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Inverse dynamics of the 6-dof out-parallel manipulator by means of the principle of virtual work

  • Yongjie Zhao (a1) and Feng Gao (a1)
  • DOI:
  • Published online: 01 March 2009

In this paper, the inverse dynamics of the 6-dof out-parallel manipulator is formulated by means of the principle of virtual work and the concept of link Jacobian matrices. The dynamical equations of motion include the rotation inertia of motor–coupler–screw and the term caused by the external force and moment exerted at the moving platform. The approach described here leads to efficient algorithms since the constraint forces and moments of the robot system have been eliminated from the equations of motion and there is no differential equation for the whole procedure. Numerical simulation for the inverse dynamics of a 6-dof out-parallel manipulator is illustrated. The whole actuating torques and the torques caused by gravity, velocity, acceleration, moving platform, strut, carriage, and the rotation inertia of the lead screw, motor rotor and coupler have been computed.

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4.K. Harib and K. Srinivasan , “Kinematic and dynamic analysis of Stewart platform-based machine tool structures,” Robotica 21 (5), 541554 (2003).

6.J. C. M. Carvalho and M. Ceccarelli , “A closed-form formulation for the inverse dynamics of a Cassino parallel manipulator,” Multibody Syst. Dyn. 5 (2), 185210 (2001).

7.B. Dasgupta and T. S. Mruthyunjaya , “Closed-form dynamic equations of the Stewart platform through the Newton–Euler approach,” Mech. Mach. Theory 33 (7), 9931012 (1998).

8.B. Dasgupta and T. S. Mruthyunjaya , “A Newton–Euler formulation for the inverse dynamics of the Stewart platform manipulator,” Mech. Mach. Theory 33 (8), 11351152 (1998).

10.W. Q. D. Do and D. C. H. Yang , “Inverse dynamic analysis and simulation of a platform type of robot,” J. Rob. Syst. 5 (52), 209227 (1988).

12.W. Khalil and S. Guegan , “Inverse and direct dynamic modeling of Gough–Stewart robots,” IEEE Trans. Rob. 20 (4), 755761 (2004).

13.B. Dasgupta and P. Choudhury , “A general strategy based on the Newton–Euler approach for the dynamic formulation of parallel manipulators,” Mech. Mach. Theory 34 (6), 801824 (1999).

14.S. S. Lee and J. M. Lee , “Design of a general purpose 6-DOF haptic interface,” Mechatronics 13 (7), 697722 (2003).

15.K. M. Lee and D. K. Shan , “Dynamic analysis of a three-degrees-freedom in-parallel actuated manipulator,” IEEE Trans. Rob. Automat. 4 (3), 361367 (1988).

16.J. Lee , J. Albus , N. G. Dagalakis and T. Tsai , “Computer simulation of a parallel link manipulator,” Rob. Comput.-Integr. Manufact. 5 (4), 333342 (1989).

17.H. Pang and M. Shahinpoor , “Inverse dynamics of a parallel manipulator,” J. Rob. Syst. 11 (8), 693702 (1994).

18.Z. Geng , L. S. Haynes , T. D. Lee and R. L. Carroll , “On the dynamic and kinematic analysis of a class of Stewart platform,” Rob. Autonom. Syst. 9 (4), 237254 (1992).

19.G. Lebret , K. Liu and F. L. Lewis , “Dynamic analysis and control of a Stewart Platform manipulator,” J. Rob. Syst. 10 (5), 629655 (1993).

21.R. Ben-Horin , M. Shoham and S. Djerassi , “Kinematics, dynamics and construction of a planarly actuated parallel robot,” Rob. Comput.-Integr. Manufact. 14 (2), 163172 (1998).

23.M. Li , T. Huang , J. P. Mei , X. M. Zhao , D. G. Chetwynd and S. J. Hu , “Dynamic formulation and performance comparison of the 3-DOF modules of two reconfigurable PKMs-the TriVariant and the Tricept,” ASME J. Mech. Des. 127 (6), 11291136 (2005).

