考虑构件弹性的电动Stewart并联机构刚度建模与仿真

基于集总解析建模方法和构件有限元分析建立包含驱动副、被动万向铰链和运动杆件弹性变形以及预载作用下的Stewart机构刚度矩阵模型。采用添加虚拟铰链等效构件弹性的方式，将分支等效为一系列刚性构件经由主、被动副以及虚拟铰链连接的形式，给出了运动关节和虚拟铰链变量对机构末端位姿的运动学Jacobian矩阵的数值计算方法，应用虚功原理得到静平衡方程，最终建立了机构无预载以及预载下的刚度矩阵模型。该模型不仅考虑了控制环路刚度，还将构件柔性的有限元分析结果与解析建模相结合，在降低计算成本的同时保证了精度。通过一机构分析实例，考察了两种模型下刚度分布的差异。

Stiffness Modeling and Simulation of Electric Stewart Parallel Mechanism Considering Elasticity of Components

Based on lumped modeling and finite element analysis, stiffness model of Stewart mechanism is established, which takes into account the elastic deformation of driving joints, passive universal joints and moving components, and the effect of preloading. By adding virtual joints to describe the elasticity of components, the branch is presented as a series of rigid components connected with active, passive and virtual joints. The numerical method of moving and virtual joints kinematic Jacobian matrix is developed. The static balance equation was obtained by applying the principle of virtual work, and stiffness matrices without/under preloading are established. The proposed model considers not only the control loop stiffness, but also the result of finite element analysis combined with analytical modeling. The computation cost was reduced while ensuring the accuracy. The stiffness distribution differences between two models were examined through an example.