A Computer-Aided Design Technique for Semi-Automated Infinite Point Coupler Curve Synthesis of Four-Bar Linkages

Abstract

At the present time, there are no satisfactory computer-aided solution schemes for solving the infinite point coupler curve synthesis problem (i.e., the problem of synthesizing a four-bar linkage whose coupler curve best approximates a fully specified closed trajectory). In order to develop a programmable solution process for this class of problems, it is necessary to devise a way of storing a catalog of coupler curves in a computer database. In addition, comparison procedures must be developed for detecting geometric similarities between curves; these procedures must be capable of observing similarities in the shapes of curves which may be scaled or oriented differently. In this paper, a data representation scheme based on uniform periodic B-splines is proposed as a viable means of storing coupler curves in a database. Automated procedures for fitting B-splines to coupler cures or other closed curves are also developed. The paper also presents a set of algorithms for comparing the shapes of curves based on the control polygons of their B-spline approximations. These algorithms are implemented in a computer program that is an effective tool for semi-automated computer-aided solution of the infinite point coupler curve synthesis problem. Example problems solved using this program are discussed, along with some suggestions for further work on this topic.