Variable Degree-of-Freedom Spatial Mechanisms Composed of Four Circular Translation Joints

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


This paper deals with the construction and reconfiguration analysis of a spatial mechanism composed of four circular translation (G) joints. Two links connected by a G joint, which can be in different forms such as a planar parallelogram, translate along a circular trajectory with respect to each other. A spatial 4G mechanism, which is composed of four G joints, usually has 1-DOF (degree-of-freedom). Firstly, a 2-DOF 4G mechanism is constructed. Then a novel variable-DOF spatial 4G mechanism is constructed starting from the 2-DOF 4G mechanism using the approach based on screw theory. Finally, the reconfiguration analysis is carried out in the configuration space using dual quaternions. The analysis shows that the variable-DOF spatial 4G mechanism has one 2-DOF motion mode and one to two 1-DOF motion modes and reveals how the 4G mechanism can switch among these motion modes. By removing one link from two adjacent G joints each and two links from each of the remaining two G joints, we can obtain a queer-rectangle and a queer-parallelogram, which are the generalization of the queer-square or derivative queer-square in the literature. The approach in this paper can be extended to the analysis of other types of coupled mechanisms using cables and gears and multi-mode spatial mechanisms involving G joints.
Original languageEnglish
Title of host publication44th Mechanisms and Robotics Conference (MR)
PublisherAmerican Society of Mechanical Engineers
ISBN (Print)9780791883990
Publication statusPublished - 3 Nov 2020
Event44th Mechanisms and Robotics Conference 2020 - St. Louis, United States
Duration: 16 Aug 202019 Sept 2020

Publication series

NameASME 2020 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference


Conference44th Mechanisms and Robotics Conference 2020
Country/TerritoryUnited States
CitySt. Louis


  • Algebraic geometry
  • Circular translation joint
  • Dual quaternions
  • Reconfiguration analysis
  • Variable-DOF mechanism

ASJC Scopus subject areas

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


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