The Optimum Quality Index for the Stability of In-Parallel Planar Platform Devices

[+] Author and Article Information
J. Lee, J. Duffy

Center for Intelligent Machines and Robotics, Mechanical Engineering Department, University of Florida, Gainesville, FL

M. Keler

F H Munich

J. Mech. Des 121(1), 15-20 (Mar 01, 1999) (6 pages) doi:10.1115/1.2829417 History: Received May 01, 1996; Revised November 01, 1998; Online December 11, 2007


The paper investigates primarily the geometrical meaning of the determinant of the Jacobian (det j) of the three connector lines of a planar in-parallel platform device using reciprocity. A remarkably simple result is deduced: The maximum value of det j namely, det jm is simply one-half of the sum of the lengths of the sides of the moving triangular platform. Further, this result is shown to be independent of the location of the fixed pivots in the base. A dimensionless ratio λ = |det j|/det jm is defined as the quality index (0 ≤ λ ≤ 1) and it is proposed here to use it to measure “closeness” to a singularity. An example which determines the optimal design by comparing different shaped moving platforms having the same det jm is given and demonstrates that the optimal shape is in fact an equilateral triangle

Copyright © 1999 by The American Society of Mechanical Engineers
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