Tolerance analysis and synthesis of cam-modulated linkages

Cam-modulated linkages that can achieve superior kinematic performance as compared with pure linkages have been widely applied in a variety of automation machinery. The tolerance analysis and synthesis are thus quite essential in the design and manufacture of precision cam-modulated linkages. This paper presents comprehensive and systematic mathematical tools for dealing with the tolerance analysis and synthesis of cam-modulated linkages. Based on the concept of equivalent linkage and the derived correlation between the radial-dimension errors and the normal-direction errors of the cam profile, the sensitivity analysis method for equivalent linkages is introduced for analyzing the tolerances in cam-modulated linkages, whose output error equations can be derived through an analytical means. Then, by incorporating the sensitivity analysis method and the concept of design for manufacturing and assembly (DFMA), an optimization model for synthesizing the tolerances in cam-modulated linkages is developed. The objective of this optimization model is to maximize the manufacturability and assembility of a cam-modulated linkage while maintaining acceptable kinematic accuracy of its output motion. A practical case study of analyzing and synthesizing the tolerances in a cam-modulated linkage type pick-and-place device is then performed to illustrate the presented methods. It shows that the mathematical tools presented can be helpful to the design and manufacture of precision cam-modulated linkages.