具有符号式位置正解的2T1R并联机构的运动学分析与尺度综合

基于方位特征方程的并联机构拓扑设计理论和方法，设计一种零耦合度且具有符号式位置正解的两平移一转动并联机器人机构，分析计算机构的方位特征集、自由度以及耦合度等拓扑特性。利用机构支链运动副布置的特点建立运动学方程，计算出正运动学和逆运动学的位置解析式，通过一组算例验证计算结果可靠性。研究机构的奇异性并给出正解奇异和逆解奇异的产生条件。分析机构的工作空间，以给定的工作空间作为约束条件，建立实际工作空间最小化的优化目标，选择天牛群优化算法优化得到满足给定的工作空间且使实际工作空间最小的设计结构参数最优解。结果表明：机构具有符号式的位置正解，且工作空间形状规则，呈对称分布、边界光滑。

Kinematics Analysis and Dimension Synthesis of 2T1R Parallel Mechanism with Symbolic Forward Position Solution

A two translation one rotation (2T1R) parallel robot mechanism with zero coupling degree and symbolic position forward solution was designed by using the parallel mechanism topology design theory and method based on position and orientation characteristics (POC) equation.The POC,degree of freedom and coupling degree of the mechanism were analyzed and calculated and so on.Based on the characteristics of the kinematic pair arrangement of the mechanism,the kinematic equation was established,and the position analytical expressions of forward kinematics and inverse kinematics were calculated.The reliability of the calculation results was verified by a group of examples.The singularity of the mechanism was studied and the conditions for the singularity of the positive solution and the inverse solution were given.The workspace of the mechanism was analyzed.Taking the given workspace as the constraint condition,the optimization objective of the actual workspace minimization was established,and the optimal solution of the design structure parameter size satisfying the given workspace and minimizing the actual workspace was obtained by beetle swarm optimization algorithm.The results show that the mechanism has symbolic positional positive solution,regular workspace shape,symmetrical distribution and smooth boundary.