Nonlinear Dynamics

, Volume 48, Issue 1–2, pp 199–215 | Cite as

Orthogonal Complement Based Divide-and-Conquer Algorithm for constrained multibody systems

Original Article


A new algorithm, Orthogonal Complement based Divide-and-Conquer Algorithm (O-DCA), is presented in this paper for calculating the forward dynamics of constrained multi-rigid bodies including topologies involving single or coupled closed kinematic loops. The algorithm is exact and noniterative. The constraints are imposed at the acceleration level by utilizing a kinematic relation between the joint motion subspace (or partial velocities) and its orthogonal complement. Sample test cases indicate excellent constraint satisfaction and robust handling of singular configurations. Since the present algorithm does not use either a reduction or augmentation approach in the traditional sense for imposing the constraints, it does not suffer from the associated problems for systems passing through singular configurations. The computational complexity of the algorithm is expected to be O(n+m) and O(log(n+m)) for serial and parallel implementation, respectively, where n is the number of generalized coordinates and m is the number of independent algebraic constraints.


Closed kinematic loops Orthogonal complement Singular configurations Logarithmic computational complexity Divide-and-Conquer 


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© Springer Science + Business Media, B.V. 2006

Authors and Affiliations

  1. 1.Computational Dynamics Laboratory, Department of Mechanical Aerospace and Nuclear EngineeringRensselaer Polytechnic InstituteTroyUSA

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