Hostname: page-component-5db6c4db9b-v64r6 Total loading time: 0 Render date: 2023-03-26T09:48:16.133Z Has data issue: true Feature Flags: { "useRatesEcommerce": false } hasContentIssue true

Mobility analysis of complex joints by means of screw theory

Published online by Cambridge University Press:  16 February 2009

Jingjun Yu*
Robotics Institute, Beihang University, Beijing 100083, China
Jian S. Dai
Department of Mechanical Engineering, King's College, University of London, the Strand, London WC2R 2LS, UK
Tieshi Zhao
Robotics Research Center, Yanshan University, Qinhuangdao 066004, China
Shusheng Bi
Robotics Institute, Beihang University, Beijing 100083, China
Guanghua Zong
Robotics Institute, Beihang University, Beijing 100083, China
*Corresponding author. Email:


In structural design of current complex mechanisms or robots like parallel kinematic machines (PKMs), surgical robots, and reconfigurable robots, there commonly exist some functional modules called complex joints (CJs). Each of them, consisting of several simple pairs and essentially a mechanism, plays the same and more important roles as simple joints in kinematics and dynamics. However, as the primarily important aspect in mechanism analysis, the type and mobility of these CJs are far from familiarity. Therefore, this paper aims at addressing the type and mobility of CJs. For this purpose, the concept and classification of CJs are first discussed, an effective method to analyze the mobility characteristics of these CJs is then developed based on the equivalent screw system. The advantage of this method is that it reveals mobility characteristics by using equivalent transformations of kinematic pair screw (KP-screw) and constraint screw (C-screw) systems. With this method, the mobility characteristics of some concrete CJs are obtained correspondingly.

Copyright © Cambridge University Press 2009

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.)


1.Phillips, J., Freedom in Machinery, Chaper 2 (Cambridge University Press, Cambridge, UK, 1984).Google Scholar
2.Gao, F., Li, W. M., Zhao, X. C., Jin, Z. L. and Zhao, H., “New kinematic structures for 2-, 3-, 4-, and 5-DOF parallel manipulator designs,” Mech. Mach. Theory 37, 13951411 (2002).CrossRefGoogle Scholar
3.Huang, Z. and Li, Q. C., “General methodology for the type synthesis of lower-mobility symmetrical parallel manipulators and several novel manipulators,” Int. J. Rob. Res. 21 (2), 131145 (2002).CrossRefGoogle Scholar
4.Liu, X. J. and Wang, J. S., “Some new parallel mechanisms containing the planar four-bar parallelogram,” Int. J. Rob. Res. 22 (9), 717732 (2003).CrossRefGoogle Scholar
5.Clavel, R., “DELTA: A fast robot with parallel geometry,” Proceedings of the 18th International Symposium on Industrial Robots, Sydney, Australia (1988) pp. 91100.Google Scholar
6.TTU's Canfield invents Canfield joint for NASA, (2008).Google Scholar
7.Dai, J. S., Li, D. L., Zhang, O. X. and Jin, G. G., “Mobility analysis of a complex structured ball based on mechanism decomposition and equivalent screw system analysis,” Mech. Mach. Theory 39 (4), 445458 (2004).CrossRefGoogle Scholar
8.Liu, X. J., Wang, J., Wu, C. and Kim, J., A new family of spatial 3-DOF parallel manipulators with two translational and one rotational DOFs, Robotica. doi:10.1017/S0263574708004633 (2008).CrossRefGoogle Scholar
9.Pierrot, F. and Company, O., “H4: A new family of 4-DoF parallel robots,” In Proceedings of the 1999 IEEE/ASME International Conference on Advanced Intelligent Mechatronics (1999), Atlanta, USA, pp. 508513.Google Scholar
10.Hervé, J. M., “Group mathematics and parallel link mechanisms,” IMACS/SICE International Symposium on Robotics, Mechatronics, and Manufacturing Systems (1992), Kobe, Japan, pp. 459464.Google Scholar
11.Tsai, L. W., Walsh, G. C. and Stamper, R., “Kinematics of a novel three DOF translational platform,” In Proceedings of IEEE International Conference on Robotics and Automation, Minneapolis, MN (1996) pp. 34463451.CrossRefGoogle Scholar
12.Baumann, R., Maeder, W., Glauser, D. and Clavel, R., “The PantoScope: A spherical remote-center-of-motion parallel manipulator for force reflection,” ICRA, Albuquerque, New Mexico (1997) pp. 718723.Google Scholar
13.Vischer, P. and Clavel, R., “Argos: A novel 3-DoF parallel wrist mechanism,” Int. J. Rob. Res. 19 (1), 511 (2000).CrossRefGoogle Scholar
14.Wenger, P. and Chablat, D., “Kinematic Analysis of a New Parallel Machine Tool: The Orthoglide,” In: Advances in Robot Kinematics, Pirano, Slovenia, (Lenarcic, J., Stanisic, M. L., eds.) (Kluwer Academic Publishers, 2000) pp. 305314.CrossRefGoogle Scholar
15.Liu, X. J., Wang, J. S. and Pritschow, G., “A new family of spatial 3-DoF fully-parallel manipulators with high rotational capability,”Mech. Mach. Theory 40 (4), 475494 (2005).CrossRefGoogle Scholar
16.Taylor, R. H., Fundal, J., Eldridge, B., Gomory, S., Gruben, K., LaRose, D., Talamini, M., Kavoussi, L. and Anderson, J., “A telerobotic assistant for laparoscopic surgery,” Eng. Med. Biol. Mag. 14 (3), 279288 (1995).CrossRefGoogle Scholar
17.Zhao, T. S., Dai, J. S. and Huang, Z., “Geometric analysis of overconstrained parallel manipulators with three and four degrees of freedom,” JSME Int. J., Ser. C, Mech. Syst., Mach. Elements Manuf. 45 (3), 730740 (2002).CrossRefGoogle Scholar
18.Huang, T., Zhao, X. Y. and Whitehouse, D. J., “Stiffness estimation of a parallel kinematic machine,” Sci. Chin. (E) 44 (5), 473478 (2001).CrossRefGoogle Scholar
19.Angeles, J., “The qualitative synthesis of parallel manipulators,” ASME J. Mech. Des. 126 (3), 617623 (2004).CrossRefGoogle Scholar
20.Rico, J. M., Gallardo, J. and Ravani, B., “Lie algebra and the mobility of kinematic chains,” J. Rob. Syst. 20, 477499 (2003).CrossRefGoogle Scholar
21.Dai, J. S., Huang, Z. and Lipkin, H., “Screw system analysis of parallel mechanisms and applications to constraint and mobility study,” 28th ASME Biennial Mechanisms and Robotics Conference, Salt Lake City, UT (Sep. 2004) DETC2004-57604.Google Scholar
22.Ball, R. S., A Treatise on the Theory of Screws (Cambridge University Press, Cambridge, UK, 1900).Google Scholar
23.Kong, X. W. and Gosselin, C. M., “Type synthesis of 3-DOF spherical parallel manipulators based on screw theory,” ASME J. Mech. Des. 126, 101108 (2004).CrossRefGoogle Scholar
24.Pham, P., Regamey, Y.-J., Fracheboud, M. and Clavel, R., “Orion MinAngle: A flexure-based, double-tilting parallel kinematics for ultra-high precision applications requiring high angles of rotation,” International Symposium on Robotics (2005), Tokyo, Japan.Google Scholar