Kinematic analysis of conventional and multi-mode spatial mechanisms using dual quaternions

Xianwen Kong*

*Corresponding author for this work

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

6 Citations (Scopus)


Although kinematic analysis of conventional mechanisms is a well-documented fundamental issue in mechanisms and robotics, the emerging reconfigurable mechanisms and robots (or mechanisms and robots with multiple operation modes) require reexamining this fundamental issue. Recent advances in mathematics, especially algebraic geometry and numerical algebraic geometry, make it possible to develop an efficient method for the kinematic analysis of not only conventional mechanisms and robots but also reconfigurable mechanisms and robots. This paper first presents a method for setting up a set of kinematic loop equations for mechanisms using dual quaternions. Using this approach, a set of kinematic loop equations of a spatial mechanism is composed of six equations. The effectiveness of the proposed kinematic loop equations is then demonstrated by deriving the explicit input-output equations of a line symmetric 1-DOF (degree-of-freedom) 7R single-loop spatial mechanism, the reconfiguration analysis of a novel multi-mode 1-DOF 7R spatial mechanism. In the former case, an explicit input-output equation of degree 8 is derived. In the latter case, it is found that the 7R multi-mode mechanism has three motion modes, including a planar 4R mode, an orthogonal Bricard 6R mode, and a plane symmetric 6R mode. Unlike the 7R multi-mode mechanisms in the literature, the 7R multi-mode mechanism presented in this paper does not have a 7R mode in which all the seven R joints can move simultaneously.

Original languageEnglish
Title of host publicationASME 2016 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
PublisherAmerican Society of Mechanical Engineers
ISBN (Electronic)9780791850169
Publication statusPublished - 2016
Event40th Mechanisms and Robotics Conference 2016 - Charlotte, United States
Duration: 21 Aug 201624 Aug 2016


Conference40th Mechanisms and Robotics Conference 2016
Country/TerritoryUnited States


  • Algebraic geometry
  • Dual quaternions
  • Kinematic analysis
  • Multi-mode mechanisms
  • Reconfiguration analysis

ASJC Scopus subject areas

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


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