柔顺杆件固定-导向1P2R伪刚体模型
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摘要
针对固定-导向模式的伪刚体模型模拟柔顺杆件末端位置精度不高且无法表现轴向变形的问题,基于伪刚体模型的原理提出了一种高精度的固定-导向1P2R伪刚体模型。首先综合考虑柔顺杆件各个方向的变形,构建了包含两个转动副和一个移动副的固定-导向1P2R伪刚体模型;其次建立了该模型的运动学方程,并根据优化算法求解了伪刚体模型的最优特征半径系数,利用一元线性回归方法得到了该模型的弹簧和扭簧刚度系数;最后通过数值算例模拟固定-导向1P2R模型末端的动作路径,并将其与固定-导向伪刚体模型及柔顺杆件的末端路径进行对比。结果表明,固定-导向1P2R伪刚体模型完全能够模拟相应柔顺杆件的末端动作过程,且模拟精度高于固定-导向伪刚体模型。研究证明了该模型的优越性,对柔顺机构的变形分析亦有重要参考意义。
Based on the principle of pseudo-rigid-body model(PRBM), a new fixed-guided 1 P2 R PRBM is presented to improve the calculation accuracy for tip locus of the fixed-guided compliant links and express the axial deformation. Firstly, a fixed-guided PRBM with one prismatic pair and two revolute pairs is proposed considering deformations of a compliant mechanism omni-directionally. Secondly, the kinematics equation of the model is set up and the optimal characteristic radius coefficients are established using the optimization algorithm, meanwhile, the stiffness coefficient of the spring and the torsional spring is acquired respectively by the linear regression method. At last, numerical examples are demonstrated by comparing the tip locus of the fixed-guided 1 P2 R PRBM with that of the fixed-guided PRBM. Further research shows that the fixed-guided 1 P2 R PRBM can actually simulate the tip locus of the compliant mechanism, furthermore, the calculation accuracy is higher compared with that of the fixed-guided PRBM, which also proves the superiority of the 1 P2 R PRBM. The content of the paper paves underlying theoretical grounds for the deformation analysis for the compliant mechanisms.
Based on the principle of pseudo-rigid-body model(PRBM), a new fixed-guided 1 P2 R PRBM is presented to improve the calculation accuracy for tip locus of the fixed-guided compliant links and express the axial deformation. Firstly, a fixed-guided PRBM with one prismatic pair and two revolute pairs is proposed considering deformations of a compliant mechanism omni-directionally. Secondly, the kinematics equation of the model is set up and the optimal characteristic radius coefficients are established using the optimization algorithm, meanwhile, the stiffness coefficient of the spring and the torsional spring is acquired respectively by the linear regression method. At last, numerical examples are demonstrated by comparing the tip locus of the fixed-guided 1 P2 R PRBM with that of the fixed-guided PRBM. Further research shows that the fixed-guided 1 P2 R PRBM can actually simulate the tip locus of the compliant mechanism, furthermore, the calculation accuracy is higher compared with that of the fixed-guided PRBM, which also proves the superiority of the 1 P2 R PRBM. The content of the paper paves underlying theoretical grounds for the deformation analysis for the compliant mechanisms.
引文
[1]Howell L L.Compliant mechanisms[M].New York:John Wiley&Sons,2001.
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[4]Uwe H,Peter H,Anderi C.Compliant mechanism synthesis by using elastic similitude[J].Chinese Journal of Mechanical Engineering,2015,28(4):769-775.
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[7]胡俊峰,郑昌虎,徐贵阳.基于有限元法的桥式柔顺机构动态性能分析[J].机械设计,2016,33(1):81-86.
[8]刘凯,曹毅,周睿,等.二自由度平板折展柔性铰链的分析及优化[J].航空学报,2017,38(2):420317.
[9]Howell L L,Midha A,Norton T W.Evaluation of equivalent spring stiffness for use in a pseudo-rigid-body model of large-deflection compliant mechanisms[J].Journal of Mechanical Design,1996,118(1):126-131.
