Operational Envelopes for Working Bodies of Mechanisms and Manipulators

Abstract

The set of all points in space that are occupied by points in the working body of a mechanism or manipulator, for some kinematically admissible configuration, is defined as its operational envelope. Criteria for points on the boundary of the operational envelope of working bodies with smooth boundaries are developed, for both parametric and equation representations of domains and boundaries of working bodies, in two-and three-dimensional space. The criteria derived involve kinematic constraint equations for the underlying mechanism and equations that characterize the shape of the working body. A row rank deficiency condition is derived as a criterion for the boundary of the operational envelope, and numerical methods based on this condition for mapping the boundary are presented. Examples involving a planar Stewart platform with a dome attached and the wheel assembly of a vehicle suspension system in three dimensions are analyzed numerically.