Tikz Figures
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1 X-Y Rotating Positioning Platform
\begin{tikzpicture} % Angle \def\thetau{25} % Rotational Stage \draw[fill=black!60!white] (0, 0) circle (4.3); \draw[fill=black!40!white] (0, 0) circle (3.8); % Label \node[anchor=north west, rotate=\thetau] at (-2.5, 2.5) {\small Rotating Stage}; % Rotating Scope \begin{scope}[rotate=\thetau] % Rotating Frame \draw[fill=black!20!white] (-2.6, -2.6) rectangle (2.6, 2.6); % Label \node[anchor=north west, rotate=\thetau] at (-2.6, 2.6) {\small X-Y Stage}; % Mass \draw[fill=white] (-1, -1) rectangle (1, 1); % Label \node[anchor=south west, rotate=\thetau] at (-1, -1) {\small Payload}; % Attached Points \node[] at (-1, 0){$\bullet$}; \draw[] (-1, 0) -- ++(-0.2, 0) coordinate(cu); \draw[] ($(cu) + (0, -0.8)$) coordinate(actu) -- ($(cu) + (0, 0.8)$) coordinate(ku); \node[] at (0, -1){$\bullet$}; \draw[] (0, -1) -- ++(0, -0.2) coordinate(cv); \draw[] ($(cv) + (-0.8, 0)$)coordinate(kv) -- ($(cv) + (0.8, 0)$) coordinate(actv); % Spring and Actuator for U \draw[actuator={0.6}{0.2}] (actu) -- node[above=0.1, rotate=\thetau]{$F_u$} (actu-|-2.6,0); \draw[spring=0.2] (ku) -- node[above=0.1, rotate=\thetau]{$k$} (ku-|-2.6,0); \draw[damper={8}{8}] (cu) -- node[above left=0.2 and -0.1, rotate=\thetau]{$c$} (cu-|-2.6,0); \draw[actuator={0.6}{0.2}] (actv) -- node[left, rotate=\thetau]{$F_v$} (actv|-0,-2.6); \draw[spring=0.2] (kv) -- node[left, rotate=\thetau]{$k$} (kv|-0,-2.6); \draw[damper={8}{8}] (cv) -- node[left=0.1, rotate=\thetau]{$c$} (cv|-0,-2.6); % % Displacement measurement % \draw[<->, dashed] (-2.6, -0.8) --node[midway, below, rotate=\thetau]{$d_u$} (-1 , -0.8); % \draw[<->, dashed] ( 0.8, -2.6) --node[midway, right, rotate=\thetau]{$d_v$} ( 0.8, -1); \end{scope} % Inertial Frame \draw[->] (-4, -4) -- ++(2, 0) node[below]{$\vec{i}_x$}; \draw[->] (-4, -4) -- ++(0, 2) node[left]{$\vec{i}_y$}; \draw[fill, color=black] (-4, -4) circle (0.06); \node[draw, circle, inner sep=0pt, minimum size=0.3cm, label=left:$\vec{i}_z$] at (-4, -4){}; \draw[->] (0, 0) -- ++(\thetau:2) node[above, rotate=\thetau]{$\vec{i}_u$}; \draw[->] (0, 0) -- ++(\thetau+90:2) node[left, rotate=\thetau]{$\vec{i}_v$}; \draw[dashed] (0, 0) -- ++(2, 0); \draw[] (1.5, 0) arc (0:\thetau:1.5) node[midway, right]{$\theta$}; \node[] at (0,0) {$\bullet$}; \node[left] at (0,0) {$(x, y)$}; \draw[->] (3.5, 0) arc (0:40:3.5) node[midway, left]{$\Omega$}; \end{tikzpicture}
2 X-Y Rotating Positioning Platform with Force Sensors
