Robotic-Like Formulation of the Approximated Body-Guidance Problem

A classical problem in the mechanics of mechanisms is the body-guidance synthesis. As first formulated by Burmester, the problem consists of finding the dimensions of a planar four-bar linkage whose coupler link attains a prescribed set of finitely separated poses. The problem is solved either in exact, up to five prescribed poses, or in approximate forms by several methods. Many of them rely on the algebraic geometry to find center- and circle-point loci of the RR dyads composing the mechanism. The method was also used to find the circle-point locus of the PR dyad. In this paper a different approach was followed. We propose a formulation of the problem by using the vector loop equations, usually employed in robotics for kinematic analysis, to obtain the set of nonlinear synthesis equations then solved by advanced and stabilized algorithms. The method allows us to achieve the approximate solution of the body-guidance problem either with RR or PR dyads with high accuracy also including prescribed timing.