A lightweight algorithm for handling closed-loop constraints based on the reduced multibody system transfer matrix method

• Published in: Nonlinear dynamics Vol. 113; no. 8; pp. 8139 - 8160
• Main Authors: Yue, Qixing, Rui, Xiaoting, Zhang, Jianshu, Li, Tang, Miao, Yangyang
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.04.2025; Springer Nature B.V
• Subjects: Algorithms; Applications of Nonlinear Dynamics and Chaos Theory; Classical Mechanics; Closed loops; Constraints; Control; Dynamical Systems; Matrix methods; Multibody systems; Physics; Physics and Astronomy; Statistical Physics and Dynamical Systems; Topology; Transfer matrices; Vibration; Transfer matrix method; Multibody systems; Closed loops; Constraint equations
• ISSN: 0924-090X; 1573-269X
• DOI: 10.1007/s11071-024-10503-3

Forward dynamics of a general multibody system may be performed recursively by utilizing the reduced transfer matrix method, via replacing closed loops by constraint equations and forces as well as adopting tree topology. A lightweight algorithm is proposed in this paper for handling these constraint equations and forces elegantly. The transfer equation of each connection point is reformulated in a form that is only directly related to the closed-loop constraint forces of the loops at which the point is located. Complementarily, the closed-loop constraint equations, as well as the constraint forces of closed loops, are evaluated at the corresponding closed loops' root markers instead, eliminating redundant recursive evaluations involved in the previous strategy. Three examples of closed-loop multibody systems are studied to illustrate the effectiveness, universality, and efficiency of the proposed algorithm respectively. It can be concluded that the proposed algorithm implies a novel treatment for closed loops and expands the applicability of the reduced multibody system transfer matrix method.