24.A. Sokolov and P. Xirouchakis , “Dynamics analysis of a 3-DOF parallel manipulator with R-P-S joint structure,” Mech. Mach. Theory 42 (5), 541557 (2007).

25.F. Caccavale , B. Siciliano and L. Villani , “The Tricept robot: Dynamics and impedance control,” IEEE/ASME Trans. Mechatron. 8 (2), 263268 (2003).

26.J. Wang and C. M. Gosselin , “A new approach for the dynamic analysis of parallel manipulators,” Multibody Syst. Dyn. 2 (3), 317334 (1998).

28.L. W. Tsai , “Solving the inverse dynamics of a Stewart–Gough manipulator by the principle of virtual work,” ASME J. Mech. Des. 122 (1), 39 (2000).

29.Z. Q. Zhu , J. S. Li , Z. X. Gan and H. Zhang , “Kinematic and dynamic modelling for real-time control of Tau parallel robot,” Mech. Mach. Theory 40 (9), 10511067 (2005).

30.A. Codourey , “Dynamic modeling of parallel robots for computed-torque control implementation,” Int. J. Rob. Res. 17 (2), 13251336 (1998).

34.C. D. Zhang and S. M. Song , “An effective method for inverse dynamics manipulators based upon virtual work principle,” J. Rob. Syst. 10 (5), 605627 (1993).

35.J. Gallardo , J. M. Rico and A. Frisoli , “Dynamics of parallel manipulators by means of screw theory,” Mech. Mach. Theory 38 (11), 11131131 (2003).

36.A. Muller and P. Maiber , “A Lie-group formulation of kinematics and dynamics of constrained MBS and its application to analytical mechanics,” Multibody Syst. Dyn. 9 (4), 311352 (2003).

37.W. A. Khan , V. A. Krovi , S. K. Saha and J. Angeles , “Recursive kinematics and inverse dynamics for a planar 3R parallel manipulator,” ASME J. Dyn. Syst., Meas. Control 127 (4), 529536 (2005).

38.A. B. Koteswara Rao , S. K. Saha and P. V. M. Rao , “Dynamics modelling of hexaslides using the decoupled natural orthogonal complement matrices,” Multibody Syst. Dyn. 15 (2), 159180 (2006).

39.F. F. Xi , O. Angelico and R. Sinatra , “Tripod dynamics and its inertia effect,” ASME J. Mech. Des. 127 (1), 144149 (2005).

41.K. Sugimoto , “Kinematics and dynamic analysis of parallel manipulator by means of motor algebra,” ASME J. Mech., Transm. Automat. Des. 109 (1), 37 (1987).

42.T. Geike and J. McPhee , “Inverse dynamic analysis of parallel manipulators with full mobility,” Mech. Mach. Theory 38 (6), 549562 (2003).

43.J. McPhee , P. Shi and J. C. Piedboeuf , “Dynamics of multibody systems using virtual work and symbolic programming,” Math. Comput. Model. Dyn. Syst. 8 (3), 137155 (2002).

44.J. M. Selig and P. R. McAree , “Constrained robot dynamics II: Parallel machines,” J. Rob. Syst. 16 (9), 487498 (1999).

45.C. M. Gosselin , “Parallel computational algorithms for the kinematics and dynamics of planar and spatial parallel manipulators,” ASME J. Dyn. Syst., Meas. Control 118 (1), 2228 (1996).

48.H. Cheng , Y. K. Yiu and Z. X. Li , “Dynamics and control of redundantly actuated parallel manipulators,” IEEE Trans. Mechatron. 8 (4), 483491 (2003).

50.S. Kemal Ider , “Inverse dynamics of parallel manipulators in the presence of drive singularities,” Mech. Mach. Theory 40 (1), 3344 (2005).

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