为研究大行程柔性微定位平台运动过程中伴生转动对其定位精度的影响,首先基于新型柔性运动副设计了一种运动解耦、低伴生转动的5-PPPR型柔性微定位平台;其次,基于矩阵法、线弹性梁变形理论、拉格朗日方程分别对其静、动态特性进行了理论分析,并对运动副及微定位平台的伴生转角进行了理论建模,继而探究了考虑伴生转动情况下平台输入、输出位移之间的关系;然后,通过有限元仿真对上述理论模型进行了验证,结果表明平台输入刚度、伴生转角及固有频率的理论与仿真值最大相对误差分别为2.20%、1.23%及1.98%,且考虑伴生转动情况下,x轴方向输出位移理论误差与不考虑伴生转动情况相比降低了94.63%;最后,对柔性微定位平台进行了灵敏度分析及参数优化,结果表明优化后微定位平台在相同驱动条件下伴生转角及丢失运动分别降低28.8%和21.5%,进一步提升了微定位平台的定位精度。
In order to investigate the influence of parasitic rotation on the positioning precision of large-stroke compliant micro-positioning stage, a novel 5-PPPR compliant micro-positioning stage with motion decoupling and low parasitic rotation is designed based on a novel compliant kinematic joint firstly. Secondly, based on matrix method, linear elastic beam deformation theory and the Lagrange's equation, theoretical analysis of both static and dynamic characteristics of the stage are carried out, respectively. Meanwhile, parasitic rotation angles of the kinematic joint and micro-positioning stage are modeled in theory. Furthermore, the relationship between the input and output displacements of the stage is explored by taking the parasitic rotation into consideration. Then, the theoretical models are verified by finite element analysis, the results show that the maximum relative errors of the theoretical and simulated values of the input stiffness, parasitic rotation angle, and natural frequency are 2.20%, 1.23%, and 1.98%, respectively. And the theoretical error of the output displacement along x-axis is reduced by 94.63% with the parasitic rotation considered. Finally, the sensitivity analysis and parameter optimization are carried out, the results show that the parasitic rotation angle and lost motion of the optimized stage are reduced by 28.8% and 21.5% respectively under the same driving displacement, which further improves the positioning precision of the stage.
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