Least-Square Optimization of Planar and Spherical Four-Bar Function Generator Under Mobility Constraints

[+] Author and Article Information
Zheng Liu, J. Angeles

McGill Research Centre for Intelligent Machines, Department of Mechanical Engineering, McGill University, Montreal, Quebec, Canada H3A2K6

J. Mech. Des 114(4), 569-573 (Dec 01, 1992) (5 pages) doi:10.1115/1.2917045 History: Received March 01, 1990; Online June 02, 2008


An optimization scheme for four-bar function generators under mobility constraints, which can be applied to both planar and spherical four bar linkages, is presented in this paper. The design error , defined as the residual in the input-output equation, is minimized over the vector of linkage parameters. The mobility constraints, given as a set of inequalities, are converted into equalities by introducing slack variables. The problem is thus formulated as an equality-constrained minimization problem, which is then solved using the orthogonal-decomposition algorithm, an iterative numerical method introduced elsewhere. To reduce the dimensional unbalance, which often occurs in solving a synthesis problem, a penalty function is combined with the original objective function, whose minimization leads to dimensionally balanced linkages. A numerical example is included.

Copyright © 1992 by The American Society of Mechanical Engineers
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