Session: MR-02-01 Theoretical & Computational Kinematics

Paper Number: 70059

Start Time: August 18, 10:00 AM

70059 - Classification of 3-DOF 3-UPU Translational Parallel Mechanisms Based on Constraint Singularity Loci Using Gröbner Cover 

A 3-UPU translational parallel mechanism (TPM) is one of the typical TPMs. Several types of 3-UPU TPMs have been pro-
posed in the literature. Comprehensive studies on 3-UPU TPMs in which the joint axes on the base and the moving platform
are coplanar have been carried out. These TPMs have different constraint singular surfaces and therefore different perfor-
mances. However, only a few 3-UPU TPMs with a skewed base and moving platform have been proposed. However, the impact of link parameters on singularity surfaces of such TPMs, which is challenging, have not been systematically investigated. The advances in computing CGS (comprehensive Gröbner system) or Gröbner cover of parametric polynomial systems provide an efficient tool for tackling this problem. This paper presents a systematic classification of 3-UPU TPMs, especially those with a skewed base and moving platform, based on constraint singular surfaces. First, the equation of singularity surface is derived. To simplify this equation, the coordinate frame on the base (or moving platform) is set up such that the centers of three U joints are located on different coordinate axes. Using Gröbner Cover, the 3-UPU TPMs is classified into 20 types based on the constraint singularity surface. Geometric characteristics of the several types of 3-UPU TPMs are then identified. Finally, a novel 3-UPU TPM is proposed. Unlike most of existing 3-UPU TPMs which can transit to two or more 3-DOF operation modes at a constraint singular configuration, the proposed 3-UPU TPM can only transit to one general 3-DOF motion mode in a constraint singularity configuration. and all the motion modes of the TPM are revealed. This work provides a solid foundation for the design and control of 3-UPU TPMs and a starting point for the classification of a general 3-UPU PM.

Presenting Author: Xianwen Kong Heriot-Watt University

Authors:

Xianwen Kong Heriot-Watt University