# How can make scope for rotating one disc around an axis?

I have a rigid body formed by one disc (D) and one rod (T):

• I want to draw the rotation of the disc around the j_1 axis.

• I want the to make a scope for moving the disc on the stem and rotate it around the j_1 axis

If anyone can help me, here is my MWE:

\documentclass[border=0.5, tikz]{standalone}
\usepackage{tikz,tikz-3dplot}
\usepackage{ifthen}
\usetikzlibrary{patterns}%
\begin{document}
\foreach \var in {0,10,...,180}{
\pgfmathsetmacro{\iAngle}{90}% change this value in degrees to show how
the rod rotates around the z component
\tdplotsetmaincoords{70}{110}
\begin{tikzpicture}[scale=5,tdplot_main_coords]%A0
\useasboundingbox[tdplot_screen_coords] (-2.05,-1.2) rectangle
(2.5,1.5);
\coordinate (O) at (0,0,0);
\coordinate (x0) at (2,0,0);
\coordinate (y0) at (0,1.5,0);
\node[red, left] at (O) {$O$};
\draw[thick,->] (O) -- (x0) node[anchor=north]{$x_0$};
\draw[thick,->] (O) -- (y0) node[anchor=west]{$y_0$};
\draw[thick,->] (O) -- (0,0,1.5) node[anchor=south]{$z_0$};
\draw[thick,->] (O) -- (0.3,0,0) node[anchor=north, left]{$\vec i_0$};
\draw[thick,->] (O) -- (0,0.3,0) node[near end, below]{$\vec j_0$};
\draw[thick,->] (O) -- (0,0,0.3) node[anchor=south, right]{$\vec k_0$};
\draw[thick, opacity=0.3] (-2,-1.5,0) -- (2,-1.5,0) -- (2,1.5,0) --
(-2,1.5,0) -- cycle;
\fill[red,opacity=0.2] (-2,-1.5,0) -- (2,-1.5,0) -- (2,1.5,0) --
(-2,1.5,0) -- cycle;
\tdplotdrawarc[thick, color=red]{(2,-1.5,0)}{-0.3}{-90}{0}{anchor=180}
{plan $P$}%
\tdplotdrawarc[thick, color=red, ->]{(O)}{0.5}{0}{\iAngle}{anchor=180,
below}{$\omega\cdot t$}%
\tdplotdrawarc[thick,dotted, color=violet, ->]{(O)}{0.55}{90}
{90+\iAngle}{anchor=180,above}{$\omega\cdot t$}
\tdplotdrawarc[thick, color=purple, dashed]{(O)}{1}{0}{360}
{anchor=180}{}

\tdplotsetrotatedcoords{\iAngle}{0}{0}
\begin{scope}[tdplot_rotated_coords]%A1
\coordinate (x1) at (2,0,0);
\coordinate (y1) at (0,1.5,0);
\draw[thick, dashed, opacity=1, ->] (O) -- (x1)node[above] {$x_1$};
\draw[thick, dashed, opacity=1, ->] (O) -- (y1)node[above] {$y_1$};
\draw[thick,->] (O) -- (0.3,0,0) node[anchor=north, above left]{$\vec i_1$};
\draw[thick,->] (O) -- (0,0.3,0) node[near end, above]{$\vec j_1$};
\draw[ultra thick, color=orange, opacity=1] (O) -- (1,0,0)node[near end, below left] {$(T)$};
\coordinate[label=below right:$A1$] (A1) at (1,0,0.3);
\fill[blue,thick] (A1) circle (0.3pt);
\coordinate[label=above:$I_1$] (I1) at (1,0,0);
\fill[blue,thick] (I1) circle (0.3pt);
\end{scope}
\tdplotsetrotatedcoords{\var}{90}{0}
\begin{scope}[tdplot_rotated_coords]%A3
\node[above=1.52cm, left] at (A1){$(D)$};

\ifthenelse{\var=180 \OR \var=0}{\draw[pattern=north west lines,
pattern color=blue, opacity=0.5 ] (A1) circle (0.3);}
{\draw[pattern=bricks, pattern color=green, opacity=0.5 ] (A1) circle
(0.3);}
\ifthenelse{\var=180 \OR \var=0}{\node[above=5.2cm, left=0.5cm] at
(A1){\textbf{\textcolor{green}{in this disposition we can look the
disk $(D)$ roll on the rod}}};}{\node[above=5.2cm, left=0.5cm] at (A1)
{\textbf{\textcolor{black}{I search the disposition of the disk $(D)$
where I can visualize its rotation on the rod around the $j_1$
component}}};}
\end{scope}

