A Symmetrical RRPRR Robust Coupling for Crossed Axes Transmission

Abstract

A new coupling solution for transmitting the rotation motion between two shafts with crossed axes is proposed. Based on structural considerations, a planar (P) pair is introduced into the structure of the mechanism, presenting the advantage of reduced costs due to the constructive and manufacturing simplicity and to high reliability. The proposed mechanism is of the RRPRR type, and the structural symmetry simplifies substantially the construction of the mechanism. The constructive parameters of the mechanism are the angle and distance between the driving and driven shaft and also the length of the common normal between the axes of driving and driven revolute (R) pairs, and the axes of the revolute pairs of the coupling chain, respectively. Due to the presence of the planar pair, the Hartenberg–Denavit method of homogenous operators is not applicable. The kinematic analysis for a specified motion of the driving element requires two stages: finding the relative motions from the revolute pairs and the motions from the planar pair. The RRPRR transmission is analysed for geometrical asymmetrical and symmetrical cases; the latter is more convenient and the design principles are presented. Concerning the dimensional optimization, it is found to be a methodology for ensuring that the transmission ratio of the mechanism can be maintained within a stipulated range. Based on the kinematical calculus and geometrical optimization, the mechanism was designed and manufactured.