Coprime Gears (corrected)

sizes = {6, 3, 5.5, 3};
gear[n_] := ((n + Cos[# n]^2) {Cos[#], Sin[#]}) &
h = 15;
Manipulate[
 Show[ParametricPlot[
   {
    RotationMatrix[
      sizes[[2]] \[Theta]/sizes[[1]]].(gear[sizes[[1]]][t]),
    RotationMatrix[-\[Theta] + Pi/(2 sizes[[2]])].(gear[sizes[[2]]][
        t]) + {sizes[[1]] + sizes[[2]] + 1, 0},
    RotationMatrix[
       sizes[[4]] \[Theta]/sizes[[3]]].(gear[sizes[[3]]][t]) + {0, -h},
    RotationMatrix[-\[Theta] + Pi/(2 sizes[[4]])].(gear[sizes[[4]]][
        t]) + {sizes[[3]] + sizes[[4]] + 1, -h}
    }
   , {t, 0, 2 Pi}, PlotStyle -> Thick,
   PlotRange -> {{-8, 16}, {-h - 10, 12}}, Axes -> None,
   MeshStyle -> None, Frame -> None],
  Graphics[
   {
    Darker@Blue, Disk[{0, 0}, 0.8],
    Darker@Purple, Disk[{sizes[[1]] + sizes[[2]] + 1, 0}, 0.8],
    Darker@Yellow, Disk[{0, -h}, 0.8],
    Darker@Green, Disk[{sizes[[3]] + sizes[[4]] + 1, -h}, 0.8],
    Red, PointSize[Large],
    Point[{sizes[[1]] + sizes[[2]] + 1, 0} +
      RotationMatrix[-\[Theta] + Pi/(2 sizes[[2]])].{sizes[[2]] + 1,
        0}], Darker@Red,
    Table[
     Block[{p},
      p =
       sizes[[1]] RotationMatrix[
          sizes[[2]] \[Theta]/sizes[[1]]  -
           Pi (i + 0.5)/sizes[[1]]].{1, 0};
      If[Mod[i, 2 sizes[[2]], 1] == 3, {Point[p]}, {}]
      ]
     , {i, 0, \[Theta] sizes[[2]]/Pi}],

    Red, PointSize[Large],
    Point[{sizes[[3]] + sizes[[4]] + 1, -h} +
      RotationMatrix[-\[Theta] + Pi/(2 sizes[[4]])].{sizes[[4]] + 1,
        0}], Orange,
    Table[
     Block[{p},
      p = {0, -h} +
        sizes[[3]] RotationMatrix[
           sizes[[4]] \[Theta]/sizes[[3]]  -
            Pi (i + 0.5)/sizes[[3]]].{1, 0};
      If[Mod[i, 2 sizes[[4]], 1] == 3, {Point[p]}, {}]
      ]
     , {i, 0, \[Theta] sizes[[4]]/Pi}]

    }
   ]
  ],

 {\[Theta], 0, 22 Pi}
 ]