Characteristic Surfaces for Three-Position Motion Generation With Planar Four-Bar Mechanisms

Abstract

This paper considers the relationship between the three-position motion generation problem and the solution space for planar four-bar mechanisms. After one half of the basic four bar had been selected, two infinities of solutions still remained. These solutions are mapped in a plane to determine where the particular types of mechanisms occur. A contour is then generated in the mapping plane which joins together all solutions which share a common characteristic in regard to their link lengths. This same contour can be displayed in the solution space and in the Cartesian plane in which the motion generation is defined. Significant useful information to assist in selecting the final solution is obtained. A numerical example is used for illustration, but the results can be applied to any three-position motion generation problem.