Skip to main content
×
×
Home

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

  • Yongjie Zhao (a1) and Feng Gao (a1)
Summary

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.

Copyright
Corresponding author
*Corresponding author. E-mail: meyjzhao@yahoo.com.cn
References
Hide All
1.Merlet, J. P., Parallel Robots, 2nd ed. (Kluwer Academic, Dordrecht, 2005).
2.Tsai, L. W., Robot Analysis—The Mechanics of Serial and Parallel Manipulators (John Wiley and Sons, New York, 1999).
3.Huang, Z., Fang, Y. F. and Kong, L. F., Theory of Parallel Robotic Mechanisms and Control (in Chinese) (China Machine Press, Beijing, 1997).
4.Harib, K. and Srinivasan, K., “Kinematic and dynamic analysis of Stewart platform-based machine tool structures,” Robotica 21 (5), 541554 (2003).
5.Riebe, S. and Ulbrich, H., “Modelling and online computation of the dynamics of a parallel kinematic with six degrees-of-freedom,” Arch. Appl. Mech. 72 (11–12), 817829 (2003).
6.Carvalho, J. C. M. and Ceccarelli, M., “A closed-form formulation for the inverse dynamics of a Cassino parallel manipulator,” Multibody Syst. Dyn. 5 (2), 185210 (2001).
7.Dasgupta, B. and Mruthyunjaya, T. S., “Closed-form dynamic equations of the Stewart platform through the Newton–Euler approach,” Mech. Mach. Theory 33 (7), 9931012 (1998).
8.Dasgupta, B. and Mruthyunjaya, T. S., “A Newton–Euler formulation for the inverse dynamics of the Stewart platform manipulator,” Mech. Mach. Theory 33 (8), 11351152 (1998).
9.Khalil, W. and Guegan, S., “A Novel Solution for the Dynamic Modeling of Gough–Stewart Manipulators,” Proceeding of the 2002 IEEE International Conference on Robotics and Automation, Washington, USA (2002) pp. 817–822.
10.Do, W. Q. D. and Yang, D. C. H., “Inverse dynamic analysis and simulation of a platform type of robot,” J. Rob. Syst. 5 (52), 209227 (1988).
11.Ji, Z., “Study of the Effect of Leg Inertia in Stewart Platform,” Proceeding of the 1993 IEEE International Conference on Robotics and Automation, Atlanta, USA (1993) pp. 212–226.
12.Khalil, W. and Guegan, S., “Inverse and direct dynamic modeling of Gough–Stewart robots,” IEEE Trans. Rob. 20 (4), 755761 (2004).
13.Dasgupta, B. and Choudhury, P., “A general strategy based on the Newton–Euler approach for the dynamic formulation of parallel manipulators,” Mech. Mach. Theory 34 (6), 801824 (1999).
14.Lee, S. S. and Lee, J. M., “Design of a general purpose 6-DOF haptic interface,” Mechatronics 13 (7), 697722 (2003).
15.Lee, K. M. and Shan, D. K., “Dynamic analysis of a three-degrees-freedom in-parallel actuated manipulator,” IEEE Trans. Rob. Automat. 4 (3), 361367 (1988).
16.Lee, J., Albus, J., Dagalakis, N. G. and Tsai, T., “Computer simulation of a parallel link manipulator,” Rob. Comput.-Integr. Manufact. 5 (4), 333342 (1989).
17.Pang, H. and Shahinpoor, M., “Inverse dynamics of a parallel manipulator,” J. Rob. Syst. 11 (8), 693702 (1994).
18.Geng, Z., Haynes, L. S., Lee, T. D. and Carroll, R. L., “On the dynamic and kinematic analysis of a class of Stewart platform,” Rob. Autonom. Syst. 9 (4), 237254 (1992).
19.Lebret, G., Liu, K. and Lewis, F. L., “Dynamic analysis and control of a Stewart Platform manipulator,” J. Rob. Syst. 10 (5), 629655 (1993).
20.Miller, K. and Clavel, R., “The Lagrange-based model of Delta-4 robot dynamics,” Robotersysteme 8 (4), 4954 (1992).
21.Ben-Horin, R., Shoham, M. and Djerassi, S., “Kinematics, dynamics and construction of a planarly actuated parallel robot,” Rob. Comput.-Integr. Manufact. 14 (2), 163172 (1998).
22.Liu, M. J., Li, C. X. and Li, C. N., “Dynamics analysis of the Gough–Stewart platform manipulator,” IEEE Trans. Rob. Automat. 16 (1), 9498 (2000).
23.Li, M., Huang, T., Mei, J. P., Zhao, X. M., Chetwynd, D. G. and Hu, S. J., “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.Sokolov, A. and Xirouchakis, P., “Dynamics analysis of a 3-DOF parallel manipulator with R-P-S joint structure,” Mech. Mach. Theory 42 (5), 541557 (2007).
25.Caccavale, F., Siciliano, B. and Villani, L., “The Tricept robot: Dynamics and impedance control,” IEEE/ASME Trans. Mechatron. 8 (2), 263268 (2003).
26.Wang, J. and Gosselin, C. M., “A new approach for the dynamic analysis of parallel manipulators,” Multibody Syst. Dyn. 2 (3), 317334 (1998).
27.Stefan, S., Laurian, S. and Radu, R., “Inverse Dynamics of Star Parallel Manipulator,” Proceedings of the 2004 IEEE International Conference on Control Applications, Taipei, Taiwan (2004) pp. 333–337.
