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Recursive modelling in dynamics of Delta parallel robot

Published online by Cambridge University Press:  01 March 2009

Stefan Staicu*
Affiliation:
Department of Mechanics, University ‘Politehnica’ of Bucharest, Romania Email: [email protected]

Summary

Recursive matrix relations in kinematics and dynamics of a Delta parallel robot having three revolute actuators are established in this paper. The prototype of the manipulator is a three degrees-of-freedom space mechanism, which consists of a system of parallel closed kinematical chains connecting to the moving platform. Knowing the translation motion of the platform, we develop first the inverse kinematics problem and determine the position, velocity and acceleration of each robot's element. Further, the inverse dynamic problem is solved using an approach based on the fundamental principle of virtual work. Finally, a comparative study on time-history evolution of the torques of the three actuators is analysed.

Type
Article
Copyright
Copyright © Cambridge University Press 2008

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References

1.Tsai, L.-W., Robot analysis: The mechanics of serial and parallel manipulator (John Wiley & Sons Inc., New York, 1999).Google Scholar
2.Chablat, D. and Wenger, P., “Architecture optimisation of a 3-DOF parallel mechanism for machining applications: The orthoglide,” IEEE Trans. Robot. Autom. 19 (3), 403410 (2003).CrossRefGoogle Scholar
3.Liu, X.-J., Jeong, J. and Kim, J., “A three translational DoFs parallel cube-manipulator Robotica 21 (6), 645653 (2003).CrossRefGoogle Scholar
4.Angeles, J., Fundamentals of Robotic Mechanical Systems: Theory, Methods and Algorithms (Springer–Verlag, New York, 2002).Google Scholar
5.Innocenti, C. and Parenti Castelli, V., “Direct position analysis of the Stewart platform mechanism,” Mech. Mach. Theory 25 (6), 611621 (1997).Google Scholar
6.Stewart, D., “A Platform with Six Degrees of Freedom”, Proceedings of the Institute of Mechanical Engineers, 1, 15, 180, Part 1, No 15, 371376 (1965).Google Scholar
7.Merlet, J.-P., Parallel robots (Kluwer Academic Publishers, Dordrecht, Boston, London, 2000).Google Scholar
8.Baron, L. and Angeles, J., “The direct kinematics of parallel manipulators under joint-sensor redundancy,” IEEE Trans. Robot. Autom. 16 (1), 1219 (2000).CrossRefGoogle Scholar
9.Parenti Castelli, V. and Di Gregorio, R., “A new algorithm based on two extra-sensors for real-time computation of the actual configuration of generalized Stewart-Gough manipulator,” J. Mech. Des. 122, 294298 (2000).CrossRefGoogle Scholar
10.Hervé, J.-M. and Sparacino, F., “Star. A New Concept in Robotics,” Proceedings of the Third International Workshop on Advances in Robot Kinematics, Ferrara (1992) pp. 176–183.Google Scholar
11.Tremblay, A. and Baron, L., “Geometrical Synthesis of Parallel Manipulators of Star-Like Topology with a Genetic Algorithm,” Proceedings of the IEEE International Conference on Robotics & Automation ICRA'1999, Detroit, Michigan, (1999) pp. 24462451.Google Scholar
12.Clavel, R., “Delta: A Fast Robot with Parallel Geometry,” Proceedings of 18th International Symposium on Industrial Robots, Sydney, Australia (1988) pp. 91100.Google Scholar
13.Tsai, L. -W. and Stamper, R., ”A Parallel Manipulator with only Translational Degrees of Freedom,” ASME Design Engineering Technical Conferences, 96-DETC-MECH-1152, Irvine, CA (1996).Google Scholar
14.Staicu, S. and Carp–Ciocardia, D. C., “Dynamic Analysis of Clavel's Delta Parallel Robot,” Proceedings of the IEEE International Conference on Robotics & Automation ICRA'2003, Taipei, Taiwan (2003) pp. 41164121.Google Scholar
15.Gosselin, C. and Angeles, J., “The optimum kinematics design of a spherical three-degree-of-freedom parallel manipulator,” ASME J. Mech. Trans. Autom. Des. 111 (2), 202207 (1989).Google Scholar
