Properties of the bennett mechanism derived from the RRRS closure ellipse

Paul Milenkovic, Morgan V. Brown

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


For many single-loop closed-chain mechanisms, mobility may be characterized by the closure of sets in the theory of Lie groups. The four-revolute (4R) Bennett mechanism remains a persistent exception, requiring the formulation and expression of solutions to the loop closure relations, either directly or indirectly through spatial geometric figures. The simpler loop closure relations of the revolute-revolute-revolute-spherical (RRRS) loop, however, place conditions on the mobility of the 4R mechanism. That loop closure in turn may be interpreted as the congruence of a pair of ellipses. This new result is applied to proving the uniqueness of the Bennett mechanism along with deriving conditions where it is free from singularities. Design parameters are also identified for overconstrained RRRS mechanisms with 1DOF that are neither plane nor line symmetric. Such mechanisms, however, place the S-joint along the revolute axis of an underlying Bennett mechanism.

Original languageEnglish (US)
Article number021012
JournalJournal of Mechanisms and Robotics
Issue number2
StatePublished - Apr 19 2011
Externally publishedYes


  • Bennett mechanism
  • Closure equations
  • Overconstrained mechanism
  • Paradoxical linkage

ASJC Scopus subject areas

  • Mechanical Engineering


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