基于Matalb的纯平动3-UPU并联机构正运动位置解及工作空间分析

采用空间机构螺旋原理,分析了3-UPU并联机构的构型和纯平动特性。给出了连续型多项式代数拓扑法,构建3-UPU并联机构的正运动位置解的非线性方程组,并对方程组进行计算。该方法无需给定值就能有效逼近并联机构非线性方程组的解,且可解决方程组求解时出现的分叉和散度问题,对超越问题的解析具有重要的参考意义。基于Matlab/Simmechanics构建3-UPU并联机构PID控制模型并分析其工作空间,验证并联机构构型设计中螺旋理论应用的准确性。该方法对求解多自由度并联机构运动学问题有切实可行的借鉴意义。

Analysis of Kinetic Positional Solution and Workspace of Pure Translational 3-UPU Parallel Mechanism based on Matlab

The configuration and pure translational performance of 3-UPU parallel mechanism is ana.lyzed by using spatial mechanism screw theory.The continuous polynomial algebraic topology method is pro.posed,the positive kinetic non-linear equations of 3-UPU parallel mechanism is built,and the solution of the equation set is calculated.By this approach,the solution of nonlinear kinetic equations of parallel mechanism can be found effectively without giving initial values.Meanwhile,the problems of divarication and divergence are also eliminated in the solving process,which have vital reference significance to the nonlinear transcen.dence problem solving.Based on Matlab/Simmechanics,the kinetic PID control model of 3-UPU parallel mechanism is built and its workspace is analyzed to verify the accuracy in the application of spiral theory on par.allel mechanism configuration design.This method provides feasible and practical reference significance to solve and analyze the kinematics problem of multiple degrees of freedom parallel mechanism.