16.Gosselin, C. and Gagné, M., “Dynamic Models for Spherical Parallel Manipulators,” Proceedings of the 9th World Congress on Theory of Machines and Mechanisms, Milan, Italy (1995) pp. 20322036.Google Scholar
17.Wang, J. and Gosselin, C., “A new approach for the dynamic analysis of parallel manipulators,” Multibody Syst. Dyn. 2 (3), 317334 (1998).CrossRefGoogle Scholar
18.Pierrot, F., Reynaud, C. and Fournier, A., “DELTA: A simple and Efficient Parallel Robot,” Robotica 8, 105109 (1990).Google Scholar
19.Li, Y.-W., Wang, J., Wang, L.-P. and Liu, X.-J., “Inverse Dynamics and Simulation of a 3-DOF Spatial Parallel Manipulator,” Proceedings of the IEEE International Conference on Robotics & Automation ICRA'2003, Taipei, Taiwan (2003) pp. 40924097.Google Scholar
20.Zaganeh, R., Sinatra, R. and Angeles, J., “Kinematics and dynamics of a six-degrees-of-freedom parallel manipulator with revolute legs,” Robotica 15 (4), 385394 (1997).CrossRefGoogle Scholar
21.Kane, T. R. and Levinson, D. A., Dynamics. Theory and Applications (Mc Graw Hill, New York, 1985).Google Scholar
22.Sorli, M., Ferarresi, C., Kolarski, M., Borovac, B. and Vucobratovic, M., “Mechanics of Turin parallel robot,” Mech. Mach. Theory 32 (1), 5177 (1997).Google Scholar
23.Geng, Z., Haynes, L. S., Lee, J. D. and Carroll, R. L., “On the dynamic model and kinematic analysis of a class of Stewart platforms,” Robot. Auton. Syst. 9, 237254 (1992).CrossRefGoogle Scholar
24.Dasgupta, B. and Mruthyunjaya, T. S., “A Newton–Euler formulation for the inverse dynamics of the Stewart platform manipulator,” Mech. Mach. Theory 33, 11351152 (1998).Google Scholar
25.Staicu, S., Mecanica teoretica (Edit. Didactica & Pedagogica, Bucharest, 1998).Google Scholar
26.Staicu, S., Zhang, D. and Rugescu, R., “Dynamic modelling of a 3-DOF parallel manipulator using recursive matrix relations,” Robotica 24 (1), 125130 (2006).Google Scholar
27.Staicu, S., “Planetary Gear Train for Robotics,” Proceedings of the IEEE International Conference on Mechatronics ICM'2005, Taipei, Taiwan (2005) pp. 840845.Google Scholar
28.Guegan, S., Khalil, W., Chablat, D. and Wenger, P., “Modélisation dynamique d'un robot parallèle à 3-DDL: l'Orthoglide”, Conférence Internationale Francophone d'Automatique, Nantes, France, 810 Juillet (2002).Google Scholar
29.Zhang, C.-D. and Song, S.-M., “An efficient method for inverse dynamics of manipulators based on virtual work principle,” J. Robot. Syst. 10 (5), 605627 (1993).Google Scholar
30.Bonev, I., Zlatanov, D. and Gosselin, C., “Singularity analysis of 3-DOF planar parallel mechanisms via screw theory,” J. Mech. Des. 125 (3), 573581 (2003).CrossRefGoogle Scholar
31.Xi, F.-F., Angelico, O. and Sinatra, R., “Tripod dynamics and its inertia effects,” J. Mech. Des. 127 (1), 144149 (2005).CrossRefGoogle Scholar
32.Yang, G., Chen, W. and Chen, I-M., “A Geometrical Method for the Singularity Analysis of 3-RRR Planar Parallel Robots with Different Actuation Schemes,” Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems, Lausanne, Switzerland (2002) pp. 2055–2060.Google Scholar
33.Miller, K. and Clavel, R., The Lagrange-Based Model of Delta-4 Robot Dynamics,” Robotersysteme 8, 4954 (1992).Google Scholar
34.Lee, M.-K. and Park, K.-W., “Kinematic and dynamic analysis of a double parallel manipulator for enlarging workspace and avoiding singularities,” IEEE Trans. Robot. Autom. 15 (6), 10241034 (1999).Google Scholar
35.Staicu, S., Liu, X.-J. and Wang, J., “Inverse dynamics of the HALF parallel manipulator with revolute actuators,” Nonlinear Dyn. 50 (1–2), 112 (2007).CrossRefGoogle Scholar
36.Staicu, S. and Zhang, D., “A novel dynamic modelling approach for parallel mechanisms analysis,” Robot. Comput. Integr. Manuf. 24 (1), 167172 (2008).Google Scholar
37.Staicu, S., “Relations matricielles de récurrence en dynamique des mécanismes,” Revue Roumaine des Sciences Techniques- Série de Mécanique Appliquée 50 (1–3), 1528 (2005).Google Scholar