含球面副间隙的空间并联机构动态特性

为了分析含球面副间隙的5-PSS/UPU并联机构的动态特性，建立含多个球面副间隙的空间并联机构的刚体动力学模型. 基于“接触-分离”二状态模型建立含球面副间隙的运动学模型；基于改进的接触模型和修正的Coulomb摩擦模型建立运动副元素之间的法向与切向接触力模型，进一步将接触力转化到运动副元素对应的部件质心；采用牛顿-欧拉法并结合拉格朗日乘子建立含间隙空间并联机构的动力学模型，利用数值仿真分析其动态特性，计算得到间隙分别为0.05、0.10、0.20、0.40 mm时的动平台角加速度均方根误差（RMSE）指标，分别为40.046、65.385、98.489、145.715 rad/s². 结果表明，在存在多个球面副间隙的情况下，当间隙增加时，空间并联机构的动态性能严重退化.

Dynamic characteristics of spatial parallel mechanism with spherical joint clearance

A rigid body dynamics model of a spatial parallel mechanism with multiple spherical joint clearances was established, in order to analyze the dynamic characteristics of the 5-PSS/UPU parallel mechanism with spherical joint clearances. A kinematic model of parallel mechanism with spherical joint clearances was established based on the 'contact-separation' two-state model. The normal and tangential contact force models between the kinematic joint elements were established based on an improved contact model and a modified Coulomb friction model, and the contact force was further transformed into the centroid of the component corresponding to the kinematic joint elements. The Newton-Eulerian method combined with the Lagrange multiplier was used to establish the dynamic model of the parallel mechanism with clearances and the dynamic characteristics were analyzed by numerical simulation.The root-mean-square error (RMSE) values of the angular acceleration of the moving platform with clearance of 0.05, 0.10, 0.20 and 0.40 mm were calculated, which were 40.046, 65.385, 98.489 and 145.715 rad/s², respectively. Results show that in the case where there are multiple spherical joint clearances, when the clearance value increases, the dynamic performance of the spatial parallel mechanism visibly deteriorates.