Gear Curve

Author

Eric W. Weisstein
May 30, 2008

This notebook downloaded from http://mathworld.wolfram.com/notebooks/PlaneCurves/GearCurve.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/GearCurve.html.

©2008 Wolfram Research, Inc. except for portions noted otherwise

Plot

GearCurve[n_][t_]:=(1+1/10 Tanh[10 Sin[n t]]){Cos[t],Sin[t]}

Plot[1+1/10 Tanh[10 Sin[12 t]],{t,0,2π}]

Plot[1+1/10 Sign[10 Sin[12 t]],{t,0,2π}]

V5

ParametricPlot[{x[t,12],y[t,12]},{t,0,2Pi},
AspectRatio->Automatic,Ticks->None,PlotStyle->Red]

MakeBoxes[label[n_],TraditionalForm]:=RowBox[{"n","==",MakeBoxes[n,TraditionalForm]}]

Show[GraphicsArray[Partition[Block[{$DisplayFunction=Identity},Table[ParametricPlot[{x[t,n],y[t,n]},{t,0,2Pi},
PlotLabel->TraditionalForm[label[n]],
AspectRatio->Automatic,Ticks->None,PlotStyle->Red],{n,12}]
],4,4,{1,1},{}]]]

V6

ParametricPlot[GearCurve[#][t],{t,0,2Pi},AspectRatio->Automatic,Ticks->None,PlotStyle->Red]&/@Range[6]