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

Xianwen Kong*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contribution


A 3-UPU translational parallel mechanism (TPM) is one of typical TPMs. Several types of 3-UPU TPMs have been proposed in the literature. 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 a skewed base and moving platform have been proposed. However, the impact of link parameters on singularity loci of such TPMs has not been systematically investigated. The advances in computing CGS (comprehensive Gröbner system) or Gröbner cover of parametric polynomial systems provide an efficient tool for solving this problem. This paper presents a systematic classification of 3-UPU TPMs, especially those with a skewed base and moving platform, based on constraint singularity loci. First, the constraint singularity equation of a 3-UPU TPM 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 are classified into 20 types based on the constraint singularity loci. 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 operation mode in a constraint singular configuration. The singularity locus divides the workspace of this 3-UPU TPM into two constraint singularity-free regions. This work provides a solid foundation for the design of 3-UPU TPMs and a starting point for the classification of a general 3-UPU parallel mechanism.

Original languageEnglish
Title of host publication45th Mechanisms and Robotics Conference (MR)
PublisherAmerican Society of Mechanical Engineers
ISBN (Electronic)9780791885451
Publication statusPublished - 17 Nov 2021
Event45th Mechanisms and Robotics Conference 2021 - Virtual, Online
Duration: 17 Aug 202119 Aug 2021


Conference45th Mechanisms and Robotics Conference 2021
Abbreviated titleMR 2021
CityVirtual, Online


  • Constraint singularity
  • Euler parameters
  • Gröbner Cover
  • Operation mode
  • Quaternion
  • Translational parallel mechanism

ASJC Scopus subject areas

  • Mechanical Engineering
  • Computer Graphics and Computer-Aided Design
  • Computer Science Applications
  • Modelling and Simulation


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