}
\item as was explained in the conceptual phase, Stewart platform have the following key elements:
\begin{itemize}
\item two plates
\item flexible joints
\item actuators
\item sensors
\end{itemize}
\item the geometry
\item This results in various designs as shown in Table \ref{tab:detail_kinematics_stewart_review}
\item The focus is here made on Stewart platforms for nano-positioning of vibration control.
Not on long stroke stewart platforms.
\item All presented Stewart platforms are using flexible joints, as it is a prerequisites for nano-positioning capabilities.
\item Most of stewart platforms are using voice coil actuators or piezoelectric actuators.
The actuators used for the Stewart platform will be chosen in the next section.
\item Depending on the application, various sensors are integrated in the struts or on the plates.
The choice of sensor for the nano-hexapod will be described in the next section.

\item[{$\square$}] Only keep integrated sensor and not external metrology
\item[{$\square$}] Check for missing information
\end{itemize}

\begin{figure}[htbp]
\begin{subfigure}{0.48\textwidth}
\begin{center}
\includegraphics[scale=1,width=0.95\linewidth]{figs/detail_kinematics_jpl.jpg}
\end{center}
\subcaption{\label{fig:detail_kinematics_jpl}California Institute of Technology - USA}
\end{subfigure}
\begin{subfigure}{0.48\textwidth}
\begin{center}
\includegraphics[scale=1,width=0.95\linewidth]{figs/detail_kinematics_uw_gsp.jpg}
\end{center}
\subcaption{\label{fig:detail_kinematics_uw_gsp}University of Wyoming - USA}
\end{subfigure}

\bigskip
\begin{subfigure}{0.53\textwidth}
\begin{center}
\includegraphics[scale=1,width=0.95\linewidth]{figs/detail_kinematics_ulb_pz.jpg}
\end{center}
\subcaption{\label{fig:detail_kinematics_ulb_pz}ULB - Belgium}
\end{subfigure}
\begin{subfigure}{0.43\textwidth}
\begin{center}
\includegraphics[scale=1,width=0.95\linewidth]{figs/detail_kinematics_uqp.jpg}
\end{center}
\subcaption{\label{fig:detail_kinematics_uqp}Naval Postgraduate School - USA}
\end{subfigure}
\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})}
\end{figure}

\begin{figure}[htbp]
\begin{subfigure}{0.48\textwidth}
\begin{center}
\includegraphics[scale=1,height=5cm]{figs/detail_kinematics_pph.jpg}
\end{center}
\subcaption{\label{fig:detail_kinematics_pph}Naval Postgraduate School - USA}
\end{subfigure}
\begin{subfigure}{0.48\textwidth}
\begin{center}
\includegraphics[scale=1,height=5cm]{figs/detail_kinematics_zhang11.jpg}
\end{center}
\subcaption{\label{fig:detail_kinematics_zhang11}Beihang University - China}
\end{subfigure}

\bigskip
\begin{subfigure}{0.43\textwidth}
\begin{center}
\includegraphics[scale=1,height=5cm]{figs/detail_kinematics_yang19.jpg}
\end{center}
\subcaption{\label{fig:detail_kinematics_yang19}Nanjing University - China}
\end{subfigure}
\begin{subfigure}{0.53\textwidth}
\begin{center}
\includegraphics[scale=1,height=5cm]{figs/detail_kinematics_naves.jpg}
\end{center}
\subcaption{\label{fig:detail_kinematics_naves}University of Twente - Netherlands}
\end{subfigure}
\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})}
\end{figure}

\begin{table}[htbp]
\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''}
\centering
\scriptsize
\begin{tabularx}{\linewidth}{llllX}
\toprule
 & \textbf{Geometry} & \textbf{Actuators} & \textbf{Sensors} & \textbf{Reference}\\
\midrule
 & 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}\\
Figure \ref{fig:detail_kinematics_jpl} & Cubic & Voice Coil (0.5 mm) & Force (collocated) & \cite{spanos95_soft_activ_vibrat_isolat,rahman98_multiax}\\
 & Cubic & Voice Coil (10 mm) & Force, LVDT, Geophones & \cite{thayer98_stewar,thayer02_six_axis_vibrat_isolat_system,hauge04_sensor_contr_space_based_six}\\
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}\\
 & Cubic & Piezoelectric (\(25\,\mu m\)) & Piezo force sensors & \cite{defendini00_techn}\\
Figure \ref{fig:detail_kinematics_ulb_pz} & Cubic & APA  (\(50\,\mu m\)) & Force sensor & \cite{abu02_stiff_soft_stewar_platf_activ}\\
Figure \ref{fig:detail_kinematics_pph} & Non-Cubic & Voice Coil & Accelerometers & \cite{chen03_payload_point_activ_vibrat_isolat}\\
 & Cubic & Voice Coil & Force & \cite{hanieh03_activ_stewar,preumont07_six_axis_singl_stage_activ}\\
Figure \ref{fig:detail_kinematics_uqp} & Cubic & Piezoelectric (\(50\,\mu m\)) & Geophone aligned with the strut & \cite{agrawal04_algor_activ_vibrat_isolat_spacec}\\
 & Non-Cubic & Piezoelectric (\(16\,\mu m\)) & Eddy Current & \cite{furutani04_nanom_cuttin_machin_using_stewar}\\
 & Cubic & Piezoelectric (\(120\,\mu m\)) & External capacitive & \cite{ting06_desig_stewar_nanos_platf,ting13_compos_contr_desig_stewar_nanos_platf}\\
 & Non-Cubic & Piezoelectric (\(160\,\mu m\)) & External capacitive (LION) & \cite{ting07_measur_calib_stewar_microm_system}\\
Figure \ref{fig:detail_kinematics_zhang11} & Non-cubic & Magnetostrictive & Inertial & \cite{zhang11_six_dof}\\
 & 6-SPS (Optimized) & Piezoelectric & Strain Gauge & \cite{du14_piezo_actuat_high_precis_flexib}\\
 & 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}\\
 & Cubic & Piezoelectric & Force Sensor + Accelerometer & \cite{wang16_inves_activ_vibrat_isolat_stewar}\\
 & Almost cubic & Voice Coil & Force Sensor + Accelerometer & \cite{beijen18_self_tunin_mimo_distur_feedf,tjepkema12_activ_ph}\\
Figure \ref{fig:detail_kinematics_yang19} & 6-UPS (Cubic?) & Piezoelectric & Force, Position & \cite{yang19_dynam_model_decoup_contr_flexib}\\
Figure \ref{fig:detail_kinematics_naves} & Non-Cubic & 3-phase rotary motor & Rotary Encoders & \cite{naves20_desig,naves20_t_flex}\\
\bottomrule
\end{tabularx}
\end{table}

