A double-faced 6R Single-loop Overconstrained Spatial Mechanism

Xianwen Kong, Xiuyun He, Duanling Li

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)
177 Downloads (Pure)


This paper deals with a 6R single-loop overconstrained spatial mechanism that has two pairs of revolute joints with intersecting axes and one pair of revolute joints with parallel axes. The 6R mechanism is first constructed from an isosceles triangle and a pair of identical circles. The kinematic analysis of the 6R mechanism is then dealt with using a dual quaternion approach. The analysis shows that the 6R mechanism usually has two solutions to the kinematic analysis for a given input and may have two circuits (closure modes or branches) with one or two pairs of full-turn revolute joints. In two configurations in each circuit of the 6R mechanism, the axes of four revolute joints are coplanar, and the axes of the other two revolute joints are perpendicular to the plane defined by the above four revolute joints. Considering that from one configuration of the 6R mechanism, one can obtain another configuration of the mechanism by simply renumbering the joints, the concept of two-faced mechanism is introduced. The formulas for the analysis of plane symmetric spatial triangle is also presented in this paper. These formulas will be useful for the analysis of multi-loop overconstrained mechanisms involving plane symmetric spatial RRR triads.
Original languageEnglish
Article number031013
JournalJournal of Mechanisms and Robotics
Issue number3
Early online date5 Apr 2018
Publication statusPublished - Jun 2018


  • Overconstrained mechanism
  • Dual quaternions
  • Two-faced mechanism
  • Plane symmetric spatial triangle
  • Geometric approach

ASJC Scopus subject areas

  • Mechanical Engineering
  • Geometry and Topology


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