Roulettes

Narasimham G.L. · science forum Guru Wannabe Joined: 28 Apr 2005 Posts: 216

What are the intrinsic and parametric equations [x(s),y(s)] traced by a
point in 2D of a rigid curve having natural equation rho1=f(s) rolling
on another fixed curve of natural equation rho2=g(s) ? and vice-versa?
( rho is radius of curvature, s arc length)

In particular,

What transformation/substitution of equations transforms a cycloid
(rigid circle rolling on a fixed line) to an involute (rigid line
rolling on a fixed circle)? And vice-versa?

Regards
Narasimham

Google