空间并联机构连续刚度非线性映射

Continuous Stiffness Nonlinear Mapping of Spatial Parallel Mechanism

基于影响系数法并借助虚功原理建立包含主、被动关节弹性变形,杆件及其平台自重的空间并联机构连续刚度非线性映射通用模型。空间并联机构连续刚度非线性映射通用模型与以往刚度模型区别在于,它不仅考虑了机构主动驱动关节、被动关节弹性变形及各部件重力对机构刚度的影响,而且考虑了机构刚度变化的连续过程,没有忽略机构在广义外力下变形时雅可比矩阵的变化,通过引进机构的二阶影响系数,从而使空间并联机构刚度非线性映射还原。从机构简化约束方程出发,推导空间并联机构几类连续刚度简化映射矩阵。在此基础上,结合刚度矩阵瑞利商定义了空间并联机构连续刚度性能判定指标k′。最后给出一空间并联机构刚度分析实例,分别计算两种模型下的刚度矩阵,并对比两种模型下机构刚度性能。

Based on influence coefficient method and principle of virtual work, continuous stiffness nonlinear mapping general model of spatial parallel mechanism is established, including the elastic deformation of active and passive hinge and gravities factor. Different from the traditional model, the stiffness nonlinear general mapping model of spatial parallel mechanism is reverted, not only considering the influence of elastic deformation of active and passive hinge and gravities factor on the mechanism stiffness, but also considering the stiffness continuous change. The change of the Jacobian matrix is not neglected under the outside force, introducing the second-order influence coefficient matrix of mechanism. Then, simple restricted equations of parallel mechanism are described, and several continuous stiffness mapping matrixes are deduced respectively. On this foundation, combining Rayleigh quotient of the continuous stiffness matrix, the performance index k＇ used to estimate the mechanism stiffness is defined, a stiffness analysis example of spatial parallel mechanism is presented. The stiffness matrixes in two models are calculated, and the stiffness performances are contrasted, respectively.