Application of the rigid finite element method to modeling multibody systems with redundant constraints

Abstract The research aimed to investigate the applicability of the Rigid Finite Element Method (Rigid-FEM), which is an alternative to the classical Finite Element Method, for modeling multibody systems with redundant constraints. The investigation focused on resolving problems with determining reaction forces. Such problems are encountered in classical rigid multibody dynamics formulations. The methods used include the development of an underlying theory, diverse simulations, and experimental verification. Specifically, the theoretical foundation of the Rigid-FEM method—discretizing rigid bodies into smaller rigid finite elements interconnected by spring-damper elements (SDEs) with appropriately defined stiffness and damping properties—was supplemented by proposed methodological modifications that significantly reduce the number of required SDEs and improve computational efficiency. To perform a variety of tests, a spatial parallelogram benchmark mechanism was used. Results from both Rigid-FEM and classic FEM models were analyzed. A comprehensive parametric study was conducted to assess the influence of selected modeling parameters on accuracy and computational efficiency, including the placement of elastic elements, discretization density, and the introduction of a shear coefficient. Ultimately, the simulation results were compared with experimental data obtained from measurements conducted on a hardware mechanism. The findings demonstrate that the modified Rigid-FEM achieves accuracy comparable to the regular FEM model, yet requires significantly fewer elements and delivers results in substantially reduced computational time. Although the Rigid-FEM is limited to plate- and beam-like structures, these components constitute the primary structural elements of many mechanisms, such as parallel robots, where constraint redundancy is frequent and renders classical rigid multibody dynamics formulations incapable of determining reaction forces. The results, validated against experimental data, confirm the suitability of Rigid-FEM as a highly efficient and accurate computational tool for analyzing overconstrained multibody systems.