弹性关节柔性操作臂的频率及振型特性分析

为了研究柔性操作臂关节弹性对频率及振型的作用机理，建立了柔性操作臂的弹性约束模型。根据弹性约束模型，得到了弹性关节柔性操作臂的频率方程及振型函数。采用数值方法，对弹性关节柔性操作臂的前三阶频率及振型特性进行了分析。结果表明：关节的弹性对柔性操作臂的频率及振型具有明显的影响，将关节视为理想刚性约束会产生明显的误差；由灵敏度分析可知，线性约束对频率的影响大于扭转约束，且高阶频率段表现较为明显；扭转约束对振型的影响比线性约束更为显著，随着扭转约束的增大，振型发生改变，且高阶振型表现较为明显。通过实验对建立的弹性约束模型进行验证，实验结果表明，所建立的弹性约束模型能够合理地表征关节的弹性约束作用，分析结果更接近实际情况，误差较小。

Natural Frequencies and Modal Shape Characteristics of a Flexible Manipulator with Elastic Joints

To investigate the effect mechanism of elastic joint on the natural frequencies and modal shapes of flexible manipulators, an elastic restraint model of the flexible manipulator was established. Based on the elastic restraint model, frequency equation and modal shape function of the flexible manipulator with elastic joint (FMEJ) were subsequently derived. Numerical method was conducted to investigate the first three natural frequencies and modal shapes of the FMEJ. The results demonstrate that the elasticity of the joint has considerable effect on the natural frequencies and modal shapes, and assuming the joint as an ideal fixed restraint a noticeable error will present. According to the sensitivity analysis, the linear restraints have a more considerable effect on the natural frequencies than torsional restraints, especially for the higher frequencies. The effect of torsional restraints on the modal shapes is more considerable, with the torsional restraint increases, the modal shapes change which is obvious for the higher modal shapes. Experiment was conducted to verify the elastic restraint model and the results indicate that the constructed model can characterize the elastic restraints of the joint, and approach to the actual situation which has a smaller error.