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Orthogonal Complement Based Divide-and-Conquer Algorithm (O-DCA) for Constrained Multibody Systems

Summary: Orthogonal Complement Based Divide-and-Conquer
Algorithm (O-DCA) for Constrained Multibody Systems
Rudranarayan M. Mukherjee, Kurt S. Anderson
Computational Dynamics Laboratory
Department of Mechanical Aerospace and Nuclear Engineering.
Rensselaer Polytechnic Institute
110 8th Street. Troy NY 12180 USA
e-mail: mukher@rpi.edu, anderk5@rpi.edu
March 15, 2006
Keywords: Closed Kinematic Loops, Orthogonal Complement, Singular Configurations, Logarithmic
Computational Complexity, Divide and Conquer.
A new algorithm is presented in this paper for calculating the forward dynamics of multi-rigid bodies
connected together by kinematic joints to form single or coupled closed loop topologies. The algorithm
is exact and non-iterative. 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


Source: Anderson, Kurt S. - Department of Mechanical, Aerospace and Nuclear Engineering, Rensselaer Polytechnic Institute


Collections: Computer Technologies and Information Sciences