This demo includes a single graphical window that displays a curve X(t) (which you may change in the appropriate textbox in the control window), the point X(t0), the unit tangent vector T(t0) with base X(t0), the involute curve I(t) = X(t) + (k – s(t))T(t) for parameter c defined in the control window, and, if the "String" box in the control window is checked, a curve showing that one can interpret the involute curve as the result of winding or unwinding a string around the curve X(t) and having the end of the string trace out a curve. The control window lists several curves that you may enter for X(t). For example, type cardioid(t) in the textbox for X(t) to make X(t) a cardioid. The control window also includes parameters used in defining these curves.
Change the value of t0 and other variables as in earlier demos.
As in earlier demos, there are "Show entire curve", "Show position vector X(t0)" and "Show Color Spectrum" options. "Show Color Spectrum" also colors the tangent vector and the involute.