Research Papers

A Family of Rotational Parallel Manipulators With Equal-Diameter Spherical Pure Rotation

[+] Author and Article Information
Kang Wu

Robotics Institute,
Beihang University,
Beijing 100191, China
e-mail: wukangjk@gmail.com

Jingjun Yu

Robotics Institute,
Beihang University,
Beijing 100191, China
e-mail: jjyu@buaa.edu.cn

Guanghua Zong

Robotics Institute,
Beihang University,
Beijing 100191, China
e-mail: ghzong@buaa.edu.cn

Xianwen Kong

School of Engineering and Physical Sciences,
Heriot-Watt University,
Edinburgh EH14 4AS, UK
e-mail: x.kong@hw.ac.uk

1Corresponidng author.

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANISMS AND ROBOTICS. Manuscript received July 6, 2013; final manuscript received September 20, 2013; published online December 27, 2013. Assoc. Editor: Yuefa Fang.

J. Mechanisms Robotics 6(1), 011008 (Dec 27, 2013) (10 pages) Paper No: JMR-13-1127; doi: 10.1115/1.4025860 History: Received July 06, 2013; Revised September 20, 2013

In this work, a family of two degrees of freedom (2-DOF) rotational parallel manipulators (RPMs) with an equal-diameter spherical pure rotation (ESPR) is presented and discussed systematically. The theoretical models of both kinematics and constraints inherited in the manipulators are analyzed through a graphical approach. Based on the established constraint model, these 2-DOF ESPR RPMs are classified into three types according to their compositions of constraint spaces and several novel parallel manipulators are illustrated correspondingly. Finally, two common necessary geometric conditions satisfied for these manipulators are discussed in details with examples. The two conditions will be helpful for engineers with designing ESPR RPMs. Moreover, as one characteristic existing in the ESPR RPMs, two cases of self-rotations accompanying revolutions around fixed axes are revealed. As a result, the corresponding loci of points in the moving platform are proved to be compositions of two subrotations, which are spatial curves and surfaces rather than spherical curves and surfaces.

Copyright © 2014 by ASME
Your Session has timed out. Please sign back in to continue.


