Kinematics Analysis and Performance Optimization of Low Coupling PRPaR/2CRR Parallel Mechanism

The mechanism is improved by adding support chains to the parallelogram mechanism in response to the performance shortcomings of the 3CRR parallel mechanism. Based on the topological structure synthesis method, a batch of spatial triple translational parallel mechanisms were synthesized, and a PRPaR/2CRR parallel mechanism with spatial triple translational motion was optimized. Characteristics such as degrees of freedom and coupling were analyzed based on the theory of directional feature sets, respectively. The nonlinear kinematics equations were established by using the geometric position relation and the constraint of the rod length, and the expression of the inverse position solution was derived. The forward and inverse position solutions were verified by numerical examples. Then, the velocity Jacobian matrix was calculated, the singularity was studied, and the conditions for generating positional anomalies were obtained. In addition, the working space and dexterity degree distribution of the mechanism were analyzed by the graphic method. What's more, a multi-objective optimization design model was established based on the comprehensive performance of the workspace volume, the global dexterity, and the global operability, and the optimal structural parameter size solution was calculated using the NSGA-Ⅱ algorithm. The research results show that the external boundary of the workspace of the PRPaR/2CRR parallel mechanism is smooth, with a semi tire shaped structure and local cavities. A conclusion can be drawn that compared with the 3CRR parallel mechanism, the PRPaR/2CRR parallel mechanism has better workspace <italic>V</italic>, global dexterity <inline-formula><alternatives><math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M4"><msub><mrow><mi>G</mi></mrow><mrow><mi mathvariant="normal">C</mi><mi mathvariant="normal">I</mi></mrow></msub></math><graphic specific-use="big" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="alternativeImage/BB82F71E-2534-420b-AB14-C438CF320FD0-M002.jpg"><?fx-imagestate width="4.31799984" height="3.72533321"?></graphic><graphic specific-use="small" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="alternativeImage/BB82F71E-2534-420b-AB14-C438CF320FD0-M002c.jpg"><?fx-imagestate width="4.31799984" height="3.72533321"?></graphic></alternatives></inline-formula>, operability <inline-formula><alternatives><math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M5"><mi>μ</mi></math><graphic specific-use="big" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="alternativeImage/BB82F71E-2534-420b-AB14-C438CF320FD0-M003.jpg"><?fx-imagestate width="2.37066650" height="3.38666677"?></graphic><graphic specific-use="small" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="alternativeImage/BB82F71E-2534-420b-AB14-C438CF320FD0-M003c.jpg"><?fx-imagestate width="2.37066650" height="3.38666677"?></graphic></alternatives></inline-formula>, and other performance. Research has shown that PRPaR/2CRR has good industrial application prospects.