[10]Howell L L,Midha A.Parametric deflection approximations for end-loaded,large-deflection beams in compliant mechanisms[J].Journal of Mechanical Design,1995,117(1):156-165.
[11]冯忠磊,余跃庆,王雯静.模拟柔顺机构中柔顺杆件末端特征的2R伪刚体模型[J].机械工程学报,2011,47(1):36-42.
[12]余跃庆,周鹏.柔顺机构PR伪刚体模型[J].北京工业大学学报,2013,39(5):641-647.
[13]余跃庆,徐齐平,周鹏.复合载荷作用下柔顺机构的PR伪刚体新模型[J].机械工程学报,2013,49(15):9-14.
[14]Wang N,Liang X,Zhang X.Pseudo-rigid-body model for corrugated cantilever beam used in compliant mechanisms[J].Chinese Journal of Mechanical Engineering,2014,27(1):122-129.
[15]李娜,赵铁石,孙东波,等.分布式全柔顺机构伪刚体建模[J].机械工程学报,2010,46(19):17-23.
[16]邱丽芳,翁海珊,柳林,等.全柔性四杆机构伪刚体模型分析计算方法的改进[J].农业机械学报,2008,39(5):142-145.
[2]Jensen B D,Howell L L,Salmon L G.Design of two-link,inplane,bistable compliant micro mechanisms[J].ASME Transactions,Journal of Mechanical Design,1999,121(3):416-423.
[3]Ma R,Slocum A H,Sung E.Torque measurement with compliant mechanisms[J].Journal of Mechanical Design,2013,135(3):22-25.
[4]Uwe H,Peter H,Anderi C.Compliant mechanism synthesis by using elastic similitude[J].Chinese Journal of Mechanical Engineering,2015,28(4):769-775.
[5]Sharma D,Deb K.Generation of compliant mechanisms using hybrid genetic algorithm[J].Journal of the Institution of Engineers,2014,95(4):295-307.
[6]于靖军,毕树生,宗光华,等.基于伪刚体模型法的全柔性机构位置分析[J].机械工程学报,2002,38(2):75-78.
[7]胡俊峰,郑昌虎,徐贵阳.基于有限元法的桥式柔顺机构动态性能分析[J].机械设计,2016,33(1):81-86.
[8]刘凯,曹毅,周睿,等.二自由度平板折展柔性铰链的分析及优化[J].航空学报,2017,38(2):420317.
[9]Howell L L,Midha A,Norton T W.Evaluation of equivalent spring stiffness for use in a pseudo-rigid-body model of large-deflection compliant mechanisms[J].Journal of Mechanical Design,1996,118(1):126-131.
[10]Howell L L,Midha A.Parametric deflection approximations for end-loaded,large-deflection beams in compliant mechanisms[J].Journal of Mechanical Design,1995,117(1):156-165.
[11]冯忠磊,余跃庆,王雯静.模拟柔顺机构中柔顺杆件末端特征的2R伪刚体模型[J].机械工程学报,2011,47(1):36-42.
[12]余跃庆,周鹏.柔顺机构PR伪刚体模型[J].北京工业大学学报,2013,39(5):641-647.
[13]余跃庆,徐齐平,周鹏.复合载荷作用下柔顺机构的PR伪刚体新模型[J].机械工程学报,2013,49(15):9-14.
[14]Wang N,Liang X,Zhang X.Pseudo-rigid-body model for corrugated cantilever beam used in compliant mechanisms[J].Chinese Journal of Mechanical Engineering,2014,27(1):122-129.
[15]李娜,赵铁石,孙东波,等.分布式全柔顺机构伪刚体建模[J].机械工程学报,2010,46(19):17-23.
[16]邱丽芳,翁海珊,柳林,等.全柔性四杆机构伪刚体模型分析计算方法的改进[J].农业机械学报,2008,39(5):142-145.