Displacement Analysis of the Generalized Clemens Coupling, The R-R-S-R-R Spatial Linkage

The Clemens Coupling is a constant-velocity, universal-type joint for nonparallel intersecting shafts. This mechanism is a spatial linkage with five links connected by four revolute pairs, R, and one spherical pair (ball-and-socket joint), S, which is located symmetrically with respect to the input and output shafts. The Clemens Coupling is a special case of the R-R-S-R-R spatial linkage with general proportions, which will, therefore, be called the Generalized Clemens Coupling. This paper gives the algebraic derivation of the input-output equation for the general R-R-S-R-R linkage and demonstrates that it is a fourth-order polynomial in the half tangents of the crank angles. The effect of housing-error tolerances on the displacements of the Clemens Coupling has also been considered. The results demonstrate feasibility of closed-form solutions for five-link mechanisms with kinematic pairs having more than two degrees of freedom.