Polynomial Solution of the Spatial Burmester Problem

[+] Author and Article Information
C. Innocenti

Dipartimento di Ingegneria delle Costruzioni Meccaniche, University of Bologna, Viale Risorgimento, 2-40136, Bologna, Italy

J. Mech. Des 117(1), 64-68 (Mar 01, 1995) (5 pages) doi:10.1115/1.2826118 History: Received January 01, 1994; Revised June 01, 1994; Online January 25, 2008


This paper presents a new method for the dimensional synthesis of the spatial guidance linkage that features the guided body connected to the base by the interposition of five rods having spherical joints at both extremities. The linkage is required to index the guided body through seven arbitrarily-chosen rigid-body positions. Core of the proposed method is an original algebraic elimination procedure that allows five unknowns to be dropped from a set of six second-order algebraic equations in six unknowns. As a result, a final univariate polynomial equation of twentieth order is obtained whose twenty roots, in the complex domain, represent as many possible placements for a connecting rod. A numerical example is reported.

Copyright © 1995 by The American Society of Mechanical Engineers
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