Classification of 3-Degree-of-Freedom 3-UPU Translational Parallel Mechanisms Based on Constraint Singularity Loci Using Gröbner Cover

Abstract A 3-degree-of-freedom (DOF) 3-UPU translational parallel mechanism (TPM) is one of the typical TPMs. Despite comprehensive studies on TPMs in which joint axes base and moving platform are coplanar, only a few with skewed have been proposed, impact link parameters constraint singularity loci such has not systematically investigated. The advances computing Gröbner system (CGS) or cover parametric polynomial systems provide an efficient tool for solving this problem. This paper presents systematic classification based loci. First, equation TPM derived. Using cover, classified into 12 types. Finally, novel proposed. Reconfiguration analysis shows that unlike most existing can transit from 3-DOF mode to two more operation modes, proposed general mode. locus divides workspace singularity-free regions. As by-product, undergo translation 1-DOF infinitesimal rotation revealed. work provides solid foundation design starting point mechanisms.