Rosheim, M. E., and Sauter, G. F., 2002, “New High-Angulation Omni-Directional Sensor mount,” Proc. SPIE, 4821, pp. 163–174. [CrossRef]
Dunlop, G. R., and Jones, T. P., 1999, “Position Analysis of a Two DOF Parallel Mechanism-the Canterbury Tracker,” Mech. Mach. Theory, 34, pp. 599–614. [CrossRef]
Gosselin, C. M., and Caron, F., 1999, “Two Degree-of-Freedom Spherical Orienting Device,” U.S. Patent No. 5,966,991.
Hervé, J. M., “Uncoupled Actuation of Pan-Tilt Wrists,” IEEE Trans. Rob., 1(22), pp. 56–64. [CrossRef]
Gogu, G., 2012, Structural Synthesis of Parallel Robots (Solid Mechanics and Its Applications), Springer, New York, vol. 183, pp. 99–142.
Kong, X. W., 2010, “Forward Displacement Analysis of a 2-DOF RR-RRR-RRR Spherical Parallel Manipulator,” 2010 IEEE/ASME International Conference on Mechatronics and Embedded Systems and Applications (MESA).
Zeng, D. X., Hou, Y. L., Huang, Z., et al. ., 2009, “Type Synthesis and Characteristic Analysis of a Family of 2-DOF Rotational Decoupled Parallel Mechanisms,” Chin. J. Mech. Eng., 6(22), pp. 833–842. [CrossRef]
Wu, K., Yu, J. J., Li, S. Z., and Lu, W. J., 2012, “Type Synthesis of Two Degrees-of-Freedom Rotational Parallel Mechanisms With a Fixed Center-of-Rotation Based on a Graphic Approach,” ASME Paper No. DETC2012-71028.
Bonev, I. A., 2002, “Geometric Analysis of Parallel Mechanisms,” Ph.D. dissertation, Laval University, Quebec, Canada.
Wu, Y. Q., Li, Z. X., and Shi, J. B., 2010, “Geometric Properties of Zero-Torsion Parallel Kinematics Machines,” 2010 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Taipei, Taiwan.
Hunt, K. H., 1973, “Constant-Velocity Shaft Couplings: A General Theory,” ASME J. Eng. Ind., 1973(5), pp. 455–464. [CrossRef]
Carricato, M., 2009, “Decoupled and Homokinetic Transmission of Rotational Motion via Constant-Velocity Joints in Closed-Chain Orientational Manipulators,” ASME J. Mech. Rob., 1(4), p. 041008. [CrossRef]
Liu, X. J., and Bonev, I. A., 2008, “Orientation Capability, Error Analysis and Dimension Optimization of Two Articulated Tool Heads With Parallel Kinematics,” ASME J. Manuf. Sci. Eng., 130(1), p. 011015. [CrossRef]
Kung, C., and Wu, R. M., 1996, “Spherical Robotic Shoulder Joint,” US. Patent No. 5,533,418.
Ting, L., and Cunyun, P., 2009, “On Grinding Manufacture Technique and Tooth Contact and Stress Analysis of Ring-Involute Spherical Gears,” Mech. Mach. Theory, 44(10), pp. 1807–1825. [CrossRef]
Hernandez, S., Bai, S., and Angeles, J., 2006, “The Design of a Chain of Spherical Stephenson Mechanisms for a Gearless Robotic Pitch-Roll Wrist,” ASME J. Mech. Des., 128(2), pp. 422–429. [CrossRef]
Wu, K., Yu, J. J., Zong, G. H., and Kong, X., 2013, “Type Synthesis of 2-DOF Rotational Parallel Mechanisms With An Equal-Diameter Spherical Pure Rolling Motion,” Proceedings of ASME 2013 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference, DETC2013-12305 Portland, OR, August 4–7, 2013.
Rosheim, M. E., and Sauter, G. F., 2003, “Free Space Optical Communication System Pointer,” Proc. SPIE, 4975, pp. 126–133. [CrossRef]
Sofka, J., Skormin, V., Nikulin, V., Nicholson, D. J., and Rosheim, M., 2004, “New Generation of Gimbals Systems for Laser Positioning Applications,” Proc. SPIE, 5160, pp. 182–191. [CrossRef]
Sofka, J., Skormin, V., Nikulin, V., and Nicholson, D. J., 2006, “New Generation of Gimbals Systems for Laser Positioning Applications,” Omni-Wrist III–A new generation of pointing devices Part I: Laser beam steering devices–mathematical modeling. IEEE Trans. Aerosp. Electron. Syst., 42(2), pp. 718–725. [CrossRef]
Isobe, H., and Sone, K., 2011, “Linkage Actuating Device,” U S. Patent No. 7971505.
Yu, J. J., Dong, X., Pei, X., and Kong, X., 2012, “Mobility and Singularity Analysis of a Class of Two Degrees of Freedom Rotational Parallel Mechanisms Using A Visual Graphic Approach,” ASME J. Mech. Rob., 4(4), p. 041006. [CrossRef]
Ruggiu, M., 2010, “Kinematic and Dynamic Analysis of a Two-Degree-of-Freedom Spherical Wrist,” ASME J. Mech. Rob., 2(3), p. 031006. [CrossRef]
Hopkins, J. B., and Culpepper, M. L., 2010, “Synthesis of Multi-Degree of Freedom, Parallel Flexure System Concepts via Freedom and Constraint Topology (FACT) Part I: Principles,” Precis. Eng., 34(2), pp. 259–270. [CrossRef]
Blanding, D. L., 1999, Exact Constraint: Machine Design Using Kinematic Processing, ASME Press, New York.
Reuleaux, F., 1963, The Kinematics of Machinery, Dover Publications, Inc., New York, NY.
Rudolf, A. B., 1963, The Kinematic Synthesis of Mechanisms, McGraw-Hill Book Company, Inc., New York, San Francisco, CA.
Suh, C. H., 1970, “Design of Spatial Linkages to Replace Gears,” J. Mech., 5(2), pp. 217–237. [CrossRef]
Devanathan, B. T., Soni, A. H., and Siddhanty, M. N., 1984, “Higher-Order Synthesis of an RSSR Mechanism With Application,” Mech. Mach. Theory, 19(1), pp. 85–96. [CrossRef]
Tischler, C. R., Hunt, K. H., and Samuel, A. E., 1998, “A Spatial Extension of Cardanic Movement: Its Geometry and Some Derived Mechanisms,” Mech. Mach. Theory, 33(8), pp. 1249–1276. [CrossRef]
Karouia, M., and Hervé, J. M., 2004, New parallel wrist: special limbs with motion dependency, On Advances in Robot Kinematics, Kluwer Academic Publishers, P.O. Box 17,3300 AA Dordrecht, The Netherlands, pp. 371–380. [CrossRef]
Callegari, M., 2008, Design and Prototyping of a Spherical Parallel Machine Based on 3-CPU Kinematics, Parallel Manipulators: New Development, I-Tech Education and Publishing, Vienna, Austria, First published April 2008, Printed in Croatia, pp. 171–198.
Canfield, S. L., 1997, “Development of the Carpal Wrist; a Symmetric Parral-Architecture Robotic Wrist,” Ph.D. dissertation, Virginia Polytechnic Institute and State University, Blackburg, VA.
Vertechy, R., and Parenti-Castelli, V., 2006, Synthesis of 2-DOF spherical fully parallel mechanisms, Advances in Robot Kinematics, Published by Springer, P.O. Box 17,3300 AA Dordrecht, The Netherlands: pp. 385–394.
Huda, S., and TakedaY., 2011, “Kinematic Design of 3-URU Pure Rotational Parallel Mechanism to Perform Precise Motion Within A Large Workspace,” Meccanica, 1(46), pp. 89–100. [CrossRef]
Sofka, J., 2007, “New Generation of Gimbals Systems for Aerospace Applications,” Ph.D. dissertation, Binghamton University, New York.
Kong, X., 2011, “Forward Displacement Analysis and Singularity Analysis of a Special 2-DOF 5R Spherical Parallel Manipulator,” ASME J. Mech. Rob., 3(2), p. 024501. [CrossRef]


