On the Successive Constraint Imposition Approach to Multibody Mechanisms

Harry Dankowicz

Research output: Contribution to journalArticlepeer-review


A method is described for the successive imposition of constraints on a free particle mechanism and the subsequent derivation of closed sets of differential equations for the evolution of the mechanism with time. Fundamental is the idea of ideal constraints as contained in d'Alembert's principle. In particular, it is shown how constraints may be added one or more at a time, thereby obtaining intermediate descriptions with more dynamic freedom than the final mechanism. As a simple example, it is shown that the rigid body is such an intermediate description. The method is also applied to the problem of a chain of n particles or n rigid rods. Both an inductive and a constructive approach are demonstrated in deriving the equations of motion for arbitrary n.

Original languageEnglish (US)
Pages (from-to)267-286
Number of pages20
JournalMultibody System Dynamics
Issue number3
StatePublished - 1999
Externally publishedYes


  • Analytical mechanics
  • Chains
  • Constraints
  • Induction
  • Orthogonal complements
  • Recursivity
  • d'Alembert's principle

ASJC Scopus subject areas

  • Modeling and Simulation
  • Aerospace Engineering
  • Mechanical Engineering
  • Computer Science Applications
  • Control and Optimization


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