Hostname: page-component-76fb5796d-45l2p Total loading time: 0 Render date: 2024-04-26T01:04:22.287Z Has data issue: false hasContentIssue false
  • English
  • Français

A force analysis of a 3-RPS parallel mechanism by using screw theory

Published online by Cambridge University Press:  23 March 2011

Y. Zhao ,
J. F. Liu  and
Z. Huang
Y. Zhao
Affiliation:
Robotics Research Center, Yanshan University, Qinhuangdao, 066004, P.R. China
J. F. Liu
Affiliation:
Robotics Research Center, Yanshan University, Qinhuangdao, 066004, P.R. China
Z. Huang*
Affiliation:
Robotics Research Center, Yanshan University, Qinhuangdao, 066004, P.R. China
*
*Corresponding author. E-mail: huangz@ysu.edu.cn
Get access Rights & Permissions [Opens in a new window]

Summary

The force analysis of parallel manipulators is one of the important issues for mechanical design and control, but it is quite difficult often because of the excessive unknowns. A new approach using screw theory for a 3-RPS parallel mechanism is proposed in this paper. It is able to markedly reduce the number of unknowns and even make the number of simultaneous equations to solve not more than six each time, which may be called force decoupling. With this method, first the main-pair reactions need to be solved for, and then, the active forces and constraint reactions of all other kinematic pairs can be simultaneously obtained by analyzing the equilibrium of each body one by one. Finally, a numerical example and a discussion are given.