\begin{itemize}
\item[{$\square$}] \url{https://research.tdehaeze.xyz/stewart-simscape/docs/bibliography.html}
\item[{$\square$}] Joints and actuators are optimized in the next section
\end{itemize}

\chapter{Effect of geometry on Stewart platform properties}
\label{sec:detail_kinematics_geometry}
\begin{itemize}
\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)
\item Important: bi (join position w.r.t top platform) and si (orientation of struts)
\end{itemize}

For the nano-hexapod:
\begin{itemize}
\item Size requirements: Maximum height, maximum radius
\end{itemize}
\section{Stiffness}

\begin{itemize}
\item Give some examples:
\begin{itemize}
\item struts further apart: higher angular stiffness, same linear stiffness
\item orientation: more vertical => increase vertical stiffness, decrease horizontal stiffness
\end{itemize}
\end{itemize}

\section{Mobility and required joint and actuator stroke}

\begin{itemize}
\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)

\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}
Will be useful to choose the actuators
\item[{$\square$}] \href{file:///home/thomas/Cloud/work-projects/ID31-NASS/matlab/stewart-simscape/org/kinematic-study.org}{Estimation of the Joint required Stroke}
Will be useful to design the flexible joints
\end{itemize}

\section*{Conclusion}
\begin{itemize}
\item[{$\square$}] Table that summarize the findings
\href{file:///home/thomas/Cloud/work-projects/ID31-NASS/documents/state-of-thesis-2020/index.org}{Optimal Nano-Hexapod Geometry}
\end{itemize}

\chapter{The Cubic Architecture}
\label{sec:detail_kinematics_cubic}
Cubic configuration \url{file:///home/thomas/Cloud/work-projects/ID31-NASS/matlab/stewart-simscape/org/cubic-configuration.org}
\section{The Cubic Architecture}

From \cite{geng94_six_degree_of_freed_activ}, 7 properties of cubic configuration:
\begin{enumerate}
\item Uniformity in control capability in all directions
\item Uniformity in stiffness in all directions
\item Minimum cross coupling force effect among actuators
\item Facilitate collocated sensor-actuator control system design
\item Simple kinematics relationships
\item Simple dynamic analysis
\item Simple mechanical design
\end{enumerate}



\begin{itemize}
\item Principle
\item Examples of Stewart platform with Cubic architecture
\item Different options?
Center of the cube above the top platform?
Where to mention that ? With examples
\end{itemize}



\section{Static Properties}

Explain that we get diagonal K matrix => static decoupling in the cartesian frame.
Uniform mobility in X,Y,Z directions

\section{Dynamical Properties?}

\cite{mcinroy00_desig_contr_flexur_joint_hexap}

\cite{afzali-far16_vibrat_dynam_isotr_hexap_analy_studies}:
\begin{itemize}
\item proposes an architecture where the CoM can be above the top platform
\item ``\textbf{Dynamic isotropy}, leading to equal eigenfrequencies, is a powerful optimization measure.''
\end{itemize}



\begin{itemize}
\item Show examples where the dynamics can indeed be decoupled in the cartesian frame (i.e. decoupled K and M matrices)
\item Better decoupling between the struts? not sure\ldots{}
Compute the coupling between the struts for a cubic and non-cubic architecture
\item Same resonance frequencies for suspension modes?
Maybe in one case: sphere at the CoM?
Could be nice to show that.
Say that this can be nice for optimal damping for instance (link to paper explaining that)
\end{itemize}

\chapter{Conclusion}
\label{sec:detail_kinematics_conclusion}

Inertia used for experiments will be very broad => difficult to optimize the dynamics
Specific geometry is not found to have a huge impact on performances.
Practical implementation is important.

Geometry impacts the static and dynamical characteristics of the Stewart platform.
Considering the design constrains, the slight change of geometry will not significantly impact the obtained results.

\printbibliography[heading=bibintoc,title={Bibliography}]
\end{document}
