Solving Motion Generation Problems Using a Gradient Method, Part 2 - Spatial Kinematic Synthesis and the Cone Angle Principle

摘要

Solutions to the planar motion generation problem for dyads with revolute joints are well understood. However, the spatial synthesis for dyads of various joint types are much more complex. This paper presents a method for solving the Spherical-Spherical (SS) dyad by extending Euclid's chord angle principle to three dimensions. The paper briefly reviews a gradient method developed to solve the planar dyad synthesis problem without use of the poles of the linkage. The paper then extends the chord angle principle to three dimensions, namely the cone angle principle. The gradient method in combination with the cone angle principle is then extended to three dimensions and examples of the spatial equivalent of Burmester curves are plotted for the SS dyad.