A Short Note on Equivalent Four-Bar Linkages of Direct-Contact Mechanisms

Abstract

In this paper, kinematic analysis for two types of classical direct-contact mechanisms, planar gear mechanisms with a pair of involute spur gears and disk cam mechanisms with a circular-arc cam and an oscillating roller follower, are presented in order to discuss the inequivalence of the direct-contact mechanisms and their equivalent four-bar linkages in jerk analysis. For the discussed gear mechanisms, it is found that the equivalent four-bar linkage is not able to give a correct value of jerk, unless the angular velocity ratio between the two mating gears is exactly negative one. For the discussed cam mechanisms, as the circular-arc cam is in contact with its follower at a point of tangency of two adjacent circular arcs, the two equivalent four-bar linkages simultaneously existing at that instant are both not able to correctly reflect an infinite jerk of the follower, because the suddenly changed curvature of the cam profile is not considered in sudden link-length variations of the equivalent linkages. The two presented case studies can give demonstrations for understanding the inequivalence of the direct-contact mechanisms and their equivalent four-bar linkages in the aspect of jerk analysis.