Grahic Jump Location
Fig. 1

A kinematic model of two equal-diameter hemispheroids generating a 2-DOF ESPR

Grahic Jump Location
Fig. 2

Reciprocal diagram of constraint lines and freedom lines in 2-DOF rotational mechanisms with an equal-diameter spherical pure rotational motion: (a) constraints and freedoms of the manipulator model; (b) geometrical relationship between constraints lines and freedom lines; (c) equivalent constraints

Grahic Jump Location
Fig. 3

Two novel 2-DOF ESPR RPMs with centro-symmetric structures: (a) 1-SS&3-CRC; (b) 1-SS&3-URU

Grahic Jump Location
Fig. 4

A novel 2-DOF ESPR RPM with hybrid limbs (1-RRRR&2-RSR)

Grahic Jump Location
Fig. 5

A 3-RRRR ESPR RPM with different link length: (a) an isosceles triangle formed by the first limb; (b) isometric view of the novel manipulator with three different isosceles triangles

Grahic Jump Location
Fig. 6

Two 1-US&3-RSR ESPR RPMs with different link lengths (nonoverconstrained). Geometric conditions for Type C.

Grahic Jump Location
Fig. 7

Two 1-RRRR&2-RSR ESPR RPMs with different link length (nonoverconstrained)

Grahic Jump Location
Fig. 8

1-DOF ESPR around a fixed axis X: (a) isometric view; (b) projective view in plane YO1Z

Grahic Jump Location
Fig. 9

1-DOF ESPR around axis Z with an incline angle θ: (a) isometric view; (b) projective view in plane YO1Z

Grahic Jump Location
Fig. 10

Loci of point A: (a) locus of motion in case I; (b) locus of motion in case II; (c) complete workspace




Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In