\begin{tikzpicture} % Angle \def\thetau{25} % Rotational Stage \draw[fill=black!60!white] (0, 0) circle (4.3); \draw[fill=black!40!white] (0, 0) circle (3.8); % Label \node[anchor=north west, rotate=\thetau] at (-2.5, 2.5) {\small Rotating Stage}; % Rotating Scope \begin{scope}[rotate=\thetau] % Rotating Frame \draw[fill=black!20!white] (-2.6, -2.6) rectangle (2.6, 2.6); % Label \node[anchor=north west, rotate=\thetau] at (-2.6, 2.6) {\small X-Y Stage}; % Mass \draw[fill=white] (-1, -1) rectangle (1, 1); % Label \node[anchor=south west, rotate=\thetau] at (-1, -1) {\small Payload}; % Attached Points \node[] at (-1, 0){$\bullet$}; \draw[] (-1, 0) -- ++(-0.2, 0) coordinate(au); \node[] at (0, -1){$\bullet$}; \draw[] (0, -1) -- ++(0, -0.2) coordinate(av); % Force Sensors \draw[fill=white] ($(au) + (-0.2, -0.5)$) rectangle ($(au) + (0, 0.5)$); \draw[] ($(au) + (-0.2, -0.5)$)coordinate(actu) -- ($(au) + (0, 0.5)$); \draw[] ($(au) + (-0.2, 0.5)$)coordinate(ku) node[above=0.1, rotate=\thetau]{$f_{u}$} -- ($(au) + (0, -0.5)$); \draw[fill=white] ($(av) + (-0.5, -0.2)$) rectangle ($(av) + (0.5, 0)$); \draw[] ($(av) + ( 0.5, -0.2)$)coordinate(actv) -- ($(av) + (-0.5, 0)$); \draw[] ($(av) + (-0.5, -0.2)$)coordinate(kv) node[left=0.1, rotate=\thetau]{$f_{v}$} -- ($(av) + ( 0.5, 0)$); % Spring and Actuator for U \draw[actuator={0.6}{0.2}] (actu) -- node[above=0.1, rotate=\thetau]{$F_u$} (actu-|-2.6,0); \draw[spring=0.2] (ku) -- node[above=0.1, rotate=\thetau]{$k$} (ku-|-2.6,0); \draw[actuator={0.6}{0.2}] (actv) -- node[left, rotate=\thetau]{$F_v$} (actv|-0,-2.6); \draw[spring=0.2] (kv) -- node[left, rotate=\thetau]{$k$} (kv|-0,-2.6); \end{scope} % Inertial Frame \draw[->] (-4, -4) -- ++(2, 0) node[below]{$\vec{i}_x$}; \draw[->] (-4, -4) -- ++(0, 2) node[left]{$\vec{i}_y$}; \draw[fill, color=black] (-4, -4) circle (0.06); \node[draw, circle, inner sep=0pt, minimum size=0.3cm, label=left:$\vec{i}_z$] at (-4, -4){}; \draw[->] (0, 0) -- ++(\thetau:2) node[above, rotate=\thetau]{$\vec{i}_u$}; \draw[->] (0, 0) -- ++(\thetau+90:2) node[left, rotate=\thetau]{$\vec{i}_v$}; \draw[dashed] (0, 0) -- ++(2, 0); \draw[] (1.5, 0) arc (0:\thetau:1.5) node[midway, right]{$\theta$}; \node[] at (0,0) {$\bullet$}; \node[left] at (0,0) {$(x, y)$}; \draw[->] (3.5, 0) arc (0:40:3.5) node[midway, left]{$\Omega$}; \end{tikzpicture}
3 Decentralized Integral Force Feedback
\begin{tikzpicture} % Angle \def\thetau{25} % Rotational Stage \draw[fill=black!60!white] (0, 0) circle (4.3); \draw[fill=black!40!white] (0, 0) circle (3.8); % Label \node[anchor=north west, rotate=\thetau] at (-2.5, 2.5) {\small Rotating Stage}; % Rotating Scope \begin{scope}[rotate=\thetau] % Rotating Frame \draw[fill=black!20!white] (-2.6, -2.6) rectangle (2.6, 2.6); % Label \node[anchor=north west, rotate=\thetau] at (-2.6, 2.6) {\small X-Y Stage}; % Mass \draw[fill=white] (-1, -1) rectangle (1, 1); % Label \node[anchor=south west, rotate=\thetau] at (-1, -1) {\small Payload}; % Attached Points \node[] at (-1, 0){$\bullet$}; \draw[] (-1, 0) -- ++(-0.2, 0) coordinate(au); \node[] at (0, -1){$\bullet$}; \draw[] (0, -1) -- ++(0, -0.2) coordinate(av); % Force Sensors \draw[fill=white] ($(au) + (-0.2, -0.5)$) rectangle ($(au) + (0, 0.5)$); \draw[] ($(au) + (-0.2, -0.5)$)coordinate(actu) -- ($(au) + (0, 0.5)$); \draw[] ($(au) + (-0.2, 0.5)$)coordinate(ku) node[above=0.1, rotate=\thetau]{$f_{u}$} -- ($(au) + (0, -0.5)$); \node[above, rotate=\thetau] at ($(av) + (-0.1, 0.5)$) {$f_{u}$}; \draw[fill=white] ($(av) + (-0.5, -0.2)$) rectangle ($(av) + (0.5, 0)$); \draw[] ($(av) + ( 0.5, -0.2)$)coordinate(actv) -- ($(av) + (-0.5, 0)$); \draw[] ($(av) + (-0.5, -0.2)$)coordinate(kv) -- ($(av) + ( 0.5, 0)$); \node[left, rotate=\thetau] at ($(av) + (-0.5, -0.1)$) {$f_{v}$}; % Spring and Actuator for U \draw[actuator={0.6}{0.2}] (actu) -- coordinate[midway](actumid) (actu-|-2.6,0); \draw[spring=0.2] (ku) -- node[above=0.1, rotate=\thetau]{$k$} (ku-|-2.6,0); % \draw[actuator={0.6}{0.2}] (actv) -- node[right, rotate=\thetau]{$F_v$} (actv|-0,-2.6); \draw[actuator={0.6}{0.2}] (actv) -- coordinate[midway](actvmid) (actv|-0,-2.6); \draw[spring=0.2] (kv) -- node[left, rotate=\thetau]{$k$} (kv|-0,-2.6); \node[block={0.8cm}{0.6cm}, rotate=\thetau] (Ku) at ($(actumid) + (0, -1.2)$) {$K_{F}$}; \draw[->] ($(au) + (-0.1, -0.5)$) |- (Ku.east); \draw[->] (Ku.north) -- ($(actumid) + (0, -0.1)$) node[below left, rotate=\thetau]{$F_u$}; \node[block={0.8cm}{0.6cm}, rotate=\thetau] (Kv) at ($(actvmid) + (1.2, 0)$) {$K_{F}$}; \draw[->] ($(av) + (0.5, -0.1)$) -| (Kv.north); \draw[->] (Kv.west) -- ($(actvmid) + (0.1, 0)$) node[below right, rotate=\thetau]{$F_v$}; \end{scope} % Inertial Frame \draw[->] (-4, -4) -- ++(2, 0) node[below]{$\vec{i}_x$}; \draw[->] (-4, -4) -- ++(0, 2) node[left]{$\vec{i}_y$}; \draw[fill, color=black] (-4, -4) circle (0.06); \node[draw, circle, inner sep=0pt, minimum size=0.3cm, label=left:$\vec{i}_z$] at (-4, -4){}; \draw[->] (0, 0) -- ++(\thetau:2) node[above, rotate=\thetau]{$\vec{i}_u$}; \draw[->] (0, 0) -- ++(\thetau+90:2) node[left, rotate=\thetau]{$\vec{i}_v$}; \draw[dashed] (0, 0) -- ++(2, 0); \draw[] (1.5, 0) arc (0:\thetau:1.5) node[midway, right]{$\theta$}; \node[] at (0,0) {$\bullet$}; \node[left] at (0,0) {$(x, y)$}; \draw[->] (3.5, 0) arc (0:40:3.5) node[midway, left]{$\Omega$}; \end{tikzpicture}
4 Decentralized Direct Velocity Feedback
