A modelling approach for kinematic equivalent mechanism and rotational transmission error of RV reducer

• Instantaneous kinematic equivalent mechanism of RV reducer. • Modelling approach for rotational transmission error of entire machine. • Explicit equations of original errors and transmission precision. • Validation by the test of prototypes. This paper presents a method for the analytical error modelling of RV reducer concerning its over-constrained structure, which explicitly establishes the relations between the original errors and the transmission precision. According to the structural characteristic, i.e., the rotation and revolution of the cycloidal gear share three crankshafts , an equivalent multi-loop mechanism of the reducer is achieved through replacing higher pairs by lower pairs, which decouples the over-constrained relations among the multi-crank actuation . And the error model of the reducer is thus developed by the loop incremental method, in which the manufacturing and assembly errors are represented by the linkage length errors in the equivalent mechanism. Finally, the proposed model is validated by the test results of prototypes, and the influence of original errors is respectively investigated. The outcomes provide a new idea for error modelling and components accuracy design of RV reducer and other precision gear systems.