Three-Position Function Generation of Planar Four-Bar Mechanisms With Equal Deviation Transmission Angle Control

Abstract

This paper is an extension of earlier work on mapping of three-position function generation of planar four-bar mechanisms. Previously, it has been shown that all of the potential solutions to a given problem may be represented in an αβ-plane which can be subdivided into mechanism types. Further, the regions in the αβ-plane may represent two possible forms of assembly plus a change of form class which are not valid solutions. In this paper, we provide a third-order polynomial which defines the locus in the αβ-plane of solutions which have equal deviation of their transmission angle from the ideal of 90° throughout the entire range of motion. When these solutions are mapped into a Cartesian plane, the ground pivot locations produce curves similar to the familiar Burmester curves for four-position synthesis problems. Additional advantages of the approach are that the input link is automatically a crank, the desired link length ratio can be controlled, and the solutions are free of defects.