Kinematic Geometry of Spherical Evolutes

In this paper, we define spherical evolutes corresponding to the trajectory of a point in spherical kinematics. We derive general expressions for the curvature properties of the nth spherical evolute in terms of the geodesic curvature and the derivative of the geodesic curvature for the (n-1)the spherical evolute. The results are illustrated by numerical examples for the motion of a circular cone rolling on a fixed circular cone, of a spherical turning-block linkage, and of a spherical four-bar linkage.