Hostname: page-component-848d4c4894-wzw2p Total loading time: 0 Render date: 2024-06-02T06:49:33.760Z Has data issue: false hasContentIssue false
  • English
  • Français

A new method for isotropic analysis of limited DOF parallel manipulators with terminal constraints

Published online by Cambridge University Press:  13 August 2010

Haibo Qu ,
Yuefa Fang  and
Sheng Guo
Haibo Qu*
Affiliation:
Robotics Research Laboratory, School of Mechanical, Electronic and Control Engineering, Beijing Jiaotong University, Beijing 100044, China
Yuefa Fang
Affiliation:
Robotics Research Laboratory, School of Mechanical, Electronic and Control Engineering, Beijing Jiaotong University, Beijing 100044, China
Sheng Guo
Affiliation:
Robotics Research Laboratory, School of Mechanical, Electronic and Control Engineering, Beijing Jiaotong University, Beijing 100044, China
*
*Corresponding author. E-mail: hbqu.andy@gmail.com
Get access Rights & Permissions [Opens in a new window]

Summary

Based on the terminal constraints system (TCS) and reciprocal screw theory, a novel method is presented to determine the isotropic configurations of limited degree-of-freedom (DOF) parallel manipulators. From the available physical meaning of isotropy, the criteria to determine the isotropic configurations can be transformed to investigate whether the TCS acting on the moving platform works equally well in all directions. From the TCS study, the simplest form of constraints system matrix can be obtained. Then the constraint condition number is defined to measure the isotropy of spatial parallel manipulator based on the TCS. This method not only avoids solving the Jacobian matrix for some complex structural parallel manipulators but also points out the physical meaning of isotropy, which indicates that the TCS acting on the moving platform works equally well in all directions. Three examples are employed to illustrate this method.

Keywords

Isotropic configurationsLimited DOF parallel manipulatorTerminal constraints systemConstraint condition numberReciprocal screw theory
Type
Articles
Information
Robotica , Volume 29 , Issue 4 , July 2011 , pp. 563 - 569
Copyright
Copyright © Cambridge University Press 2010

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.Kircanski, M., “Kinematic isotropy and optimal kinematic design of planar manipulators and a 3-DOF spatial manipulator,” Int. J. Robot. Res. 15 (1), 61–77 (1996).CrossRefGoogle Scholar
2.Klein, C. A. and Miklos, T. A., “Spatial robotic isotropy,” Int. J. Robot. Res. 10 (4), 426–437 (1991).CrossRefGoogle Scholar
3.Tsai, K. Y. and Huang, K. D., “The design of isotropic 6-DOF parallel manipulators using isotropy generators,” Mech. Mach. Theory 38 (11), 1199–1214 (2003).CrossRefGoogle Scholar
4.Zanganeh, K. E. and Angele, J., “Kinematic isotropy and the optimum design of parallel manipulators,” Int. J. Rob. Res. 16 (2), 185–197 (1997).CrossRefGoogle Scholar
5.Fattah, A. and Hasan> Ghasemi, A. M., “Isotropic design of spatial parallel manipulators,” Int. J. Robot. Res. 21 (9), 811–824 (2002).CrossRefGoogle Scholar
6.Gogu, G., “Structural synthesis of fully isotropic parallel robots with Schönflies motions via theory of linear transformations and evolutionary morphology,” Eur. J. Mech. A/Solids 26 (2), 242–269 (2007).CrossRefGoogle Scholar
7.Gogu, G., “Structural synthesis of fully isotropic translational parallel robots via theory of linear transformations,” Eur. J. Mech. A/Solids 23 (6), 1021–1039 (2003).CrossRefGoogle Scholar
8.Gogu, G., “Fully Isotropic T3R1-Type Parallel Manipulators,” In: On advances in Robot Kinematics (Lenari, J. and Galletti, C., eds.) (Kluwer Academic Publishers, Dordrecht, The Netherlands, 2004), pp. 265–272.CrossRefGoogle Scholar
9.Carricato, M. and Parenti-Castelli, V., “Singularity-free fully isotropic translational parallel mechanisms,” Int. J. Robot. Res. 21 (2), 161–174 (2002).CrossRefGoogle Scholar
10.Salisbury, J. K. and Craig, J. J., “Articulated hands: Force control and kinematic issues,” Int. J. Robot. Res. 1 (1), 4–12 (1982).CrossRefGoogle Scholar
11.Angeles, J., Fundamentals of Robotic Mechanical Systems: Theory, Methods and Algorithm, 2nd ed. (Springer-Verlag, New York, 2003).CrossRefGoogle Scholar
12.Gogu, G., “Fully-Isotropic Over-Constrained Planar Parallel Manipulators,” Proceedings of 2004 IEEE/RSJ International Conference on Intelligent Robots and Systems, Sendai, Japan (2004), pp. 3519–3524.Google Scholar
13.Baron, L. and Bernier, G., “The Design of Parallel Manipulators of Star Topology Under Isotropic Constraint,” Proceedings of the ASME Design Engineering Technical Conference and Computers and Information in Engineering Conference, Pittsburgh, PA, USA (2001), pp. 169–175.Google Scholar
14.Tsai, L.-W., Robot Analysis: The Mechanics of Serial and Parallel Manipulators (Wiley, New York, 1999).Google Scholar
15.Zhao, J.-S., Feng, Z.-J., Wang, L.-P., et al. , “The free mobility of a parallel manipulator,” Robotica 24, 635–641 (2006).CrossRefGoogle Scholar
16.Huang, Z., Zhao, Y. S. and Zhao, T. S., Advanced Spatial Mechanism (Higher Education Press, Beijing, China, 2006) (in Chinese).Google Scholar
17.Fang, Y. F. and Tsai, L.-W., “Structure synthesis of 4-DoF and 5-DoF parallel manipulators with identical limb,” Int. J. Rob. Res. 21 (9), 799–810 (2002).CrossRefGoogle Scholar
18.Pond, G. T. and Carretero, J. A., “Formulating Jacobian matrices for the dexterity analysis of parallel manipulators,” Mech. Mach. Theory 41 (12), 1505–1519 (2006).CrossRefGoogle Scholar
19.Merlet, J. P., “Jacobian, manipulability, condition number, and accuracy of parallel robots,” J. Mech. Des. 128 (1), 199–206 (2006).CrossRefGoogle Scholar
20.Zhao, J.-S., Feng, Z.-J., Zhou, K., et al. , “Analysis of the singularity of spatial parallel manipulator with terminal constraints,” Mech. Mach. Theory 40 (3), 275–284 (2005).CrossRefGoogle Scholar
21.Sameer, J. and Tsai, L.-W., “Jacobian analysis of limited-DOF parallel manipulators,” J. Mech. Des. 124 (2), 254–258 (2002).Google Scholar
22.Liu, X.-J. and Bonev, I. A., “Orientation capability, error analysis, and dimensional optimization of two articulated tool heads with parallel kinematics,” J. Manuf. Sci. Eng. Trans. ASME 130 (1), 011015 (2008).CrossRefGoogle Scholar
23.Zhao, J.-S., Zhou, K., Feng, Z.-J., et al. , “A theory of degrees of freedom for mechanisms,” Mech. Mach. Theory 39 (6), 621–643 (2004).CrossRefGoogle Scholar