Studies on Synthesis of Symmetrical Coupler Curves Having Ball’s Points

Abstract

This paper deals with the synthesis of four-bar linkage symmetrical coupler curves having Ball’s point on each flank. These are synthesized for driving a jerk free internal Geneva mechanism for a given locking to moving period ratio. The synthesis procedure uses the analytical trigonometric equations based on the properties of triangles unlike the approach documented in literature. These set of trigonometric equations have been solved numerically. Advantage of this method of synthesis is that the mechanism can be easily synthesized for a given locking to moving period ratio which is important while replacing a traditional internal Geneva with a four-bar driven Geneva mechanism, for maintaining the overall manufacturing and assembly process times. Also, the mechanisms are synthesized for equal critical transmission angles, yielding the same results as reported previously, thus validating the current approach. The evolutes of the synthesized coupler curves are plotted and the characteristics are studied to indicate the Ball’s point. A new method of synthesizing Ball’s point is presented. The synthesis procedure is also applied to synthesize a coupler curve for driving a coupler point in a V-channel to be used for developing a scrappping machine. The present problem could be of much interest to the computational kinematics researchers working with polynomial elimination methods for testing their efficacy. © 2024, The Author(s), under exclusive license to Springer Nature Switzerland AG.