Hostname: page-component-78c5997874-xbtfd Total loading time: 0 Render date: 2024-11-10T16:18:35.383Z Has data issue: false hasContentIssue false
  • English
  • Français

Solving stiffness and deformation of a 3-UPU parallel manipulator with one translation and two rotations

Published online by Cambridge University Press:  05 January 2011

Bo Hu  and
Yi Lu
Bo Hu*
Affiliation:
Robotics Research Center, College of Mechanical Engineering, Yanshan University, Qinhuangdao, Hebei, 066004P. R. China
Yi Lu
Affiliation:
Robotics Research Center, College of Mechanical Engineering, Yanshan University, Qinhuangdao, Hebei, 066004P. R. China
*
*Corresponding author. E-mails: hbz0001@yahoo.com.cn, hb_zly2007@163.com
Get access Rights & Permissions [Opens in a new window]

Summary

The stiffness modeling and elastic deformation of 3 degrees of freedom, 3-universal joints–prismatic pairs–universal joints (UPU) parallel manipulator (PM) with one translation and two rotations are studied. First, the constraint wrenches are derived corresponding to the special orientation of universal joints in each of the UPU legs. Second, the elastic deformation of active legs produced by these active forces and constrained wrenches are derived. Third, a 6 × 6 Jacobian matrix is derived from constraint and active forces, and the statics is solved. Finally, the stiffness matrix of 3-UPU PM is established and its elastic deformation is solved.

Keywords

StiffnessParallel manipulatorConstrained forces
Type
Articles
Information
Robotica , Volume 29 , Issue 6 , October 2011 , pp. 815 - 822
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.Merlet, J. P., Parallel Robots (Kluwer, London, 2000).CrossRefGoogle Scholar
2.Angeles, J.Fundamentals of Robotic Mechanical Systems (Springer-Verlag, New York, 2003).Google Scholar
3.Tsai, L. W. and Joshi, S., “Kinematics and optimization of a spatial 3UPU parallel manipulator,” ASME J. Mech. Des. 122 (4), 439–446 (2000).CrossRefGoogle Scholar
4.Di Gregorio, R. and Parenti-Castelli, V., “Mobility analysis of the 3UPU parallel mechanism assembled for a pure translational motion,” ASME J. Mech. Des. 124 (2), 259–264 (2002).CrossRefGoogle Scholar
5.Di Gregorio, R., “Kinematics of the 3UPU wrist,” Mech. Mach. Theory 38 (3), 253–263 (2003).CrossRefGoogle Scholar
6.Chanhee, H., Jinwook, K., Jongwon, K. and Frank, C. P., “Kinematic sensitivity analysis of the 3UPU parallel mechanism,” Mech. Mach. Theory 37 (8), 787–798 (2002).Google Scholar
7.Lu, Y. and Hu, B., “Analysis of kinematics and solution of active/constrained forces of asymmetric 2UPU + X parallel manipulators,” Proc Mech Eng., Part C: J. Mech. Eng. Sci. 220 (12)1819–1830 (2006).CrossRefGoogle Scholar
8.Ji, P. and Wu, H., “Kinematics analysis of an offset 3-UPU translational parallel robotic manipulator,” Robot. Auton. Syst. 42 (2), 117–123 (2003).CrossRefGoogle Scholar
9.Zheng, X. Z., Luo, Y. G., Deng, Z. Y. and Bin, H. Z., “Statics of Rotational 3-UPU Parallel Mechanisms Based on Principle of Virtual Work. 2007,” Proceedings of the IEEE International Conference on Robotics and Biomimetics, Sanya (Dec. 15–18, 2007), pp. 1954–1959.Google Scholar
10.Lu, Y., Shi, Y. and Hu, B., “Kinematic analysis of two novel 3UPU I and 3UPU II PKMs,” Robot. Auton. Syst. 56 (4), 296–305 (2008).CrossRefGoogle Scholar
11.Gosselin, C. M., “Stiffness mapping for parallel manipulators,” IEEE Trans. Robot. Autom. 6 (3), 377–382 (1990).CrossRefGoogle Scholar
12.Joshi, S. and Tsai, L. W., “A comparison study of two 3-DOF parallel manipulators: One with three and the other with four supporting legs,” IEEE Int. Conf. Robot. Autom. 4, 3690–3697 (2002).Google Scholar
13.Dai, J. S., Zhao, T. S. and Nester, C., “Sprained ankle physiotherapy-based mechanism synthesis and stiffness analysis of a robotic rehabilitation device,” Auton. Robots 16 (2), 207–218 (2004).CrossRefGoogle Scholar
14.Zhang, D. and Lang Sherman, Y. T., “Stiffness modeling for a class of reconfigurable PKMs with three to five degrees of freedom,” J. Manuf. Syst. 23 (4), 316–327 (2004).CrossRefGoogle Scholar
15.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).CrossRefGoogle Scholar
16.Li, Y. M. and Xu, Q. S., “Stiffness analysis for a 3-PUU parallel kinematic machine,” Mech. Mach. Theory 43 (2), 186–200 (2008).CrossRefGoogle Scholar
17.Carbone, G. and Ceccarelli, M., “A stiffness analysis for a hybrid parallel–serial manipulator,” Robotica 22 (5), 567–576 (2004).CrossRefGoogle Scholar
18.Liu, X. J., Jin, Z. L. and Gao, F., “Optimum design of 3-DOF spherical parallel manipulators with respect to the conditioning and stiffness indices,” Mech. Mach. Theory 35 (9), 1257–1267 (2000).CrossRefGoogle Scholar
19.Sadjadian, H. and Taghirad, H. D., “Kinematic singularity and stiffness analysis of the hydraulic shoulder: A 3-d.o.f. redundant parallel manipulator,” Adv. Robot. 20 (7), 763–781 (2006).CrossRefGoogle Scholar
20.Lu, Y. and Hu, B., “Unification and simplification of velocity/acceleration of limited-dof parallel manipulators with linear active legs,” Mech. Mach. Theory 43 (9), 1112–1128 (2008).CrossRefGoogle Scholar