Multibody System Dynamics

, Volume 29, Issue 2, pp 139–168 | Cite as

Constraint-wrench analysis of robotic manipulators

  • Afshin Taghvaeipour
  • Jorge Angeles
  • Larry Lessard


The constraint-wrench analysis of mechanisms, with focus on parallel robots, is the subject of this paper. Although the method proposed here can be generalized for parallel robots with multiple-loop kinematic chains, here, single-loop chains are targeted. To this end, a novel representation of the constraints imposed by the kinematic pairs is introduced. With this representation, the constraint matrix of a mechanism is readily derived. For the calculation of the constraint wrenches, by means of the constraint matrix and based on the Newton–Euler formulation, a new procedure is introduced. As a case study, the constraint wrench analysis of the McGill Schönflies Motion Generator (SMG), while undergoing a test cycle adopted by the industry, is conducted.


Constraint-wrench analysis Parallel robots Constraint matrix Newton–Euler formulation Schönflies motion generators (SMG) 



The authors would like to thank Canada’s Natural Sciences and Engineering Research Council (NSERC) for providing funds to support this research via an Idea to Innovation Grant, which allowed the team to produce the experimental platform motivating the work reported here. Further work has been supported under NSERC’s Discovery Grants program and partly through a James McGill Professorship to the second author.


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Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  • Afshin Taghvaeipour
    • 1
  • Jorge Angeles
    • 1
  • Larry Lessard
    • 2
  1. 1.Department of Mechanical Engineering and Centre for Intelligent MachinesMcGill UniversityMontrealCanada
  2. 2.Department of Mechanical EngineeringMcGill UniversityMontrealCanada

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