基于Kane方法的Stewart传感器动力学及固有频率分析

通过线性化动力学方程并应用Kane方法，研究了Stewart传感器的固有频率．将Stewart传感器的上平台、上连杆、敏感元件及下连杆作为独立的子结构分别处理，依据矢量和张量理论对其运动学方程和动力学方程进行系统的推导，并经过简化导出Stewart传感器简洁的固有频率方程形式．为验证Kane方法的有效性，提供了MATHEMATICA数值算例．相比于传统的牛顿一欧拉方法及拉格朗日方法，Kane方法既简洁又高效，特别适合于计算机计算．

The natural frequencies analysis for stewart transducer rased on the Kane's method

This paper analyzed the natural frequencies for the Stewart transducer based on the Kane's method. In this method, the upper platform, the upper leg, the elastic element and the lower leg of the Stewart transducer were treated as independent substructure, and the equations of kinematics and dynamics were derived systematically according to the theory of the vector and the tensor. Moreover the equations of the natural frequencies for the Stewart transducer were obtained by simplifying the equations of kinematics and dynamics. In order to testify the validation of the Kane's method, a numerical simulation was proposed in mathematica routines. Compared with the traditional Newton-Euler method and the Lagrange method, the Kane's method is explicit and efficient, and especially suitable for calculating with computer.