28.Tsai, L. W., “Solving the inverse dynamics of a Stewart–Gough manipulator by the principle of virtual work,” ASME J. Mech. Des. 122 (1), 39 (2000).
29.Zhu, Z. Q., Li, J. S., Gan, Z. X. and Zhang, H., “Kinematic and dynamic modelling for real-time control of Tau parallel robot,” Mech. Mach. Theory 40 (9), 10511067 (2005).
30.Codourey, A., “Dynamic modeling of parallel robots for computed-torque control implementation,” Int. J. Rob. Res. 17 (2), 13251336 (1998).
31.Codourey, A. and Burdet, E., “A Body Oriented Method for Finding a Linear Form of the Dynamic Equations of Fully Parallel Robot,” Proceeding of the 1997 IEEE International Conference on Robotics and Automation, Albuquerque, USA (1997) pp. 1612–1618.
32.Zhao, Y. J., Yang, Z. Y. and Huang, T., “Inverse dynamics of Delta robot based on the principle of virtual work,” Trans. Tianjin Univ. 11 (4), 268273 (2005).
33.Staicu, S. and Carp-Ciocardia, D. C., “Dynamic Analysis of Clavel's Delta Parallel Robot,” Proceedings of the 2003 IEEE International Conference on Robotics and Automation, Taipei, Taiwan (2003) pp. 4116–4121.
34.Zhang, C. D. and Song, S. M., “An effective method for inverse dynamics manipulators based upon virtual work principle,” J. Rob. Syst. 10 (5), 605627 (1993).
35.Gallardo, J., Rico, J. M. and Frisoli, A., “Dynamics of parallel manipulators by means of screw theory,” Mech. Mach. Theory 38 (11), 11131131 (2003).
36.Muller, A. and Maiber, P., “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.Khan, W. A., Krovi, V. A., Saha, S. K. and Angeles, J., “Recursive kinematics and inverse dynamics for a planar 3R parallel manipulator,” ASME J. Dyn. Syst., Meas. Control 127 (4), 529536 (2005).
38.Rao, A. B. Koteswara, Saha, S. K. and Rao, P. V. M., “Dynamics modelling of hexaslides using the decoupled natural orthogonal complement matrices,” Multibody Syst. Dyn. 15 (2), 159180 (2006).
39.Xi, F. F., Angelico, O. and Sinatra, R., “Tripod dynamics and its inertia effect,” ASME J. Mech. Des. 127 (1), 144149 (2005).
40.Lee, M. K. and Park, K. W., “Kinematics and dynamics analysis of a double parallel manipulator for enlarging workspace and avoiding singularities,” IEEE Trans. Rob. Automat. 15 (6), 10241034 (1999).
41.Sugimoto, K., “Kinematics and dynamic analysis of parallel manipulator by means of motor algebra,” ASME J. Mech., Transm. Automat. Des. 109 (1), 37 (1987).
42.Geike, T. and McPhee, J., “Inverse dynamic analysis of parallel manipulators with full mobility,” Mech. Mach. Theory 38 (6), 549562 (2003).
43.McPhee, J., Shi, P. and Piedboeuf, J. C., “Dynamics of multibody systems using virtual work and symbolic programming,” Math. Comput. Model. Dyn. Syst. 8 (3), 137155 (2002).
44.Selig, J. M. and McAree, P. R., “Constrained robot dynamics II: Parallel machines,” J. Rob. Syst. 16 (9), 487498 (1999).
45.Gosselin, C. M., “Parallel computational algorithms for the kinematics and dynamics of planar and spatial parallel manipulators,” ASME J. Dyn. Syst., Meas. Control 118 (1), 2228 (1996).
46.Wiens, G. J., Shamblin, S. A. and Oh, Y. H., “Characterization of PKM dynamics in terms of system identification,” Proc. Instn. Mech. Engrs. Part K: J. Multi-Body Dyn. 216 (1), 5972 (2002).
47.Yiu, Y. K., Cheng, H., Xiong, Z. H., Liu, G. F. and Li, Z. X., “On the Dynamics of Parallel Manipulators,” Proceeding of the 2001 IEEE International Conference on Robotics and Automation, Seoul, Korea (2001) pp. 3766–3771.
48.Cheng, H., Yiu, Y. K. and Li, Z. X., “Dynamics and control of redundantly actuated parallel manipulators,” IEEE Trans. Mechatron. 8 (4), 483491 (2003).
49.Huang, Q., Hadeby, H. and Sohlenius, G., “Connection method for dynamic modelling and simulation of parallel kinematic mechanism (PKM) machines,” Int. J. Adv. Manufact. Technol. 19 (3), 163173 (2002).
50.Ider, S. Kemal, “Inverse dynamics of parallel manipulators in the presence of drive singularities,” Mech. Mach. Theory 40 (1), 3344 (2005).
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Robotica
  • ISSN: 0263-5747
  • EISSN: 1469-8668
  • URL: /core/journals/robotica
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×

Keywords

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 62 *
Loading metrics...

Abstract views

Total abstract views: 381 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 19th July 2018. This data will be updated every 24 hours.