Keywords

Parallel mechanismScrew theoryForce analysisActive forceConstraint reaction
Type
Articles
Information
Robotica , Volume 29 , Issue 7 , December 2011 , pp. 959 - 965
Copyright
Copyright © Cambridge University Press 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Kumar, V. and Waldron, K. J., “Force Distribution in Closed Kinematic Chains,” Proceedings of the 1988 IEEE International Conference on Robotics and Automation, Philadelphia, PA, USA (1988) pp. 114–119.CrossRefGoogle Scholar
2.Nahon, M. and Angeles, J., “Real-Time Force Optimization in Parallel Kinematic Chains under Inequality Constraints,” Proceedings of the 1991 IEEE International Conference on Robotics and Automation, Sacramento, CA, USA (1991) pp. 2198–2203.CrossRefGoogle Scholar
3.Nahon, M. and Angeles, J., “Optimization of dynamic forces in mechanical hands,” ASME J. Mech. Des. 113 (2), 167–173 (1991).CrossRefGoogle Scholar
4.Buttolo, P. and Hannaford, B., “Advantages of Actuation Redundancy for the Design of Haptic Displays,” Proceedings of the 1995 ASME International Mechanical Engineering Congress and Exposition – Part 2, San Francisco, CA, USA (1995) pp. 623–630.Google Scholar
5.Dasgupta, B. and Mruthyunjaya, T. S., “Force redundancy in parallel manipulators: Theoretical and practical issues,” Mech. Mach. Theory 33 (6), 727–742 (1998a).Google Scholar
6.Dasgupta, B. and Mruthyunjaya, T. S., “A Newton-Euler formulation for the inverse dynamics of the stewart platform manipulator,” Mech. Mach. Theory 33 (8), 1135–1152 (1998b).CrossRefGoogle Scholar
7.Merlet, J. P., “Efficient Estimation of the External Articular Forces of a Parallel Manipulator in a Translational Workspace,” Proceedings of the 1998 IEEE International Conference on Robotics and Automation, Leuven, Belgium (1998) pp. 1982–1987.Google Scholar
8.Kim, H. S. and Choi, Y. J., “The Kinetostatic Capability Analysis of Robotic Manipulators,” Proceedings of the 1999 IEEE/RSJ International Conference on Intelligent Robots and Systems, Kyongju, South Korea (1999) pp. 1241–1246.Google Scholar
9.Merlet, J. P., Parallel Robots (Kluwer Academic Publishers, 2000).Google Scholar
10.Zhang, D. and Gosselin, C. M., “Kinetostatic modeling of n-dof parallel mechanisms with passive constraining leg and prismatic actuators,” ASME J. Mech. Des. 123 (3), 375–381 (2001).CrossRefGoogle Scholar
11.Zhang, D. and Gosselin, C. M., “Kinetostatic modeling of parallel mechanisms with a passive constraining leg and revolute actuators,” Mech. Mach. Theory 37 (6), 599–617 (2002).Google Scholar
12.Gallardo, J., Rico, J. M., Frisoli, A., Checcacci, D. and Bergamasco, M., “Dynamics of parallel manipulators by means of screw theory,” Mech. Mach. Theory 38 (11), 1113–1131 (2003).Google Scholar
13.Firmani, F. and Podhorodeski, R. P., “Force-unconstrained poses for a redundantly-actuated planar parallel manipulator,” Mech. Mach. Theory 39 (5), 459–476 (2004).CrossRefGoogle Scholar
14.Nokleby, S. B., Fisher, R., Podhorodeski, R. P. and Firmani, F., “Force capabilities of redundantly-actuated parallel manipulators,” Mech. Mach. Theory 40 (5), 578–599 (2005).Google Scholar
15.Li, M., Huang, T., Mei, J., Zhao, X., Chetwynd, D. G. and Hu, S. J., “Dynamic formulation and performance comparison of the 3-dof modules of two reconfigurable PKM-the Tricept and the TriVariant,” ASME J. Mech. Des. 127, 1129–1136 (2005).Google Scholar
16.Russo, A., Sinatra, R. and Xi, F., “Static balancing of parallel robots,” Mech. Mach. Theory 40 (2), 191–202 (2005).CrossRefGoogle Scholar
17.Lu, Y., Shi, Y. and Hu, B., “A CAD Variation Geometrical Approach of Solving Active/Constrained Forces of Some Parallel Manipulators with SPR-type Active Legs,” Proceedings of the ASME International Design Engineering Technical Conference (DETC2007), Report No. MECH-34308, Las Vegas, Nevada, USA (2007) pp. 839–845.Google Scholar
18.Lu, Y., “Using virtual work theory and CAD functionalities for solving active and passive force of spatial parallel manipulators,” Mech. Mach. Theory 42 (7), 839–858 (2007).Google Scholar
19.Ceccarelli, M., Fundamentals of Mechanics of Robotic Manipulators (Kluwer Academic Publishers, Netherlands, 2004).CrossRefGoogle Scholar
20.Ball, R. S., Theory of Screws (Cambridge University Press, London, 1900).Google Scholar
21.Hunt, K. H., Kinematic Geometry of Mechanisms (Oxford University Press, Oxford, 1978).Google Scholar
22.Huang, Z. and Li, Q. C., “General methodology for type synthesis of lower-mobility symmetrical parallel manipulators and several novel manipulators,” Int. J. Robot. Res. 21 (2), 131–145 (2002).CrossRefGoogle Scholar
23.Frisoli, A., Checcacci, D., Salsedo, F. and Bergamasco, M., “Synthesis by screw algebra of translating in-parallel actuated mechanisms,” In: Advances in Robot Kinematics (Lenarčič, J. and Stanišič, M. M., eds.) (Kluwer Academic Publishers, 2000) pp. 433–440.CrossRefGoogle Scholar
24.Huang, Z. and Li, Q. C., “Construction and kinematic properties of 3-UPU parallel mechanisms,” Proceedings of the Design Engineering Technical Conferences (DETC2002), ASME Paper MECH-34321, Montreal, Canada (2002) pp. 1027–1033.Google Scholar
25.Zeng, D. X. and Huang, Z., “Mobility and Position Analysis of a Novel 3-DOF Translational Parallel Mechanism,” Proceedings of the International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, ASME Paper No. DETC2006–99031, Philadelphia, PA, USA (2006) pp. 957–963.Google Scholar
26.Huang, Z. and Li, Q. C., “On the Type Synthesis of Lower-Mobility Parallel Manipulators,” 2002 ASME Conference Workshop, Quebic (2002).Google Scholar
27.Huang, Z. and Li, Q. C., “Type synthesis of symmetrical lower-mobility parallel mechanisms using constraint-synthesis method,” Int. J. Robot. Res. 22 (1), 59–79 (2003).Google Scholar
28.Di Gregorio, R., “The 3-RRS wrist: A new, very simple and not overconstrained spgerical parallel manipulator,” Proceedings of the 2002 ASME Design Engineering Technical Conferences, Report No. MECH-34344, Montreal, Canada (2002) pp. 1193–1199.Google Scholar
29.Li, Q.C. and Huang, Z., “A family of symmetrical lower-mobility parallel mechanisms with spherical and parallel subchains,” J. Robot. Syst. 20 (6), 297–305 (2003).CrossRefGoogle Scholar
30.Huang, Z., Kong, L. F. and Fang, Y. F., Mechanism Theory of Parallel Robotic Manipulator and Control (China Mechanical Press, Beijing, 1997).Google Scholar
31.Huang, Z. and Li, Q. C., “General methodology for type synthesis of lower-mobility symmetrical parallel manipulators and several novel manipulators,” Int. J. Robot Res. 21 (2), 131–145 (2002).CrossRefGoogle Scholar
32.Huang, Z., Liu, J. F. and Li, Q. C., “Unified methodology for mobility analysis based on screw theory,” In: Smart Devices and Machines for Advanced Manufacturing (Wang, L. and Xi, J., eds.) (Springer-Verlag, London, 2008).Google Scholar
33.Huang, Z., Zhao, Y. and Liu, J. F., “Kinetostatic analysis of 4-R(CRR) parallel manipulator with overconstraints via reciprocal-screw theory,” Adv. Mech. Eng. 2010, 11 pp. (2010).Google Scholar