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

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

Automated summary

This paper presents a systematic study of 3-UPU translational parallel mechanisms (TPMs) with skewed base and moving platform. The classification of these TPMs is based on their constraint singularity loci, and a novel 3-UPU TPM is proposed. Reconfiguration analysis shows that this new TPM can only transition from a 3-DOF translational mode to one general 3-DOF operation mode. The work also reveals a 3-UPU parallel mechanism that allows for 3-DOF translation and 1-DOF infinitesimal rotation of the moving platform.