Skip to main content

Workspace optimization of a class of zero-torsion parallel wrists

  • Yuanqing Wu (a1) and Marco Carricato (a1)

We present singularity-free workspace optimization of a class of two-degree-of-freedom (2-DoF) parallel wrists with large rotation range capability. The wrists in consideration are kinematically equivalent to two families of 2-DoF homokinetic couplings. The first family comprises fully parallel wrists with N (N ≥ 3) double-universal ( $\mathcal{UU}$ ) legs. The second family comprises spherical N- $\mathcal{UU}$ parallel wrists with interconnecting revolute ( $\mathcal{R}$ ) joints. Both families belong to the more general class of zero-torsion parallel manipulators, and are, therefore, collectively referred to as zero-torsion wrists (ZTWs). We carry out a unified singularity-free workspace optimization by utilizing geometric properties of zero-torsion motion manifolds. Our work may serve as a conceptual guide to the design of ZTWs for large tilt-angle applications.

Corresponding author
*Corresponding author. E-mail:
Hide All
1. Merlet, J.-P., Parallel Robots, volume 128 (Springer Science & Business Media, Dordrecht, The Netherlands, 2006).
2. Gosselin, C. and Angeles, J., “Singularity analysis of closed-loop kinematic chains,” IEEE Trans. Robot. Autom. 6 (3), 281290 (1990).
3. Conconi, M. and Carricato, M., “A new assessment of singularities of parallel kinematic chains,” IEEE Trans. Robot. 25 (4), 757770 (2009).
4. Chablat, D. and Wenger, P., “Architecture optimization of a 3-DOF translational parallel mechanism for machining applications, the orthoglide,” IEEE Trans. Robot. Autom. 19 (3), 403410 (2003).
5. Pierrot, F., Reynaud, C. and Fournier, A., “Delta: A simple and efficient parallel robot,” Robotica 8 (2), 105109 (1990).
6. Kong, X. and Gosselin, C. M., “Type synthesis of 3-DOF translational parallel manipulators based on screw theory,” J. Mech. Des. 126 (1), 8392 (2004).
7. Pierrot, F., Nabat, V., Company, O., Krut, S. and Poignet, P., “Optimal design of a 4-DOF parallel manipulator: From academia to industry,” IEEE Trans. Robot. 25 (2), 213224 (2009).
8. Gosselin, C. M. and Hamel, J.-F., “The Agile Eye: A High-Performance Three-Degree-of-Freedom Camera-Orienting Device,” Proceedings of the IEEE International Conference on Robotics and Automation, IEEE, San Diego, CA, USA (1994) pp. 781–786.
9. Vischer, P. and Clavel, R., “Argos: A novel 3-DoF parallel wrist mechanism,” Int. J. Robot. Res. 19 (1), 511 (2000).
10. Rosheim, M. E. and Sauter, G. F., “New High-Angulation Omni-Directional Sensor Mount,” Proceedings of the International Symposium on Optical Science and Technology, International Society for Optics and Photonics, Seattle, WA, United States (2002) pp. 163–174.
11. Carricato, M. and Parenti-Castelli, V., “A novel fully decoupled two-degrees-of-freedom parallel wrist,” Int. J. Robot. Res. 23 (6), 661667 (2004).
12. Kong, X. and Gosselin, C. M., “Type synthesis of 3-dof spherical parallel manipulators based on screw theory,” J. Mech. Des. 126 (1), 101108 (Mar. 2004).
13. Hervé, J. M., “Uncoupled actuation of pan-tilt wrists,” IEEE Trans. Robot. 22 (1), 5664 (2006).
14. Wu, Y. and Carricato, M., “Design of a Novel 3-DoF Serial-Parallel Robotic Wrist: A Symmetric Space Approach,” Proceedings of the International Symposium on Robotics Research (ISRR 2015), Sestri Levante, Italy (2015) pp. 389–404.
15. Bonev, I. A. and Ryu, J., “A new approach to orientation workspace analysis of 6-DOF parallel manipulators,” Mech. Mach. Theory 36 (1), 1528 (2001).
16. Carricato, M., “Decoupled and homokinetic transmission of rotational motion via constant-velocity joints in closed-chain orientational manipulators,” J. Mech. Robot. 1 (4), 041008 (2009).
17. Hunt, K. H., “Constant-velocity shaft couplings: A general theory,” J. Eng. Ind. 95 (2), 455464 (1973).
18. Culver, I. H., “Constant velocity universal joint,” US Patent 3,477,249, Nov. 11, 1969.
19. Sone, K., Isobe, H. and Yamada, K., “High angle active link,” In: Special Issue Special Supplement to Industrial Machines, NTN Corporation, Osaka, Japan (2004).
20. Kong, X., Yu, J. and Li, D., “Reconfiguration analysis of a two degrees-of-freedom 3-4R parallel manipulator with planar base and platform,” J. Mech. Robot. 8 (1), 011019 (2016).
21. Wu, Y., Li, Z. and Shi, J., “Geometric Properties of Zero-Torsion Parallel Kinematics Machines,” Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), IEEE, Taipei, Taiwan (2010) pp. 2307–2312.
