Recursive Dynamics Algorithms for Serial, Parallel, and Closed-chain Multibody Systems

In this paper, it is shown how to obtain recursive dynamics algorithms for multibody systems with serial, parallel, and closed-loop chains using the concept of Decoupled Natural Orthogonal Complement (DeNOC) matrices. The DeNOC is the product of two block matrices to yield the Natural Orthogonal Complement (NOC), which is a velocity transformation matrix orthogonal to the kinematic constraint matrix of the system at hand. Note that one of the two DeNOC matrices is a lower block triangular and the other one is a block diagonal. This representation allows one to compute the inverse and forward dynamics algorithms of the constrained multibody systems recursively, which was not possible with the original representation of the NOC. As a result, the computational complexities of the algorithms are reduced in many instances, particularly, in forward dynamics with large number of bodies in a system, e.g., space robots, parallel robots, vehicle systems, etc. Moreover, many physical interpretations are available, for example, articulated body inertia, etc., which can be exploited for debugging of a program and architecture design. Illustrations with several multibody systems, e.g., two six-degrees-of-freedom serial manipulators, a parallel manipulator, a carpet scrapping machine with general closed-chain, are presented.

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