A Unified Algorithm for Geometric Design of Platform Linkages With Spherical and Plane Constraints

Abstract

This paper studies the constrained motion of a rigid body such that one or more of its points stays on a sphere or a plane. It extends Innocenti’s spatial Burmester problem from purely spherical constraints to include any combination of spherical and planar constraints for seven position synthesis of a spatial rigid body. The present paper provides a unified formulation using homogeneous coordinates and dual quaternions for simultaneous dimensional and type synthesis of spatial platform linkages and manipulators involving spherical and planar constraints. The algorithm is an extension of our previous work on unified solution for planar Burmester problem for geometric synthesis of planar dyads involving a combination of revolute and prismatic joints.