Synthesis of Function-Generating Linkages with Minimax Design Error: The Linear Case

摘要

The kinematic synthesis of both planar and spatial linkages for function generation is a well-known problem whose algebraic formulation was reported by Freudenstein in the fifties. The same problem for approximate synthesis, i.e., the kinematic problem leading to an overdetermined system of algebraic equations, became a research subject in the seventies, when the use of computers in mechanical design became currency. Methods of solution for least-square approximations have been proposed, that are numerically efficient in both the linear and the nonlinear cases. The problem of approximate synthesis to produce linkages with the minimum largest (minimax) design error, however, has received scant attention. Using a modification of Lawson's algorithm for the solution of the linear minimax approximation problem, that accelerates substantially its convergence, the authors propose in this paper the solution of this problem associated with both planar and spatial linkages. Only synthesis equations of the linear type are considered here.