Dynamic modeling of parallel robots with flexible platforms

Abstract This paper presents a method for calculating the direct and inverse dynamic models of a parallel robot with a flexible platform. The system considered in this study is a Gough–Stewart 6-DOF parallel robot however the method is general and can be used for other structures. The platform of the parallel manipulator is considered as a flexible body and modeled using distributed flexibility while the links of the legs are considered as rigid. The direct dynamic model gives the elastic and Cartesian accelerations in terms of the input torques and the current state of the system i.e. the position and velocities of both the rigid and elastic variables. The inverse dynamic model calculates the elastic accelerations and the actuator torques from the current state variables and the desired acceleration of the platform.

[1]  Wisama Khalil,et al.  A new geometric notation for open and closed-loop robots , 1986, Proceedings. 1986 IEEE International Conference on Robotics and Automation.

[2]  Soumya Bhattacharya,et al.  An on-line parameter estimation scheme for generalized stewart platform type parallel manipulators , 1997 .

[3]  L. Tsai Solving the Inverse Dynamics of a Stewart-Gough Manipulator by the Principle of Virtual Work , 2000 .

[4]  Hassan Zohoor,et al.  Comments to the: “Closed-form dynamic equations of the general Stewart platform through the Newton–Euler approach” and “A Newton–Euler formulation for the inverse dynamics of the Stewart platform manipulator” , 2008 .

[5]  Masaru Uchiyama,et al.  A recursive formula for the inverse of the inertia matrix of a parallel manipulator , 1998 .

[6]  K. Sugimoto,et al.  Computational scheme for dynamic analysis of parallel manipulators , 1988 .

[7]  Bhaskar Dasgupta,et al.  A Newton-Euler Formulation for the Inverse Dynamics of the Stewart Platform Manipulator , 1998 .

[8]  G. Rodríguez Spatial operator approach to flexible manipulator inverse and forward dynamics , 1990, Proceedings., IEEE International Conference on Robotics and Automation.

[9]  Wisama Khalil,et al.  General Solution for the Dynamic Modeling of Parallel Robots , 2007, J. Intell. Robotic Syst..

[10]  B. Dasgupta,et al.  A general strategy based on the Newton-Euler approach for the dynamic formulation of parallel manipulators , 1999 .

[11]  Eric Courteille,et al.  A Systematic Procedure for the Elastodynamic Modeling and Identification of Robot Manipulators , 2010, IEEE Transactions on Robotics.

[12]  C. Reboulet,et al.  Dynamic models of a six degree of freedom parallel manipulators , 1991, Fifth International Conference on Advanced Robotics 'Robots in Unstructured Environments.

[13]  M. Mahboubkhah,et al.  A comprehensive study on the free vibration of machine tools’ hexapod table , 2009 .

[14]  M. Bergamasco,et al.  Dynamics of parallel manipulators by means of screw theory , 2003 .

[15]  Frank L. Lewis,et al.  Dynamic analysis and control of a stewart platform manipulator , 1993, J. Field Robotics.

[16]  Zhiming Ji Study of the effect of leg inertia in Stewart platforms , 1993, [1993] Proceedings IEEE International Conference on Robotics and Automation.

[17]  Leonard S. Haynes,et al.  On the dynamic model and kinematic analysis of a class of Stewart platforms , 1992, Robotics Auton. Syst..

[18]  Bodo Heimann,et al.  Computational efficient inverse dynamics of 6-DOF fully parallel manipulators by using the Lagrangian formalism , 2009 .

[19]  Wisama Khalil,et al.  Modeling of mechanical systems with lumped elasticity , 2000, Proceedings 2000 ICRA. Millennium Conference. IEEE International Conference on Robotics and Automation. Symposia Proceedings (Cat. No.00CH37065).

[20]  Stefan Staicu,et al.  Dynamics of the 6-6 Stewart parallel manipulator , 2011 .

[21]  Frédéric Boyer,et al.  Modeling and Control of Flexible Robots , 2010 .

[22]  Clément Gosselin,et al.  On the Modeling of Leg Constraints in the Dynamic Analysis of Gough/Stewart-Type Platforms , 2009 .

[23]  Kok-Meng Lee,et al.  Dynamic analysis of a three-degrees-of-freedom in-parallel actuated manipulator , 1988, IEEE J. Robotics Autom..

[24]  Wisama Khalil,et al.  A novel solution for the dynamic modeling of Gough-Stewart manipulators , 2002, Proceedings 2002 IEEE International Conference on Robotics and Automation (Cat. No.02CH37292).

[25]  Clément Gosselin Parallel computational algorithms for the kinematics and dynamics of parallel manipulators , 1993, [1993] Proceedings IEEE International Conference on Robotics and Automation.

[26]  Shaowen Fu,et al.  Comments on “A Newton–Euler formulation for the inverse dynamics of the Stewart platform manipulator” by B. Dasgupta and T.S. Mruthyunjaya [Mech. Mach. Theory 33 (1998) 1135–1152] , 2007 .

[27]  Min-Jie Liu,et al.  Dynamics analysis of the Gough-Stewart platform manipulator , 2000, IEEE Trans. Robotics Autom..

[28]  Sébastien Briot,et al.  Recursive and symbolic calculation of the elastodynamic model of flexible parallel robots , 2014, Int. J. Robotics Res..

[29]  A. K. Mallik,et al.  Dynamic stability index and vibration analysis of a flexible Stewart platform , 2007 .

[30]  Simon Wiedemann,et al.  Comparison of Results in Flexible Multibody Dynamics Using Various Approaches , 2003 .

[31]  Laurent Vermeiren,et al.  Revisiting the inverse dynamics of the Gough–Stewart platform manipulator with special emphasis on universal–prismatic–spherical leg and internal singularity , 2012 .

[32]  Etienne Burdet,et al.  A body-oriented method for finding a linear form of the dynamic equation of fully parallel robots , 1997, Proceedings of International Conference on Robotics and Automation.

[33]  Frédéric Boyer,et al.  An Efficient Calculation of Flexible Manipulator Inverse Dynamics , 1998, Int. J. Robotics Res..