4-RRS冗余球面并联机构的静力学与刚度分析

Statics and Stiffness Analysis of 4-RRS Redundant Spherical Parallel Mechanism

为提升球面并联机构的承载能力,提出一种4-RRS冗余球面并联机构。给出4-RRS冗余球面并联机构的构型设计。然后,建立机构的静力学模型。在锁定驱动关节的情况下,通过互易积运算求解支链作用于动平台上的反螺旋力系。基于建立的静力学模型,得出了各个关节的受力情况和各条支链的变形情况。以实例求解了冗余和非冗余情况下,支链关节受到的最大力和力矩。冗余时支链关节受到的最大力和力矩小于非冗余的情况。对机构进行刚度分析。构造机构的柔度矩阵,得出动平台中心点在受力时的广义位移。以实例对比冗余与非冗余机构的刚度与受力性能,得出了冗余时动平台的广义位移小于非冗余的情况。

In order to improve the load capacity of spherical parallel mechanism, a novel 4-RRS redundant spherical parallel mechanism is proposed. The structural configuration of such 4-RRS parallel mechanism is introduced and sketched out. The statics model is built. When the actuated joints are locked, the reciprocal screw system applied on the moving platform is obtained by using the reciprocal product. The force of each joint and the deformation of limbs are solved based on the built statics model. Take the redundant and non-redundant mechanisms as the examples, the maximum force and torque applied on the limb joint are obtained. The maximum force and torque of redundant mechanism are less than the ones of non-redundant mechanism. The stiffness analysis of performed. The compliance matrix and the generalized displacement of the center of the moving platform are derived. Compared the stiffness and force performance of the redundant mechanism with the non-redundant mechanism, the generalized displacement of the center of the moving platform of the redundant mechanism is less than the ones of the non-redundant mechanism.