Computational kinematics of multibody systems: Two formulations for a modular approach based on natural coordinates

Abstract Multibody systems can be divided into an ordered set of kinematically determined modules, known as structural groups, in order to compute their kinematics more efficiently. In this work a procedure for the kinematic analysis of any kind of structural group is introduced, and two different methods for their solution in natural coordinates are presented: the time derivative (TD) and the third-order tensor (3OT) approaches. Moreover, the newly derived methods are compared in terms of efficiency with a global formulation, consisting in solving the kinematics of the multibody system as a whole using dense and sparse solvers. Two scalable case studies have been considered: a 2D four-bar linkage and a 3D slider-crank mechanism with an increasing number of constraint equations. The results show that the TD approach performs better in all cases with speed ups in a range of 27 to 61 times faster in 2D, and of 2.3 to 3.7 times faster in 3D with respect to the global sparse solution.

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