摘要
基于Kane方法,针对约束多体系统,建立了一种新型的自动组集系统动力学方程的方法.首先提出偏速度矩阵和偏角速度矩阵的概念,将各体对系统广义惯性力的贡献用简洁、统一的数学形式表达.然后引入各个运动学变量的递推关系以提高建模效率.最后对新型的Kane方程进行扩展,用于处理多体系统中的运动约束.该算法适用于任意多体系统,建立的动力学模型不含待定乘子,维数与系统广义速率相同,利于控制系统设计.对带有闭环约束的空间多机械臂系统的数值仿真验证了方法的正确性.
This paper presents an improved Kane＇s method for automatically generating the equations of motion of arbitrary multibody systems. The notions of partial velocity matrix and partial angular velocity matrix are introduced. Each body＇s contribution to the system＇s generalized inertial force is expressed in a similar manner, which makes it amenable to computer solutions. All the kinematic quantities＇ recursive relations are developed to improve the modeling efficiency. The motion constraints are handled by the new form of Kane＇s equation. The final mathematical model is of the same dimensions with the generalized speeds and involves no Lagrange multipliers; therefore, it＇s useful for control system design. The simulation of a space platform with two manipulators is compared between the proposed method and recursive algorithm. The results validate the algorithm＇s accuracy.
出处
《力学学报》
EI
CSCD
北大核心
2011年第5期968-972,共5页
Chinese Journal of Theoretical and Applied Mechanics
基金
国家自然科学基金资助项目(10872028)~~
关键词
约束
多体系统
动力学
KANE方程
motion constraints, multibody system, dynamics, Kane＇s equation
