The Potential of the 7R-R Closed Loop Mechanism to Transfer Motion Between Two Shafts with Varying Angular Position

Abstract

Transmission of the motion between two shafts can be obtained by a Double Cardan Joint (DCJ), which, under particular geometrical conditions, can be homokinetic. A DCJ can be regarded as a 7R closed loop mechanism, which highly reduces the technical/manufacturing complexity when compliant joints are used to replace the R revolute joints. The case of intersecting shaft axes with varying relative orientation is of particular interest in many applications and can be efficiently modeled by a symmetric 7R-R closed loop mechanism to get a homokinetic transmission. This paper deals with the analysis of a type of symmetric 7R-R mechanism, for the homokinetic motion transmission between two incident shafts. Specialized closure equations are written to obtain a closed-form solution of the position analysis. The analysis of both the radial envelope (which affects the mechanism size) and the mechanism singularities are conducted. In particular, a direct relation between the maximum value of the radial envelope and the angle between the shafts is presented. Moreover, the geometrical parameters that determine singularity conditions of the mechanism are found. The singularity configurations are also geometrically analyzed, which disclose the feature of the mechanism to evolve into two different configurations, namely a spherical 4R and a symmetric 7R mechanism. These results can be used for the mechanism dimensioning.