树形多体系统动力学约束力算法

多体系统高效动力学算法一直是多体系统动力学的重要研究方向.近年来,众多高效算法虽然在提高解算效率方面取得了一定研究成果,但大多无法直接给出多体系统的显式动力学方程或解算系统约束力.基于以上问题,研究了适用于任意树形多体系统动力学解算的约束力算法(constraint force algorithm,CFA)及其串行化应用.约束力算法可在解算多体系统动力学的过程中对系统约束力进行求解,该算法串行化后计算量仅与自由度成线性关系.通过分析树形多体系统中任意节点处的动力学、运动学递推关系并讨论系统方程的组集方法,将仅适用于链状系统的算法推广至任意树形系统,并给出了其串行化应用方法以提高算法效率.在数值仿真中,将所提算法与递推算法进行对比,验证了所提出的约束力算法的准确性;此外,通过对比4种不同算法在相同工作环境下解算同一模型时的处理器运行时间,证实了串行化约束力算法的高效性.

CONSTRAINT FORCE ALGORITHM FOR TREE-LIKE MULITBODY SYSTEM DYNAMICS

The e cient dynamics algorithm for multibody system has always been a research hotspot. In recent years, many e cient dynamics algorithms made progresses in improving the computational e ciency, but most of them cannot provide an explicit expression of the system's dynamics or resolve the constraint forces. Based on the above issue, a constraint force algorithm (CFA) and its serialized application for the dynamics modelling of an arbitrary multibody system in tree-topology are studied in this paper. The constraint forces for the system can be directly obtained by solving for the system motion through CFA. The presented algorithm is an extension of the original CFA which is only applicable to a single-chained system. It is obtained by analysing the dynamics and kinematics of an arbitrary node in a treelike system. Serialization of the algorithm is developed to reduce the computational cost to a linear relationship with the number of degrees of freedoms (DOFs). The accuracy of the proposed method is validated through a numerical simulation of a space robot with multiple manipulators. The e ciency of the serialized CFA is verified by comparing the CPU time of di erent algorithms.