Algebraic insight on the concomitant motion of 3RPS and 3PRS PKMs

Abstract

This study presents an algebraic method to detect, count, and identify concomitant motions of parallel robots at the velocity level. The pose and orientation of moving platform of parallel manipulators (PMs) with f-DOF could be commonly described by f possible motion variables on the instantaneous motion space (IMS) and (6−f) (6−f) restriction motion variables on the instantaneous restriction space (IRS). However, in some situations, PMs moving platform may accompanied by a concomitant (parasitic) motions along the direction of restriction space. Therefore, the commonly understood one-to-one correspondence between joint space and task space mobility of non-redundant PMs would be compromised. This phenomenon occurred due to the fact that the alignment of screws can change the reciprocal screws while the given screw systems are still maintained. To demonstrate the proposed method, an amplitude-based concomitant motion comparison is performed on two widely utilized lower-mobility parallel mechanisms, 3RPS and 3PRS. The result has shown that for the selected mechanisms, concomitant motion is identical regardless of their difference in joint arrangements in each limbs.