22. Bonev, I. A., Zlatanov, D. and Gosselin, C. M., “Advantages of the Modified Euler Angles in the Design and Control of PKMs,” Proceedings of the Parallel Kinematic Machines International Conference, Citeseer, Chemnitz, Germany (2002) pp. 171–188.
23. Wu, Y., Löwe, H., Carricato, M. and Li, Z., “Inversion symmetry of the Euclidean group: Theory and application to robot kinematics,” IEEE Trans. Robot. 32 (2), 312326 (2016).
24. Wu, Y. and Carricato, M., “Synthesis and singularity analysis of N- parallel wrists: A symmetric subspace approach,” J. Mech. Robot. 9 (5), 051013-1–051013–11, (Aug. 2017).
25. Yu, J., Dong, X., Pei, X. and Kong, X., “Mobility and singularity analysis of a class of two degrees of freedom rotational parallel mechanisms using a visual graphic approach,” J. Mech. Robot. 4 (4), 041006 (2012).
26. Murray, R. M., Li, Z., Sastry, S. S. and Sastry, S. S.,” A Mathematical Introduction to Robotic Manipulation (CRC Press, Boca Raton, FL, 1994).
27. Ben-Horin, P. and Shoham, M., “Application of Grassmann–Cayley algebra to geometrical interpretation of parallel robot singularities,” Int. J. Robot. Res. 28 (1), 127141 (2009).
28. Kanaan, D., Wenger, P., Caro, S. and Chablat, D., “Singularity analysis of lower mobility parallel manipulators using Grassmann–Cayley algebra,” IEEE Trans. Robot. 25 (5), 9951004 (2009).
29. Zoppi, M., Zlatanov, D. and Molfino, R., “On the velocity analysis of interconnected chains mechanisms,” Mech. Mach. Theory 41 (11), 13461358 (2006).
30. Venanzi, S. and Parenti-Castelli, V., “A new technique for clearance influence analysis in spatial mechanisms,” J. Mech. Des. 127 (3), 446455 (2005).
31. Meng, J., Zhang, D. and Li, Z., “Accuracy analysis of parallel manipulators with joint clearance,” J. Mech. Des. 131 (1), 011013 (2009).
32. Meng, J., Zhang, D. and Li, Z., “Assembly Problem of Overconstrained and Clearance-Free Parallel Manipulators,” Proceedings of the IEEE International Conference on Robotics and Automation, IEEE, Roma, Italy (2007) pp. 1183–1188.
33. Pottmann, H., Peternell, M. and Ravani, B., “An introduction to line geometry with applications,” Comput.-Aided Des. 31 (1), 316 (1999).
34. Voglewede, P. A. and Ebert-Uphoff, I., “Overarching framework for measuring closeness to singularities of parallel manipulators,” IEEE Trans. Robot. 21 (6), 10371045 (2005).
35. Bohigas, O., Numerical Computation and Avoidance of Manipulator Singularities Ph.D. Thesis (Universidad Politécnica de Cataluña, 2013).
36. Chablat, D. and Wenger, P., “A Six Degree-of-Freedom Haptic Device Based on the Orthoglide and A Hybrid Agile Eye,” Proceedings of the ASME 2006 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, American Society of Mechanical Engineers, Philadelphia, Pennsylvania, USA (Sept. 10–13, 2006) pp. 795–802.
37. Wu, Y., Wang, H. and Li, Z., “Quotient kinematics machines: Concept, analysis, and synthesis,” J. Mech. Robot. 3 (4), 041004 (2011).
38. Merlet, J.-P., “Jacobian, manipulability, condition number, and accuracy of parallel robots,” J. Mech. Des. 128 (1), 199206 (2006).
39. Gosselin, C. and Angeles, J., “A global performance index for the kinematic optimization of robotic manipulators,” J. Mech. Des. 113 (3), 220226 (1991).
40. O'Brien, J. F. and Wen, J. T., “Redundant Actuation for Improving Kinematic Manipulability,” Proceedings of the IEEE International Conference on Robotics and Automation, IEEE, Detroit, MI, USA, USA (1999) pp. 1520–1525.
41. Müller, A., “Redundant Actuation of Parallel Manipulators,” In: Parallel Manipulators, Towards New Applications (InTech, Vienna, Austria, 2008).
42. Chakarov, D., “Study of the antagonistic stiffness of parallel manipulators with actuation redundancy,” Mech. Mach. Theory 39 (6), 583601 (2004).
43. Li, C., Wu, Y., Wu, J., Shi, W., Dai, D., Shi, J. and Li, Z., “Cartesian Stiffness Evaluation of a Novel 2-DoF Parallel Wrist Under Redundant and Antagonistic Actuation,” Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems, IEEE, Tokyo, Japan (2013) pp. 959–964.
44. Müller, A., “Internal preload control of redundantly actuated parallel manipulators–its application to backlash avoiding control,” IEEE Trans. Robot. 21 (4), 668677 (2005).
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

  • ISSN: 0263-5747
  • EISSN: 1469-8668
  • URL: /core/journals/robotica
Please enter your name
Please enter a valid email address
Who would you like to send this to? *



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