%%%%% I want to add this scope to show how the disk rolling on the rod
(T), can you complete this part%%%

\tdplotsetrotatedcoords{\var}{90}{0}
\begin{scope}[tdplot_rotated_coords]%A3
\draw[-latex,blue] (A1) -- ++(-0.7,0,0)node[right]{$\vec k_1\equiv \vec k_0$}; %<-
\draw[-latex,blue] (A1) -- ++(0,0,0.7)node[below]{$\vec i_1$};  %<-
\end{scope}

\tdplotsetrotatedcoords{\var}{45}{0} %90-45 angle
\begin{scope}[tdplot_rotated_coords]
\draw[-latex,blue] (A1) -- ++(-0.7,0,0)node[right]{$\vec k_2$}; %<-
\draw[-latex,blue] (A1) -- ++(0,0,0.7)node[below]{$\vec i_2$};  %<-

% Also, I want to show how the disk rotates around the $\vec j_1$ axis by $\theta$ angle in the plan formed by the $z_0Ox_1$.
\end{scope}
\end{tikzpicture}}
\end{document}


Update: This is an animated version of this code: I want to add ($\vec i_1, \vec j_1, \vec k_1\equiv\vec k_0$) the coordinate system related to the disk, and the ($\vec i_2, \vec j_1, k_2$) the coordinate system related to its motion. If we compile this code we can look at page 12 of the .pdf and BOTH the coordinates systems are not in the plane of the disk. So, I want to add scope for those coordinates to show in the animated version of how the disk rolls on the rod illustrated in the figure with orange.

In order to complete this animation:

1. I want to add an iteration to show the backward motion of the disk on the rod

2. I don't have any idea how can I add the following commands: %\tdplotdrawarc[thick, color=blue,->]{(A1)}{0.5}{45}{90}{anchor=105, above, left}{$\theta$} % %\tdplotdrawarc[thick, color=red, ->]{(A1)}{0.5}{\iBngle}{180}{anchor=180, above}{$\theta$}%

3. As the rod coincides with the x1 axis, the reference systems attached to the disk $(\vec i_1, \vec k_0)$ should figure out the \vec k_0 parallel to the \overrightarrow{Oz_0} axis, and the \vec i_1 is parallel to the \overrightarrow{Ox_1} axis. The coordinate systems $(\vec i_2, \vec j_1, \vec k_2)$ showing how the disk moves backward and forward along the rod and it should coincide with the fixed axes Ox_1k_0 before the movement.

Here's my modification:

