Nonlinear Dynamics

, Volume 31, Issue 2, pp 167–195 | Cite as

Formulation of Three-Dimensional Joint Constraints Using the Absolute Nodal Coordinates

  • Hiroyuki Sugiyama
  • José L. Escalona
  • Ahmed A. Shabana


A wide variety of mechanical and structural multibody systems consist ofvery flexible components subject to kinematic constraints. The widelyused floating frame of reference formulation that employs linear modelsto describe the local deformation leads to a highly nonlinear expressionfor the inertia forces and can be applied to only small deformationproblems. This paper is concerned with the formulation and computerimplementation of spatial joint constraints and forces using the largedeformation absolute nodal coordinate formulation. Unlike the floatingframe of reference formulation that employs a mixed set of absolutereference and local elastic coordinates, in the absolute nodalcoordinate formulation, global displacement and slope coordinates areused. The nonlinear kinematic constraint equations and generalized forceexpressions are expressed in terms of the absolute global displacementsand slopes. In particular, a new formulation for the sliding jointbetween two very flexible bodies is developed. A surface parameter isintroduced as an additional new variable in order to facilitate theformulation of this sliding joint. The constraint and force expressionsdeveloped in this paper are also expressed in terms of generalizedCholesky coordinates that lead to an identity inertia matrix. Severalexamples are presented in order to demonstrate the use of theformulations developed in the paper.

flexible multibody systems large deformation problems joint formulations sliding joints 


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Copyright information

© Kluwer Academic Publishers 2003

Authors and Affiliations

  • Hiroyuki Sugiyama
    • 1
  • José L. Escalona
    • 2
  • Ahmed A. Shabana
    • 1
  1. 1.Department of Mechanical EngineeringUniversity of Illinois at ChicagoChicagoU.S.A
  2. 2.Department of Mechanical and Materials EngineeringUniversity of SevilleSevilleSpain

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