Burmester Lines of Spatial Five Position Synthesis from the Analysis of a 3-CPC Platform

[+] Author and Article Information
A. P. Murray

Department of Mechanical and Aerospace Engineering, University of Dayton, Dayton, OH 45469-0210

J. M. McCarthy

Department of Mechanical and Aerospace Engineering, University of California at Irvine, Irvine, CA 92697

J. Mech. Des 121(1), 45-49 (Mar 01, 1999) (5 pages) doi:10.1115/1.2829428 History: Received November 01, 1997; Revised December 01, 1998; Online December 11, 2007


This paper presents a new technique for determining the fixed axis for a spatial CC chain that guides a rigid body through five finitely separated positions, termed a Burmester Line. It is known that there can be as many as six Burmester lines for a given set of five spatial positions. Here we show that these six lines can be obtained from the analysis of a 3-CPC platform, constructed from relative screw axes associated with the five specified displacements. The screw axes of the displacement of this platform to each of its assemblies are the desired Burmester lines. Roth’s original example is presented to verify the calculations.

Copyright © 1999 by The American Society of Mechanical Engineers
Topics: Screws , Chain , Displacement
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