%%%%%%%%%%%  update  %%%%%%%%%%%%%%
\documentclass[border=5pt, tikz]{standalone}
\usepackage{tikz,tikz-3dplot}
\usepackage{animate}
\usepackage{ifthen}
\usetikzlibrary{patterns}%
\def\RodLength{1.65}
\begin{document}
\tdplotsetmaincoords{70}{110}
%\begin{animateinline}[loop, poster = first, controls=false]{24}
\foreach \iBngle in {0,2,...,100}{
%\multiframe{100}{iBngle=0+2}{
\pgfmathsetmacro{\iAngle}{140}%35
\tdplotsetmaincoords{70}{110}
\begin{tikzpicture}[scale=5,tdplot_main_coords]
\useasboundingbox[tdplot_screen_coords] (-2.05,-1.2) rectangle
(2.5,1.5);
\coordinate (O) at (0,0,0);
\node[red, left] at (O) {$O$};
\draw[thick,->] (O) -- (2,0,0) node[anchor=north]{$x_0$};
\draw[thick,->] (O) -- (0,1.5,0) node[anchor=west]{$y_0$};
\draw[thick,->] (O) -- (0,0,1.5) node[anchor=south]{$z_0$};
\draw[thick,->] (O) -- (0.3,0,0) node[anchor=north, left]{$\vec i_0$};
\draw[thick,->] (O) -- (0,0.3,0) node[near end, below]{$\vec j_0$};
\draw[thick,->] (O) -- (0,0,0.3) node[anchor=south, right]{$\vec k_0$};
\draw[thick, opacity=0.3] (-2,-1.5,0) -- (2,-1.5,0) -- (2,1.5,0) --(-2,1.5,0) -- cycle;
\fill[red,opacity=0.2](-2,-1.5,0) -- (2,-1.5,0) -- (2,1.5,0) --(-2,1.5,0) -- cycle;
\tdplotdrawarc[thick, color=red]{(2,-1.5,0)}{-0.3}{-90}{0}{anchor=180}
{$\pi/2$}% <-
\tdplotdrawarc[thick, color=red, ->]{(O)}{0.5}{0}{\iAngle+\iBngle}
{anchor=180, below}{$\omega\cdot t$}%
\tdplotdrawarc[thick,dotted, color=violet, ->]{(O)}{0.55}{90}
{90+\iAngle+\iBngle}{anchor=180,above}{$\omega\cdot t$}
\tdplotdrawarc[thick, color=purple, dashed]{(O)}
{\RodLength*\iBngle/180}{0}{360}{anchor=180}{} %%changed
\tdplotsetrotatedcoords{\iAngle+\iBngle}{00}{0}%%changed
\begin{scope}[tdplot_rotated_coords]
\draw[thick, dashed, opacity=1, ->] (0,0,0) -- (2.5,0,0)node[above]
{$x_1$};
\draw[thick, dashed, opacity=1, ->] (0,0,0) -- (0,2.5,0)node[above]
{$y_1$};
\draw[thick,->] (O) -- (0.3,0,0) node[anchor=north, above left]{$\vec i_1$};
\draw[thick,->] (O) -- (0,0.3,0) node[near end, above]{$\vec j_1$};
\end{scope}
\tdplotsetrotatedcoords{{\iAngle+\iBngle}}{00}{0} %<- changed that in
order to rotate the rod
\begin{scope}[tdplot_rotated_coords]
\draw[ultra thick, color=orange, opacity=1] (0,0,0) --
(\RodLength,0,0)node[near end, below left] {$(T)$};
\coordinate[label=below right:$C$] (A1) at
({\RodLength*\iBngle/180},0,0.3);
\fill[blue,thick] (A1) circle (0.3pt);
\coordinate[label=above:$I_1$] (I1) at
({\RodLength*\iBngle/180},0,0);%changed
\fill[blue,thick] (I1) circle (0.3pt);
\end{scope}
\tdplotsetrotatedcoords{{\iAngle+130}}{90}{0} %<-
\begin{scope}[tdplot_rotated_coords]
\draw[pattern=north west lines, pattern color=blue, opacity=0.5 ] (A1)
\node[] at (45:0.4cm){$D$};
\draw[-latex,blue] (A1) -- ++(0,0,0.7)node[below]{$k_1$};  %<-
\draw[-latex,blue] (A1) -- ++(0,0,0.7)node[below]{$i_1$};  %<-
\draw[-latex,blue] (A1) -- ++({-0.7*cos(\iBngle/\relRad+\iAngle)},0,{0.7*sin(\iBngle/\relRad+\iAngle)})node[right]{$i_2$}; %<-
\draw[-latex,blue] (A1) -- ++({-0.7*sin(\iBngle/\relRad)},0,{-0.7*cos(\iBngle/\relRad)})node[below]{$k_2$};  %<-
\end{scope}
\tdplotsetrotatedcoords{\iAngle}{90}{45}
\begin{scope}[tdplot_rotated_coords]
% \draw[-latex, violet] (A1) -- ++(-0.7,0,0)node[right]{$\vec k_2$};

%\draw[-latex, violet] (A1) -- ++(0,0.7,0)node[right]{$\vec j_2$};
%\pgfmathtruncatemacro{\iBngle}{135}
%\tdplotdrawarc[thick, color=blue,->]{(A1)}{0.5}{45}{90}{anchor=105, above, left}{$\theta$} %
%\tdplotdrawarc[thick, color=red, ->]{(A1)}{0.5}{\iBngle}{180}{anchor=180, above}{$\theta$}%
\end{scope}
\end{tikzpicture}
}
%\end{animateinline}
\end{document}

