How may I create this limacon graph (rolling circles included) in LaTex?

documentclass[tikz,border=3mm]{standalone}
newififtikzepitrochoidhasxis
tikzepitrochoidhasxistrue
tikzset{pics/epitrochoid/.style={code={%
  tikzset{epitrochoid/.cd,#1}
  defpv##1{pgfkeysvalueof{/tikz/epitrochoid/##1}}
  pgfmathsetmacro{mymax}{2*max(abs(pv{r}),abs(pv{d}))+abs(pv{R})+0.5}
  iftikzepitrochoidhasxis
   draw[-stealth] (-mymax,0) -- (mymax,0) node[below left]{$x$};
   draw[-stealth] (0,-mymax) -- (0,mymax) node[below left]{$y$};
  else 
   path (-mymax,-mymax) rectangle (mymax,mymax);
  fi 
  draw[blue,semithick] circle[radius=pv{R}];
  draw[semithick] ({deg(pv{t})}:{abs(pv{r})+abs(pv{R})}) coordinate (c) circle[radius=pv{r}];
  pgfmathtruncatemacroitest{(pv{t}>0?1:0)}
  ifnumitest=1
   pgfmathsetmacro{isamples}{5+2*(pv{R}+pv{r})*int(pv{t})}
   draw[red,thick] plot[smooth,samples=isamples,domain=0:pv{t},variable=t,smooth]
    ({(pv{R}+pv{r})*cos(deg(t))-pv{d}*cos((pv{R}+pv{r})*deg(t)/pv{r})},
     {(pv{R}+pv{r})*sin(deg(t))-pv{d}*sin((pv{R}+pv{r})*deg(t)/pv{r})})
     node[circle,inner sep=1.2pt,fill](e){};
    draw  (c) node[circle,inner sep=1.2pt,fill]{}  -- (e); 
   fi
}},
epitrochoid/.cd,R/.initial=3,r/.initial=1,d/.initial=0.5,t/.initial=1,
    axis/.is if=tikzepitrochoidhasxis,axis/.default=true}
begin{document}
foreach Time in {0,0.1,...,6.2}
{begin{tikzpicture}
 pic{epitrochoid={t=Time}};
end{tikzpicture}}
end{document}