Sorry, the engineer inside couldn't resist

Edit

Here is the code:

gearCurve[a_, b_, n_, c_, h_] := 
  ParametricPlot[{c + (a + 1/b Tanh[b Sin[n t + h]]) Cos[t + h], 
                      (a + 1/b Tanh[b Sin[n t + h]]) Sin[t + h]}, {t, 0, 2 Pi}, 
   Axes -> False, 
   Method -> {Refinement -> {ControlValue -> 1 Degree}}];

Animate[Show[gearCurve[10, 5, 38, 0, h], gearCurve[10, 5, 38, 20, -h],
             PlotRange -> {{-10, 30}, {-10, 10}}], {h, 0, 2 Pi, .01}, 
             DisplayAllSteps -> True]

Sorry, the engineer inside couldn't resist

Edit

Here is the code:

gearCurve[a_, b_, n_, c_, h_] := 
  ParametricPlot[{c + (a + 1/b Tanh[b Sin[n t + h]]) Cos[t + h], 
                      (a + 1/b Tanh[b Sin[n t + h]]) Sin[t + h]}, {t, 0, 2 Pi}, 
   Axes -> False, 
   Method -> {Refinement -> {ControlValue -> 1 Degree}}];

Animate[Show[gearCurve[10, 5, 38, 0, h], gearCurve[10, 5, 38, 20, -h],
             PlotRange -> {{-10, 30}, {-10, 10}}], {h, 0, 2 Pi, .01}, 
             DisplayAllSteps -> True]

Sorry, the engineer inside couldn't resist

Sorry, the engineer inside couldn't resist

Edit

Here is the code:

gearCurve[a_, b_, n_, c_, h_] := 
  ParametricPlot[{c + (a + 1/b Tanh[b Sin[n t + h]]) Cos[t + h], 
                      (a + 1/b Tanh[b Sin[n t + h]]) Sin[t + h]}, {t, 0, 2 Pi}, 
   Axes -> False, 
   Method -> {Refinement -> {ControlValue -> 1 Degree}}];

Animate[Show[gearCurve[10, 5, 38, 0, h], gearCurve[10, 5, 38, 20, -h],
             PlotRange -> {{-10, 30}, {-10, 10}}], {h, 0, 2 Pi, .01}, 
             DisplayAllSteps -> True]