• Thanks for the update! I'll be happy to do that provided I understand what needs to be done. Unfortunately, that is not the case. So let me ask some very simple questions. 1. Should the rod move? If so, how? 2. Should the blue circle move? If yes, should it roll along the rod? Or should it roll along the dashed circle? Then: how is ($\vec i_1, \vec i_1, \vec k_0$) a coordinate system? Two vectors are identical. And what is k_2 in ($\vec i_2, \vec j_2, k_2$)? I could not see anything labeled $k_2$ in your second MWE, and your handwritten annotations in the first are unreadable (to me).
– user121799
Mar 12 '18 at 22:45
• thank you @marmot, for the first question: the rod rotate around the $\vec k_0$ axis by the velocity $\omega\cdot t$, the rod is related to $x_1$ axis, for the blue circle it rotate in the plan $z_0Ox_1$ without sliding, then it move along the rod from $O$ to the right extremity of the rod. the dashed circle show how the point $I$ of contact of two solids rotate, its radius varies from the zero to the length of stem, i update my code. Mar 13 '18 at 1:14
• my goal is to make an animated version showing the two motion Mar 13 '18 at 1:20
• I am so sorry, but I still do not quite understand what you want. I updated my answer below and now the rod is moving. Is that what you want? How should the circle move? Or should it move? (I couldn't figure out what  rotate in the plan $z_0Ox_1$ without sliding, then it move along the rod from $O$ to the right extremity of the rod means.) One suggestion is to use Google translate for your next instructions.
– user121799
Mar 13 '18 at 12:06
• OK, I added another iteration. Now the blue disk moves along the rod as it rotates. Most likely the frame attached to the disk does not yet what you want it to do, please let me know what it should do.
– user121799
Mar 13 '18 at 13:06

UPDATE: I am pretty sure that this is not yet what you want, but there seems to be a language barrier so we probably have to go in small steps. In this revision, the blue disk moves along the (orange) rod as it rotates.

\documentclass[border=5pt]{standalone}
\usepackage{tikz,tikz-3dplot}
\usepackage{animate}
\usepackage{ifthen}
\usetikzlibrary{patterns}%
\def\RodLength{1.65}
\begin{document}
\tdplotsetmaincoords{70}{110}
\begin{animateinline}[loop, poster = first, controls=false]{24}
\multiframe{30}{iBngle=0+6}{
\pgfmathsetmacro{\iAngle}{140}%35
\tdplotsetmaincoords{70}{110}
\begin{tikzpicture}[scale=5,tdplot_main_coords]
\useasboundingbox[tdplot_screen_coords] (-2.05,-1.2) rectangle (2.5,1.5);
\coordinate (O) at (0,0,0);
\node[red, left] at (O) {$O$};
\draw[thick,->] (O) -- (2,0,0) node[anchor=north]{$x_0$};
