Zobniki

r0[φ_]:=2+ Sin[4φ];
ParametricPlot[{r0[φ]Cos[φ],r0[φ]Sin[φ]},{φ,0,2 Pi}]

v = 1;ω=0.5;ParametricPlot[{v t+r0[φ]Cos[φ-ω t],r0[φ]Sin[φ-ω t]},{t,0,15},{φ,0,2 Pi},Mesh->{10,0},PlotPoints->60]

R =6;ω=3;ParametricPlot[{R Cos[t]+r0[φ]Cos[φ+ω t],R Sin[t]+r0[φ]Sin[φ+ω t]},{t,0,2 Pi},{φ,0,2 Pi},Mesh->{20,0},PlotPoints->60]

Manipulate[ParametricPlot[{R Cos[t]+r0[φ]Cos[φ+ω t],R Sin[t]+r0[φ]Sin[φ+ω t]},{φ,0,2 Pi},PlotRange->{{-10,10},{-10,10}}],{t,0,2 Pi}]