RESEARCH PAPERS: Mechanisms and Robotics

Operational Envelopes for Working Bodies of Mechanisms and Manipulators

[+] Author and Article Information
E. J. Haug

Department of Mechanical Engineering, The University of Iowa, Iowa City, Iowa

F. A. Adkins, Chi-Mei Luh

Program in Applied Mathematics and Computational Science, The University of Iowa, Iowa City, Iowa

J. Mech. Des 120(1), 84-91 (Mar 01, 1998) (8 pages) doi:10.1115/1.2826681 History: Received January 01, 1996; Revised August 01, 1997; Online December 11, 2007


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.

Copyright © 1998 by The American Society of Mechanical Engineers
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