Solution for the Kinematics of Non-H-D Couplings Applied to RPCR Mechanism

Abstract

The paper presents a proposed mechanism, RPCR, for the coupling of two shafts with crossed axes. For the analytical kinematics, the Hartenberg–Denavit methodology cannot be applied due to the planar pair occurrence. To apply the screw theory, the planar pair should be replaced by an assembly of cylindrical pairs, but this is also cumbersome. This work proposes an analytical solution obtained from the structural condition of planar joint based on the formulated expressions with respect to adequately chosen reference frames. A system of trigonometrical equations is obtained, but confusions may occur from classical solving; then, this paper presents the methodology with the correct approach. With the analytical solution for the displacements from the joints found, the conditions required for the constructive parameters of a realistic mechanism are found. The kinematical calculus of the mechanism is presented, and analytical relations are obtained for all relative motions from the pairs of the mechanism. The correctness of the analytical solutions is validated by the results of a numerical simulation.