3 DOF Bicycle Model in Latex

Question

A common way of modeling a vehicle's dynamics is to use a 3DOF bicycle model

I tried to create this in tikzpictures, but I am having some difficulty. I was going to just give up and do it in Inkscape, but one of the nice things about LaTeX is that I get all of the math symbols that I need for my paper. Is this something that would be very difficult to create in tikzpictures? If someone can do it easily any suggestions or help would be greatly appreciated.

Thanks!

Answer 1

It is not too difficult to draw this sort of pictures. You may want to make yourself familiar with the calc syntax, which is described with many neat examples in section 13.5 of the pgfmanual. Further libraries which simplify things here are quotes and angles, and the arrows.meta library lets you draw pretty much any arrow you can imagine.

\documentclass[tikz, margin=3.14mm]{standalone} 
\usetikzlibrary{calc,angles,quotes,arrows.meta}

\tikzset{pill/.style={minimum width=1.2cm,minimum height=6mm,rounded
corners=3mm,draw},
reactor/.style={circle,draw,minimum size=6mm,path picture={
\draw (-3mm,0) -- (3mm,0) (0,-3mm) -- (0,3mm);
\fill (0,0) -- (3mm,0) arc(0:-90:3mm) -- cycle;
\fill (0,0) -- (-3mm,0) arc(180:90:3mm) -- cycle;
}}}

\begin{document}    
\begin{tikzpicture}
\draw[thick,{Triangle[length=2mm]}-{Triangle[length=2mm]}] (0,6) coordinate (Y) -- (0,0) coordinate (O)-- (10,0)
coordinate (X);
\draw[thick,dashed] (O) -- (9.5,4.3) coordinate[pos=0.28] (F1) coordinate[pos=0.8] (F2) coordinate (TR);
\draw[thick,dotted] (O |- F2) node[left]{$x$} -- (F2) -- (O -| F2) node[below] {$y$};
\draw[thick] (F1)  -- (F2) node[pos=0.55,sloped,reactor] (M){~}
node[pos=0,sloped,pill]{};
\draw[green!70!black,thick,-latex] (M.center) -- ($(M.center)!1cm!0:(F2)$)
node[above]{$U$};
\draw[green!70!black,thick,-latex] (M.center) -- ($(M.center)!1cm!90:(F2)$)
node[left]{$V$};
\draw[thick,dashed] (F2) -- ++ (48:2) coordinate(H)  node[pos=0,sloped,pill,solid]{}
pic ["$\delta_f$",draw,solid,->,angle radius=1cm,angle eccentricity=1.3] {angle = TR--F2--H};
\draw[thick,red,-latex] (F2) -- ++ (62:2) coordinate (A2) node{$\alpha_f$}
pic [draw,solid,black,->,angle radius=1.3cm] {angle = H--F2--A2};;
\draw[thick,red,-latex] (F1) -- ++ (48:2) coordinate (A1)
pic ["$\alpha_r$",draw,->,red,thick,angle radius=1cm,angle eccentricity=1.3] {angle = F2--F1--A1};
\draw[->] let \p1=($(F2)-(F1)$),\n1={-180+atan2(\y1,\x1)},\n2={\n1+180} in 
($($(M)!8mm!00:(F1)$)+({cos(\n1+90)*1mm},{sin(\n1+90)*1mm})$) arc(\n1:\n2:8mm)
node[midway,below,red]{$\omega_z$};
\draw[latex-] ($(F1)!1mm!-90:(M)$) -- ($(F1)!5mm!-90:(M)$) node[below]{$F_{\gamma r}$};
\draw[latex-] ($(F2)!1mm!90:(M)$) -- ($(F2)!5mm!90:(M)$) node[below]{$F_{\gamma f}$};
\draw[{Bar}{Latex}-{Latex}{Bar}] ($(F1)!1.5cm!90:(M)$) -- 
($(M)!1.5cm!90:(F2)$) node[midway,sloped,fill=white]{$L_r$};
\draw[{Bar}{Latex}-{Latex}{Bar}] ($(M)!1.5cm!90:(F2)$) -- 
($(F2)!1.5cm!-90:(M)$) node[midway,sloped,fill=white]{$L_f$};
\end{tikzpicture}
\end{document}

Answer 2

I was also working on a solution, but @marmot beat me to it! :) Here it is anyway...

