An improved kane's method for multibody dynamics
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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.
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关键词:
- Kane 方程
Abstract: This paper presents an improved Kane's method forautomatically generating the equations of motion of arbitrary multibodysystems. The notions of partial velocity matrix and partial angular velocitymatrix are introduced. Each body's contribution to the system's generalizedinertial force is expressed in a similar manner, which makes it amenable tocomputer solutions. All the kinematic quantities' recursive relations aredeveloped to improve the modeling efficiency. The motion constraints arehandled by the new form of Kane's equation. The final mathematical model isof the same dimensions with the generalized speeds and involves no Lagrangemultipliers; therefore, it's useful for control system design. Thesimulation of a space platform with two manipulators is compared between theproposed method and recursive algorithm. The results validate thealgorithm's accuracy.-
Key words:
- Kane's equation
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