Geometric algebra approach to analyzing the singularity of six-DOF parallel mechanism

Shili Cheng, Ping Ji

Research output: Journal article publicationJournal articleAcademic researchpeer-review

3 Citations (Scopus)


Singular configurations must be avoided in the practical manipulation of parallel mechanism. This paper presents an approach of singularities analysis of six degrees of freedom (DOF) parallel mechanism applying geometric algebra. Twists of all passive joints in each limb are described in geometric algebra while all the active joints are locked. And wrenches produced from each limb and acting on the moving platform are derived from the calculations of the outer product and its dual of the corresponding twists. The singular condition of parallel mechanism depends on whether the wrenches acting on the moving platform failed to constrain all the motions, which can be accomplished by the outer product with its duality followed. Two six-DOF parallel mechanisms 6-UPS and 6-PUS are introduced to verify the approach proposed in this paper. The results indicate that geometric algebra can also be used for singularity analysis of six-DOF parallel mechanism.

Original languageEnglish
JournalJournal of Advanced Mechanical Design, Systems and Manufacturing
Issue number4
Publication statusPublished - 1 Jan 2019


  • 6-PUS
  • 6-UPS
  • : Singularity analysis
  • Duality
  • Geometric algebra
  • Parallel mechanism
  • Screw

ASJC Scopus subject areas

  • Mechanical Engineering
  • Industrial and Manufacturing Engineering


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