\begin{tikzpicture} % Angle \def\thetau{25} % Rotational Stage \draw[fill=black!60!white] (0, 0) circle (4.3); \draw[fill=black!40!white] (0, 0) circle (3.8); % Label \node[anchor=north west, rotate=\thetau] at (-2.5, 2.5) {\small Rotating Stage}; % Rotating Scope \begin{scope}[rotate=\thetau] % Rotating Frame \draw[fill=black!20!white] (-2.6, -2.6) rectangle (2.6, 2.6); % Label \node[anchor=north west, rotate=\thetau] at (-2.6, 2.6) {\small X-Y Stage}; % Mass \draw[fill=white] (-1, -1) rectangle (1, 1); % Label \node[anchor=south west, rotate=\thetau] at (-1, -1) {\small Payload}; % Attached Points \node[] at (-1, 0){$\bullet$}; \draw[] (-1, 0) -- ++(-0.2, 0) coordinate(au); \node[] at (0, -1){$\bullet$}; \draw[] (0, -1) -- ++(0, -0.2) coordinate(av); % Attached Points \node[] at (-1, 0){$\bullet$}; \draw[] (-1, 0) -- ++(-0.2, 0) coordinate(cu); \draw[] ($(cu) + (0, -0.5)$) coordinate(actu) -- ($(cu) + (0, 0.5)$) coordinate(ku); \node[] at (0, -1){$\bullet$}; \draw[] (0, -1) -- ++(0, -0.2) coordinate(cv); \draw[] ($(cv) + (-0.5, 0)$)coordinate(kv) -- ($(cv) + (0.5, 0)$) coordinate(actv); % Spring and Actuator for U \draw[actuator={0.6}{0.2}] (actu) -- coordinate[midway](actumid) (actu-|-2.6,0); \draw[spring=0.2] (ku) -- node[above=0.1, rotate=\thetau]{$k$} (ku-|-2.6,0); \draw[actuator={0.6}{0.2}] (actv) -- coordinate[midway](actvmid) (actv|-0,-2.6); \draw[spring=0.2] (kv) -- node[left, rotate=\thetau]{$k$} (kv|-0,-2.6); % Displacement measurement \draw[<->, dashed] (-2.6, -0.8) -- (-1 , -0.8) coordinate(dutop); \draw[<->, dashed] ( 0.8, -2.6) -- ( 0.8, -1) coordinate(dvtop); % Controllers \node[block={0.6cm}{0.6cm}, rotate=\thetau] (Ku) at ($(actumid) + (0, -1.2)$) {$K_{V}$}; \draw[->] ($(dutop) + (-0.1, 0)$) node[below left, rotate=\thetau]{$v_u$} |- (Ku.east); \draw[->] (Ku.north) -- ($(actumid) + (0, -0.1)$); \node[block={0.6cm}{0.6cm}, rotate=\thetau] (Kv) at ($(actvmid) + (1.2, 0)$) {$K_{V}$}; \draw[->] ($(dvtop) + (0, -0.1)$) node[below right, rotate=\thetau]{$v_v$} -| (Kv.north); \draw[->] (Kv.west) -- ($(actvmid) + (0.1, 0)$); \node[above=0.1, rotate=\thetau] at (actumid) {$F_u$}; \node[left=0.1, rotate=\thetau] at (actvmid) {$F_v$}; \end{scope} % Inertial Frame \draw[->] (-4, -4) -- ++(2, 0) node[below]{$\vec{i}_x$}; \draw[->] (-4, -4) -- ++(0, 2) node[left]{$\vec{i}_y$}; \draw[fill, color=black] (-4, -4) circle (0.06); \node[draw, circle, inner sep=0pt, minimum size=0.3cm, label=left:$\vec{i}_z$] at (-4, -4){}; \draw[->] (0, 0) -- ++(\thetau:2) node[above, rotate=\thetau]{$\vec{i}_u$}; \draw[->] (0, 0) -- ++(\thetau+90:2) node[left, rotate=\thetau]{$\vec{i}_v$}; \draw[dashed] (0, 0) -- ++(2, 0); \draw[] (1.5, 0) arc (0:\thetau:1.5) node[midway, right]{$\theta$}; \node[] at (0,0) {$\bullet$}; \node[left] at (0,0) {$(x, y)$}; \draw[->] (3.5, 0) arc (0:40:3.5) node[midway, left]{$\Omega$}; \end{tikzpicture}
