Skip to main content Accessibility help

Singularity robust balancing of parallel manipulators following inconsistent trajectories

  • Mustafa Özdemir (a1)


When compared to serial manipulators, parallel manipulators have small workspaces mainly due to their closed-loop structure. As opposed to type I singularities (or inverse kinematic singularities) that are generally encountered at the workspace boundaries, type II singularities characteristically arise within the workspace, and around them, the inverse dynamic solution becomes unbounded. Hence, a desired trajectory passing through a type II singular position cannot be achieved by the manipulator, and its useful workspace becomes further and substantially reduced. It has been previously shown in the literature that if the trajectory is replanned in such a way that the dynamic equations of motion of the manipulator are consistent at a type II singularity, i.e. if the trajectory is consistent, then the manipulator passes through this singular configuration in a controllable manner, while the inverse dynamic solution remains finite. An inconsistent trajectory, on the other hand, is stated in the literature to be unrealizable. However, although seems a promising technique, trajectory replanning itself is also a deviation from the originally desired trajectory, and there might be cases in applications where, due to some task-specific reasons, the desired trajectory, although inconsistent, is not allowed to be replanned to satisfy the consistency conditions. In this paper, a method of singularity robust balancing is proposed for parallel manipulators passing through type II singular configurations while following inconsistent trajectories. By this means, an originally unrealizable inconsistent trajectory passing through a type II singularity can be followed without any deviation, while the required actuator forces remain bounded after the manipulator is balanced according to the design methodology presented in this study. The effectiveness of the introduced method is shown through numerical simulations considering a planar 3-DOF 2-PRR parallel manipulator under different balancing scenarios.


Corresponding author

*Corresponding author. E-mail:


Hide All
1. Boudreau, R. and Nokleby, S., “Force optimization of kinematically-redundant planar parallel manipulators following a desired trajectory,” Mech. Mach. Theory 56, 138155 (2012).
2. Choi, H.-B. and Ryu, J., “Singularity analysis of a four degree-of-freedom parallel manipulator based on an expanded 6 × 6 Jacobian matrix,” Mech. Mach. Theory 57, 5161 (2012).
3. Gosselin, C. and Angeles, J., “Singularity analysis of closed-loop kinematic chains,” IEEE Trans. Robot. Autom. 6, 281290 (1990).
4. Choudhury, P. and Ghosal, A., “Singularity and controllability analysis of parallel manipulators and closed-loop mechanisms,” Mech. Mach. Theory 35, 14551479 (2000).
5. Jui, C. K. K. and Sun, Q., “Path tracking of parallel manipulators in the presence of force singularity,” J. Dyn. Syst. Meas. Control 127, 550563 (2005).
6. Dasgupta, B. and Mruthyunjaya, T. S., “Force redundancy in parallel manipulators: Theoretical and practical issues,” Mech. Mach. Theory 33, 727742 (1998).
7. Özgören, M. K., “Motion control of constrained systems considering their actuation-related singular configurations,” Proc. Inst. Mech. Eng. I 215, 113123 (2001).
8. Ider, S. K., “Inverse dynamics of parallel manipulators in the presence of drive singularities,” Mech. Mach. Theory 40, 3344 (2005).
9. Ider, S. K., “Singularity robust inverse dynamics of planar 2-RPR parallel manipulators,” Proc. Inst. Mech. Eng. C 218, 721730 (2004).
10. Merlet, J.-P., “Singular configurations of parallel manipulators and Grassmann geometry,” Int. J. Robot. Res. 8, 4556 (1989).
11. Basu, D. and Ghosal, A., “Singularity analysis of platform-type multi-loop spatial mechanisms,” Mech. Mach. Theory 32, 375389 (1997).
12. St-Onge, B. M. and Gosselin, C. M., “Singularity analysis and representation of the general Gough–Stewart platform,” Int. J. Robot. Res. 19, 271288 (2000).
13. Collins, C. L. and Long, G. L., “The singularity analysis of an in-parallel hand controller for force-reflected teleoperation,” IEEE Trans. Robot. Autom. 11, 661669 (1995).
14. Muller, A., “Internal preload control of redundantly actuated parallel manipulators-Its application to backlash avoiding control,” IEEE Trans. Robot. 21, 668677 (2005).
15. Krut, S., Company, O. and Pierrot, F., “Velocity performance indices for parallel mechanisms with actuation redundancy,” Robotica 22, 129139 (2004).
16. Nokleby, S. B., Fisher, R., Podhorodeski, R. P. and Firmani, F., “Force capabilities of redundantly-actuated parallel manipulators,” Mech. Mach. Theory 40, 578599 (2005).
17. Briot, S. and Arakelian, V., “Optimal force generation in parallel manipulators for passing through the singular positions,” Int. J. Robot. Res. 27, 967983 (2008).


Singularity robust balancing of parallel manipulators following inconsistent trajectories

  • Mustafa Özdemir (a1)


Full text views

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

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed