Alternating Error Effects on Decomposition Method in Function Generation Synthesis

Abstract

In approximate function generation synthesis methods, error between the desired function's output and designed mechanism's output oscillate about zero error while crossing the zero error margin at precision points. The common goal of these methods is to minimize the error within the selected working region of the mechanism. For mechanisms like Bennett overconstrained six-revolute jointed linkages that have relatively large number of construction parameters, it is a difficult task to solve for them at once. Decomposition method enables to divide such linkages into two loops and independently solve for each loop with less construction parameters. Although some approximation methods are proven to produce smaller errors than others for a single-loop synthesis, in this work, it is shown that smaller errors are not guaranteed for a certain method when used along with decomposition method. Numerical examples indicate that in decomposition method, more attention should be given to the alternation of the error of each decomposed mechanism, rather than the approximation method used.