| Author | R. M. Mukherjee & K.S. Anderson |
|---|---|
| Title | Orthogonal Complement Based Divide-and-Conquer Algorithm (O-DCA) for Constrained Multibody Systems |
| Year | 2006 |
| Journal | Nonlinear Dynamics |
| Abstract | Abstract 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 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 constraint |
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