\draw[thick,->] (O) -- (0,1.5,0) node[anchor=west]{$y_0$};
\draw[thick,->] (O) -- (0,0,1.5) node[anchor=south]{$z_0$};
\draw[thick,->] (O) -- (0.3,0,0) node[anchor=north, left]{$\vec i_0$};
\draw[thick,->] (O) -- (0,0.3,0) node[near end, below]{$\vec j_0$};
\draw[thick,->] (O) -- (0,0,0.3) node[anchor=south, right]{$\vec k_0$};
\draw[thick, opacity=0.3] (-2,-1.5,0) -- (2,-1.5,0) -- (2,1.5,0) -- (-2,1.5,0) -- cycle;
\fill[red,opacity=0.2]
(-2,-1.5,0) -- (2,-1.5,0) -- (2,1.5,0) -- (-2,1.5,0) -- cycle;
\tdplotdrawarc[thick, color=red]{(2,-1.5,0)}{-0.3}{-90}{0}{anchor=180}
{$\pi/2$}% <-
\tdplotdrawarc[thick, color=red, ->]{(O)}{0.5}{0}{\iAngle}{anchor=180,
below}{$\omega\cdot t$}%
\tdplotdrawarc[thick,dotted, color=violet, ->]{(O)}{0.55}{90}{90+\iAngle}{anchor=180,above}{$\omega\cdot t$}
\tdplotdrawarc[thick, color=purple, dashed]{(O)}{\iBngle/180}{0}{360}{anchor=180}{}
\tdplotsetrotatedcoords{\iAngle}{00}{0}
\begin{scope}[tdplot_rotated_coords]
\draw[thick, dashed, opacity=1, ->] (0,0,0) -- (2.5,0,0)node[above] {$x_1$};
\draw[thick, dashed, opacity=1, ->] (0,0,0) -- (0,2.5,0)node[above] {$y_1$};
\draw[thick,->] (O) -- (0.3,0,0) node[anchor=north, above left]{$\vec i_1$};
\draw[thick,->] (O) -- (0,0.3,0) node[near end, above]{$\vec j_1$};
\end{scope}
\tdplotsetrotatedcoords{{\iAngle+\iBngle}}{00}{0} %<- changed that in order to rotate the rod
\begin{scope}[tdplot_rotated_coords]
\draw[ultra thick, color=orange, opacity=1] (0,0,0) -- (\RodLength,0,0)node[near end, below left] {$(T)$};
\coordinate[label=below right:$C$] (A1) at ({\RodLength*\iBngle/180},0,0.3);
\fill[blue,thick] (A1) circle (0.3pt);
\coordinate[label=above:$I_1$] (I1) at (1,0,0);
\fill[blue,thick] (I1) circle (0.3pt);
\end{scope}
\tdplotsetrotatedcoords{{\iAngle+130}}{90}{0} %<-
\begin{scope}[tdplot_rotated_coords]
\draw[pattern=north west lines, pattern color=blue, opacity=0.5 ] (A1) circle
\node[] at (45:0.4cm){$D$};
\draw[-latex,blue] (A1) -- ++({-0.7*cos(\iBngle/\relRad)},{0.7*sin(\iBngle/\relRad)},0)node[right]{$k_0$}; %<-
\draw[-latex,blue] (A1) -- ++(0,0,0.7)node[below]{$k_1$};  %<-
\draw[-latex,blue] (A1) -- ++({-0.7*sin(\iBngle/\relRad)},{-0.7*cos(\iBngle/\relRad)},0)node[below]{$k_2$};  %<-
\end{scope}
\tdplotsetrotatedcoords{\iAngle}{90}{45}
\begin{scope}[tdplot_rotated_coords]
% \draw[-latex, violet] (A1) -- ++(-0.7,0,0)node[right]{$\vec k_2$};
%\draw[-latex, violet] (A1) -- ++(0,0.7,0)node[right]{$\vec j_2$};
%\pgfmathtruncatemacro{\iBngle}{135}
%\tdplotdrawarc[thick, color=blue,->]{(A1)}{0.5}{45}{90}{anchor=105, above, left}{$\theta$} %
%\tdplotdrawarc[thick, color=red, ->]{(A1)}{0.5}{\iBngle}{180}{anchor=180, above}{$\theta$}%
\end{scope}
\end{tikzpicture}
}
\end{animateinline}