\documentclass[border=1mm,tikz]{standalone}
\usetikzlibrary{calc,quotes,angles}

\begin{document}

\begin{tikzpicture}

\pgfmathsetmacro{\y}{4.5}
\pgfmathsetmacro{\x}{2.5}
\pgfmathsetmacro{\Angle}{atan2(\x,\y)}
\pgfmathsetmacro{\AngleR}{30}
\pgfmathsetmacro{\AngleF}{45}
\pgfmathsetmacro{\AngleDelta}{25}
\pgfmathsetmacro{\COMradius}{0.15}

\coordinate (Origin) at (0,0);
\draw [-latex,thick] (Origin)--++(0,\x+1.5) coordinate (yaxis); 
\draw [-latex,thick] (Origin)--++(\y+1.5,0) coordinate (xaxis); 
\draw [dashed] (Origin)--++(\Angle:6.5cm) coordinate (AngleEnd);
\draw [dotted,thick] (\y,0) node [below] {$y$} --++(0,\x) coordinate (Fyf);
\draw [dotted,thick] (0,\x) node [left] {$x$} --++(\y,0);
\draw pic["$\Psi$", draw=black, text=black, -latex, angle eccentricity=1.25, angle radius=0.8cm]
              {angle=xaxis--Origin--Fyf};

% Fyr
\coordinate (Fyr) at ($ (Origin) + (\Angle:2cm) $);
\node at (Fyr) [rotate=\Angle,draw,thick,rounded corners=2mm,minimum width=1cm, minimum height=0.4cm] {};
\draw [red,-latex,thick] (Fyr)--++(\Angle+\AngleR:1.3cm) coordinate (RedArrowOne);
\draw pic["$\alpha_r$", draw=black, text=red, -latex, angle eccentricity=1.45, angle radius=0.8cm]
              {angle=Fyf--Fyr--RedArrowOne};
\draw [latex-,thick,blue] (Fyr)--++(\Angle-90:0.5cm) node [rotate=\Angle,right] {$F_{yr}$};           

\draw [thick] (Fyr)--(Fyf); 

% Fyf  
\node at (Fyf) [rotate=\Angle+\AngleDelta,draw,thick,rounded corners=2mm,minimum width=1cm, minimum height=0.4cm] {};         
\draw [red,-latex,thick] (Fyf)--++(\Angle+\AngleF:1.3cm) coordinate (RedArrowTwo);
\draw [dashed] (Fyf)--++(\Angle+\AngleDelta:1.3cm) coordinate (DeltaAngleEnd);
\draw pic["$\delta_f$", draw=black, text=black, -latex, angle eccentricity=1.35, angle radius=0.8cm]
           {angle=AngleEnd--Fyf--DeltaAngleEnd};
\draw pic["$\alpha_f$", draw=black, text=red, -latex, angle eccentricity=1.45, angle radius=1cm]
      {angle=DeltaAngleEnd--Fyf--RedArrowTwo};
\draw [latex-,thick,blue] (Fyf)--++(\Angle-90:0.5cm) node [rotate=\Angle,right] {$F_{yf}$};       

% COM
\coordinate (COM) at ($ (Origin) + (\Angle:3.7cm) $);
\begin{scope}[rotate=\Angle]
\fill [radius=\COMradius] (COM) -- ++(\COMradius,0) arc [start angle=0,end angle=90] -- ++(0,-2*\COMradius) arc [start angle=270, end angle=180];
\draw [thick,radius=\COMradius] (COM) circle;
\end{scope}
\draw [-latex,thick,green] (COM)--++(\Angle+90:0.5cm) node [left,rotate=\Angle] {$V$};
\draw [-latex,thick,green] (COM)--++(\Angle:0.8cm) node [below,rotate=\Angle] {$U$};

% Labels
\coordinate (LrLabel) at ($ (Fyr) +  (\Angle+90:1cm) $);
\coordinate (COMLabel) at ($ (COM) +  (\Angle+90:1cm) $);
\coordinate (LfLabel) at ($ (Fyf) +  (\Angle+90:1cm) $);
\draw [{Bar}{latex}-{latex}{Bar}] (LrLabel)--(COMLabel) node [midway,sloped,fill=white] {$L_r$};
\draw [{Bar}{latex}-{latex}{Bar}] (COMLabel)--(LfLabel) node [midway,sloped,fill=white] {$L_f$};

\end{tikzpicture}

\end{document}