Abstract
Based on the finite element method and Lagrange equation, high dimensions, time-invariant, nonlinear rigid-elastic coupling dynamic equations are established, in which the coupling influence of elastic deformation motion and the rigid body motion are considered. A comparative analysis of one-step method and two-step method for solving nonlinear rigid-elastic coupling dynamic equations is given. The simulation results show that the elastic vibrations of the flexible links have important effect on rigid body motion, particularly for angular velocity and angular acceleration. There are some errors in the amplitudes and phases of the elastic displacements and the elastic rotation angle for the two methods, rigid-elastic coupling of flexible links will critical influence elastic deformation displacements and elastic rotate angle of the moving platform, but change rule of the kinematic variables are basically consistent. So, one-pass method is used to solve dynamic equation of rigid-elastic coupling system that can reflect the dynamic characteristics well, it can provide guidance for controller design in future.
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References
Gasparetto, A.: On the modeling of flexible-link planar mechanisms: experimental validation of an accurate dynamic model. ASME J. Dyn. Syst. Meas. Control 126(2), 365–375 (2004)
Nagarajan, S., Turcic, D.A.: Lagrangian formulation of the equations of motion for elastic mechanisms with mutual dependence between rigid body and elastic motions. Part I: element level equations. ASME. J. Dyn. Syst. Meas. Control 112(2), 203–214 (1990)
El-Absy, H., Shabana, A.A.: Coupling between rigid body and deformation modes. J. Sound Vibr. 198(5), 617–637 (1996)
Yang, Z., Sadler, J.P.: A one-pass approach to dynamics of high-speed machinery through three-node lagrangian beam elements. Mech. Mach. Theory 34(7), 995–1007 (1999)
Karkoub, K., Yigit, A.S.: Vibration control of a four-bar mechanism with a flexible coupler link. J. Sound Vibr. 222(2), 171–189 (1999)
Xuping, Z., Mills, J.K., Cleghorn, W.L.: Coupling characteristics of rigid body motion and elastic deformation of a 3-PRR parallel manipulator with flexible links. Multibody Syst. Dyn. 21, 167–192 (2009)
Zhang, Q.H., Zhang, X.M.: Dynamicmodeling and analysis of planar 3-RRR flexible parallel robots. J. Vibr. Eng. 26(2), 239–245 (2013)
Zhang, Q., Fan, X., Zhang, X.: Dynamic analysis of planar 3-RRR flexible parallel robots with dynamic stiffening. Shock Vibr. 2014, 1–13 (2014). doi:10.1155/2014/370145. Article ID: 370145
Acknowledgments
This work was supported by the National Natural Science Foundation of China (Grants nos. U1501247, 61603103, and 51505092), the of Natural Science Foundation Guangdong Province (Grants nos. 2014A030313616, 2015A030310181, and 2016A030310293), the Science and Technology Planning Project of Guangdong Province (2014A010104017 and 2015B010101015), and the Science and Technology Innovation Project of Foshan (2015AG10018). These supports are greatly acknowledged.
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Zhang, Q., Lu, Q. (2017). Analysis on Rigid-Elastic Coupling Characteristics of Planar 3-RRR Flexible Parallel Mechanisms. In: Huang, Y., Wu, H., Liu, H., Yin, Z. (eds) Intelligent Robotics and Applications. ICIRA 2017. Lecture Notes in Computer Science(), vol 10463. Springer, Cham. https://doi.org/10.1007/978-3-319-65292-4_34
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DOI: https://doi.org/10.1007/978-3-319-65292-4_34
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