Mdthbs

I'm a beginner to the latex tikz and I want to draw this picture but dunno what's the best command or idea here

This is a special case of a cycloid curve, known as hypotrochoid.

documentclass[tikz,border=3.14mm]{standalone}

usetikzlibrary{decorations.markings}

begin{document}

begin{tikzpicture}[insert arrow/.style={decoration={

        markings,

         mark=at position #1 with {arrow{stealth}}},postaction=decorate},

         bullet/.style={draw,fill=white,circle,thick,inner sep=2pt}]

 draw[thick,insert arrow/.list={0.125,0.35,0.4,0.625,0.85,0.9}] 

  plot[variable=t,domain=0:360,samples=101,smooth]

  ({45+t-30*sin(4*t)}:{2-0.8*cos(4*t)});

 draw[very thick]  (-3,0) -- (3,0);

 path (-2.8,0) node[bullet]{} (1.2,0) node[bullet]{};

end{tikzpicture}

end{document}

For your convenience I declared a style for that.

documentclass[tikz,border=3.14mm]{standalone}

usetikzlibrary{decorations.markings}

begin{document}

begin{tikzpicture}[insert arrow/.style={decoration={

        markings,

         mark=at position #1 with {arrow{stealth}}},postaction=decorate},

         bullet/.style={draw,fill=white,circle,thick,inner sep=2pt},

         hypotrochoid/.style={/utils/exec=tikzset{hypotrochoid/.cd,#1},

         insert path={

         plot[variable=t,domain=0:360,samples=101,smooth]

  ({pgfkeysvalueof{/tikz/hypotrochoid/rot}+t

  -(360/(pgfkeysvalueof{/tikz/hypotrochoid/n}*pgfkeysvalueof{/tikz/hypotrochoid/m}))

  *sin(pgfkeysvalueof{/tikz/hypotrochoid/n}*t)

  }:{

  pgfkeysvalueof{/tikz/hypotrochoid/outer radius}

  -pgfkeysvalueof{/tikz/hypotrochoid/inner radius}*cos(pgfkeysvalueof{/tikz/hypotrochoid/n}*t)

  })}}, hypotrochoid/.cd,outer radius/.initial=2,

         inner radius/.initial=1,

         rot/.initial=45,n/.initial=4,m/.initial=1]

 draw[thick,insert arrow/.list={0.125,0.35,0.4,0.625,0.85,0.9},

    hypotrochoid={outer radius=2,inner radius=0.8,n=4,m=2.5}];



 draw[very thick]  (-3,0) -- (3,0);

 path (-2.8,0) node[bullet]{} (1.2,0) node[bullet]{};

end{tikzpicture}

end{document}

Then you can change e.g. n easily

draw[thick,hypotrochoid={outer radius=2,inner radius=0.8,n=6,m=2.5}];

A solution with pstricks:

documentclass{article}

usepackage{pst-plot,pst-node,multido}



defx{4*cos(t) + 2*cos(5*t)}

defy{4*sin(t)+2*sin(5*t)}



begin{document}



psset{unit=0.8cm}

begin{pspicture}(-6.5,-6.5)(6.5,6.5)

psline[linewidth=1.2pt]{-}(-6.5,0)(6.5,0)

{psset{plotpoints=500, plotstyle=curve, algebraic,linewidth=1.5pt}

psparametricplot[linecolor=red, ArrowInside=->, ArrowInsideNo=4]{0}{6.28}{x|y}}

% define nodes on the curve

curvepnodes[plotpoints=4]{0}{4.712}{x|y}{P}

curvepnodes[plotpoints=2]{0.25}{3.0}{x|y}{Q}

curvepnodes[plotpoints=2]{3.30}{6.05}{x|y}{R}

psset{dotstyle =triangle*, dotscale =1.4 , linecolor =red}

multido{i=0 + 1,irot =0+ 90}{4}{psdot[dotangle=irot,](Pi)}

multido{i=0 + 1,irot =55+ 95}{2}{psdot[dotangle=irot](Qi)}

multido{i=0 + 1,irot =-25+ 95}{2}{psdot[dotangle=irot](Ri)}

psset{ dotscale =1.6, linecolor=black, dotstyle =Bo}

psdots(P2)(2.5,0)

end{pspicture}



end{document}