On the Intrinsic Properties of Point Trajectories in Three-Dimensional Kinematics

In this paper we derive analytical expressions for curvature, torsion, and radius of osculating sphere of the point trajectory in three-dimensional kinematics. Corresponding to a design position we obtain equations of loci of points tracing straight lines, helical curves, and spherical curves. It is hoped that the result of this study will provide another step toward rational design of spatial mechanisms and control systems for robot manipulators.