Computational Kinematics of Multibody Systems: The Advantages of a Topological Method Based on its Kinematic Structure

In this work a topological formulation that automatically models and solves the kinematics of multibody systems taking advantage of their kinematic structure is presented. The kinematic structure of a multibody system specifies the set and the order of the kinematic chains (structural groups) into which it can be divided, and allows the automatic definition of dependent and independent sets of coordinates needed to solve the kinematics of each one of its structural groups. A systematic method to solve the kinematics of any structural group using two different types of coordinates and formulations is presented. These solutions can be programmed in specific subroutines and called from a main program in the order specified by its kinematic structure so as to analyse the whole multibody system. These formulations have been implemented in the MATLAB programming environment, and their efficiency compared against other two formulations - global and global sparse -, making use of a scalable four-bar linkage whose number of constraint equations can be controlled by adding a different number of dyads. The computing time distribution among the main mathematical operations is compared and the main advantages of the topological methods are discussed.

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