Computation of velocity in a plane joint, with application to the Tracta coupling

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A methodology designed for practical computer coding is developed to implement the velocity analysis of mechanisms with a plane joint, that is, a joint consisting of two flat surfaces held in contact to permit one rotational and two translational degrees of freedom. The analysis utilizes the 3 × 3 dual-number coordinate transformation modelling of joints and links of a mechanism to develop the results in a compact form amenable to object-oriented programming of displacement and velocity calculations. The velocity analysis of the Tracta coupling, an RRERR mechanism (rotation-rotation-plane-rotation-rotation joints) that has been used as a constant-velocity shaft coupling, is given as an example for a mechanism with a plane joint. An explanation is given of the relationship between the calculated speeds and the physical speeds in a plane joint.

Original languageEnglish (US)
Pages (from-to)263-270
Number of pages8
JournalProceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-body Dynamics
Issue number3
StatePublished - 2002

All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics
  • Mechanical Engineering


  • Constant-velocity coupling
  • Dual number
  • Plane joint
  • Tracta coupling
  • Velocity


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