5 Springs in parallel
\begin{tikzpicture} % Angle \def\thetau{25} % Rotational Stage \draw[fill=black!60!white] (0, 0) circle (4.3); \draw[fill=black!40!white] (0, 0) circle (3.8); % Label \node[anchor=north west, rotate=\thetau] at (-2.5, 2.5) {\small Rotating Stage}; % Rotating Scope \begin{scope}[rotate=\thetau] % Rotating Frame \draw[fill=black!20!white] (-2.6, -2.6) rectangle (2.6, 2.6); % Label \node[anchor=north west, rotate=\thetau] at (-2.6, 2.6) {\small X-Y Stage}; % Mass \draw[fill=white] (-1, -1) rectangle (1, 1); % Label \node[anchor=south west, rotate=\thetau] at (-1, -1) {\small Payload}; % Attached Points \draw[] (-1, 0) -- ++(-0.2, 0) coordinate(au); \draw[] (0, -1) -- ++(0, -0.2) coordinate(av); % Force Sensors \draw[fill=white] ($(au) + (-0.2, -0.5)$) rectangle ($(au) + (0, 0.5)$); \draw[] ($(au) + (-0.2, -0.5)$)coordinate(actu) -- ($(au) + (0, 0.5)$); \draw[] ($(au) + (-0.2, 0.5)$)coordinate(ku) -- ($(au) + (0, -0.5)$); \node[below=0.1, rotate=\thetau] at ($(au) + (-0.1, -0.5)$) {$f_{u}$} \draw[fill=white] ($(av) + (-0.5, -0.2)$) rectangle ($(av) + (0.5, 0)$); \draw[] ($(av) + ( 0.5, -0.2)$)coordinate(actv) -- ($(av) + (-0.5, 0)$); \draw[] ($(av) + (-0.5, -0.2)$)coordinate(kv) -- ($(av) + ( 0.5, 0)$) ; \node[right=0.1, rotate=\thetau] at ($(av) + (0.5, -0.1)$) {$f_{v}$} % Spring and Actuator for U \draw[actuator={0.6}{0.2}] (actu) -- node[below=0.1, rotate=\thetau]{$F_u$} (actu-|-2.6,0); \draw[spring=0.2] (ku) -- node[below=0.1, rotate=\thetau]{$k$} (ku-|-2.6,0); \draw[spring=0.2] (-1, 0.8) -- node[above=0.1, rotate=\thetau]{$k_{p}$} (-1, 0.8-|-2.6,0); \draw[actuator={0.6}{0.2}] (actv) -- node[right=0.1, rotate=\thetau]{$F_v$} (actv|-0,-2.6); \draw[spring=0.2] (kv) -- node[right=0.1, rotate=\thetau]{$k$} (kv|-0,-2.6); \draw[spring=0.2] (-0.8, -1) -- node[left=0.1, rotate=\thetau]{$k_{p}$} (-0.8, -1|-0,-2.6); \end{scope} % Inertial Frame \draw[->] (-4, -4) -- ++(2, 0) node[below]{$\vec{i}_x$}; \draw[->] (-4, -4) -- ++(0, 2) node[left]{$\vec{i}_y$}; \draw[fill, color=black] (-4, -4) circle (0.06); \node[draw, circle, inner sep=0pt, minimum size=0.3cm, label=left:$\vec{i}_z$] at (-4, -4){}; \draw[->] (0, 0) -- ++(\thetau:2) node[above, rotate=\thetau]{$\vec{i}_u$}; \draw[->] (0, 0) -- ++(\thetau+90:2) node[left, rotate=\thetau]{$\vec{i}_v$}; \draw[dashed] (0, 0) -- ++(2, 0); \draw[] (1.5, 0) arc (0:\thetau:1.5) node[midway, right]{$\theta$}; \node[] at (0,0) {$\bullet$}; \node[left] at (0,0) {$(x, y)$}; \draw[->] (3.5, 0) arc (0:40:3.5) node[midway, left]{$\Omega$}; \end{tikzpicture}