基于改进微梁理论的空间柔性机械臂建模方法

Space flexible manipulator modeling method based on improved Cosserat rod theory

针对传统Cosserat梁模型中运动学方程组变量冗余、并非独立及模型中材料模量设定方法不明确的问题,提出一种基于方向余弦阵的Cosserat梁运动学方程简化形式和一种基于多项式拟合的模量设定方法.改进后的建模方法不仅具有更高的模型求解效率,而且求解结果可以更加准确地反映超弹性材料属性.数学仿真及有限元分析验证结果表明:所提出的模量设定方法能够很好地反映柔性臂稳态弯曲形状,同时算法的求解时间得到了较为明显的减少.

In the traditional Cosserat beam model,the variables of kinematic equations are redundant and not independent,and the setting method of material modulus value in the model is unclear.To solve these two problems,a simplified form of kinematic equation of Cosserat beam based on direction consine matrix and a method of modulus setting based on polynomial fitting were proposed.The improved modeling method not only has higher model solving efficiency,but also can reflect the properties of hyperelastic materials more accurately.Finally,mathematical simulation and finite element analysis were carried out.The results show that the modulus setting method proposed in this paper can well reflect the steady-state bending shape of the flexible arm,and the solution time of the algorithm is significantly reduced.