工作空间最大化的4-RUP_aR并联机构尺度优化设计

Optimal Design of Dimensions of 4-RUP_aR Parallel Mechanism through Maximizing Workspace

对一种新型3T1R并联机构-4RUPaR并联机构进行工作空间分析和尺度参数优化设计。首先利用解析几何中的坐标变换理论,以机构的杆长作为约束条件,得到了运动学反解方程;然后根据运动学反解方程,建立工作空间的约束条件,通过MATLAB编程实现机构的定姿态工作空间的可视化,并通过"点集"近似表达工作空间的大小;最后采用单一变量分析法得出了并联机构尺度参数与定姿态工作空间的关系。以工作空间最大化作为优化目标,采用差分进化算法求解该优化问题,获得了良好的机构尺度参数,使得并联机构的有效工作空间更大更健壮,也更加符合工程实用要求。

Workspace analysis and dimension parameter optimal design of a new type of 3T1R parallel mechanism,namely 4-RUP aR parallel mechanism,are carried out.Firstly,the link-length of the mechanism is taken as the constraint condition to obtain the inverse kinematic equation with the coordinate transformation theory in analytic geometry.Secondly,the constraint condition of workspace is established based on the inverse kinematics equation and the visualization of the workspace of the mechanism is programmed in MATLAB.The dimension of the workspace is approximately expressed with point sets.Finally,the relationship between the dimensional parameters of the parallel mechanism and the fixed attitude workspace is obtained with the single variable analysis method.To maximize the workspace as the optimization objective,the differential evolution algorithm is used to solve the optimization problem.Good dimensional parameters are obtained;the effective workspace of the parallel mechanism is larger and more robust and is in agreement with practical engineering requirements.