基于虚关节法的3T1R混联机构静刚度特性分析

基于虚关节法和构件有限元分析建立了考虑驱动副、滚珠丝杆副、线性导轨和运动杆件弹性变形的3T1R混联机构静刚度矩阵模型。通过在构件末端添加多自由度虚拟关节的方式来等效构件的弹性，将支链等效为一系列刚性构件，通过主动副、被动副以及虚拟关节连接的形式，给出了运动关节和虚拟关节变量对机构末端位姿的映射，应用虚功原理得到机构静平衡方程，推导了机构在一定外载下的刚度矩阵模型，采用无量纲变换法定义了局部线刚度和角刚度评价指标与全局线刚度和角刚度评价指标，据此分析了混联机构在典型位姿和工作空间域内的静刚度性能，并利用有限元仿真验证了刚度模型的准确性。结果表明，所建半解析刚度模型具有较高的精度；机构z向线刚度在工作空间内关于x=y轴线对称分布；机构x向、y向的线刚度沿x轴、y轴方向不变，具有解耦性；机构线刚度远大于角刚度。

Static Stiffness Analysis of 3T1R Hybrid Manipulator Based on Virtual Joint Method

Based on the virtual joint method, the static stiffness matrix model of a 3T1R hybrid manipulator was established considering the elastic deformation of driving joints, ball screw pair, linear guide rail and moving bar. The elasticity deformation of the component was described as one multi-degree of freedom virtual joint at the end of the component, and the branch was then equivalent to a series of rigid components connected by active joint, passive joints and virtual joints. The mapping of kinematic joint and virtual joint variables to the end platform of the mechanism was given. The static equilibrium equation of the manipulator was obtained by using the virtual work principle, and the stiffness matrix model of the manipulator under external load was derived. The evaluation indices of local linear/angular stiffness and global linear/angular stiffness were defined by the dimensionless transformation method, and the static stiffness performance of the hybrid manipulator at the typical configurations as well as throughout the workspace was analyzed accordingly, and the accuracy of the stiffness model was verified by finite element simulation. The results showed that the semi-analytical stiffness model had good accuracy. The z-direction linear stiffness of the mechanism was symmetrically distributed in the workspace. The linear stiffness of the mechanism in the x(y)-direction was decoupled. Linear stiffness of mechanism was much larger than angular stiffness. The research results can provide a theoretical basis for the engineering design and application of the institute.