OLD(ER) ANSWER: This code looks somehow familiar... (It might be appropriate to give links to all sources.) To give you a start:

\documentclass[border=5pt]{standalone}
\usepackage{tikz,tikz-3dplot}
\usepackage{animate}
\usepackage{ifthen}
\usetikzlibrary{patterns}%
% \newcounter{MyCounter}
% \def\StartValue{5}
% \def\MaxValue{10}
\begin{document}
\tdplotsetmaincoords{70}{110}
\begin{animateinline}[loop, poster = first, controls]{24}
\multiframe{30}{iBngle=0+3}{
\pgfmathsetmacro{\iAngle}{140}%35
\tdplotsetmaincoords{70}{110}
\begin{tikzpicture}[scale=5,tdplot_main_coords]
\useasboundingbox[tdplot_screen_coords] (-2.05,-1.2) rectangle (2.5,1.5);
\coordinate (O) at (0,0,0);
\node[red, left] at (O) {$O$};
\draw[thick,->] (O) -- (2,0,0) node[anchor=north]{$x_0$};
\draw[thick,->] (O) -- (0,1.5,0) node[anchor=west]{$y_0$};
\draw[thick,->] (O) -- (0,0,1.5) node[anchor=south]{$z_0$};
\draw[thick,->] (O) -- (0.3,0,0) node[anchor=north, left]{$\vec i_0$};
\draw[thick,->] (O) -- (0,0.3,0) node[near end, below]{$\vec j_0$};
\draw[thick,->] (O) -- (0,0,0.3) node[anchor=south, right]{$\vec k_0$};
\draw[thick, opacity=0.3] (-2,-1.5,0) -- (2,-1.5,0) -- (2,1.5,0) -- (-2,1.5,0) -- cycle;
\fill[red,opacity=0.2]
(-2,-1.5,0) -- (2,-1.5,0) -- (2,1.5,0) -- (-2,1.5,0) -- cycle;
\tdplotdrawarc[thick, color=red]{(2,-1.5,0)}{-0.3}{-90}{0}{anchor=180}
{$\pi/2$}% <-
\tdplotdrawarc[thick, color=red, ->]{(O)}{0.5}{0}{\iAngle}{anchor=180,
below}{$\omega\cdot t$}%
\tdplotdrawarc[thick,dotted, color=violet, ->]{(O)}{0.55}{90}{90+\iAngle}{anchor=180,above}{$\omega\cdot t$}
\tdplotdrawarc[thick, color=purple, dashed]{(O)}{1}{0}{360}{anchor=180}{}
\tdplotsetrotatedcoords{\iAngle}{00}{0}
\begin{scope}[tdplot_rotated_coords]
\draw[thick, dashed, opacity=1, ->] (0,0,0) -- (2.5,0,0)node[above] {$x_1$};
\draw[thick, dashed, opacity=1, ->] (0,0,0) -- (0,2.5,0)node[above] {$y_1$};
\draw[thick,->] (O) -- (0.3,0,0) node[anchor=north, above left]{$\vec i_1$};
\draw[thick,->] (O) -- (0,0.3,0) node[near end, above]{$\vec j_1$};
\end{scope}
\tdplotsetrotatedcoords{{\iAngle+\iBngle}}{00}{0} %<- changed that in order to rotate the rod
\begin{scope}[tdplot_rotated_coords]
\draw[ultra thick, color=orange, opacity=1] (0,0,0) -- (1.65,0,0)node[near end, below left] {$(T)$};
\coordinate[label=below right:$C$] (A1) at (1,0,0.3);
\fill[blue,thick] (A1) circle (0.3pt);
\coordinate[label=above:$I_1$] (I1) at (1,0,0);
\fill[blue,thick] (I1) circle (0.3pt);
\end{scope}
\tdplotsetrotatedcoords{{\iAngle+\iBngle}}{90}{0} %<-
\begin{scope}[tdplot_rotated_coords]
\draw[pattern=north west lines, pattern color=blue, opacity=0.5 ] (A1) circle
\node[] at (45:0.4cm){$D$};
\draw[-latex,blue] (A1) -- ++({-0.7*cos(\iBngle/\relRad)},{0.7*sin(\iBngle/\relRad)},0)node[right]{$k_0$}; %<-
\draw[-latex,blue] (A1) -- ++(0,0,0.7)node[below]{$k_1$};  %<-
\draw[-latex,blue] (A1) -- ++({-0.7*sin(\iBngle/\relRad)},{-0.7*cos(\iBngle/\relRad)},0)node[below]{$k_2$};  %<-
\end{scope}
\tdplotsetrotatedcoords{\iAngle}{90}{45}
\begin{scope}[tdplot_rotated_coords]
% \draw[-latex, violet] (A1) -- ++(-0.7,0,0)node[right]{$\vec k_2$};
%\draw[-latex, violet] (A1) -- ++(0,0.7,0)node[right]{$\vec j_2$};
%\pgfmathtruncatemacro{\iBngle}{135}
%\tdplotdrawarc[thick, color=blue,->]{(A1)}{0.5}{45}{90}{anchor=105, above, left}{$\theta$} %
%\tdplotdrawarc[thick, color=red, ->]{(A1)}{0.5}{\iBngle}{180}{anchor=180, above}{$\theta$}%
\end{scope}
\end{tikzpicture}
}
\end{animateinline}
\end{document} I hope that's closer to what you want. BTW, the angle labeled \pi in the front left corner is just \pi/2.

NOTICE: The code produces an inline animation. It can be converted to an animated gif by using this cool post. (Note also that this post which works for beamer animations.)

• thank you for your reply,@marmot, yes the rod rotate around the k_0 axis, but the disk rotate around the j_1 axis, so, i must to show how the disk rolling on the rod when rotate around the j_1 axis, k_1 cannot in any case parallel with the j_1 axis, it rotate around it in the plan fomed by the disk Mar 11 '18 at 7:52
• thank you @marmot, so i want to shaw how the disk roll along the rod, my representation in the graph above of the disk is wrong, then i want to add a scope for this command in may code \draw[pattern=north west lines, pattern color=blue, opacity=0.5 ] (A1) circle (0.3); Mar 11 '18 at 17:27
• because the specific commands \tdplotsetrotatedcoords{{\iAngle+90}}{90}{\iAngle}, doesn't allow me to draw what i want Mar 11 '18 at 17:33
• thank you @marmot, i updated my question, I hope you can help me to complete this code to show how the disk roll on the rod in animated version. Mar 12 '18 at 17:18
• thank you @marmot, the dashed circle figure out how the contact point between the disk and the rod $I$ move on the rod, so, its position is not fixed, it **varied from 0 to $L$ (length of rod) . an other point the rod is fixed on the $x_1$ axis it also rotate with $\omega\cdot t$ angle, the last point, the disk should be parallel to plan $Z_0Ox_1$ during of the motion thereof Mar 13 '18 at 12:29