Research Papers: Design of Mechanisms and Robotic Systems

Screw-System-Variation Enabled Reconfiguration of the Bennett Plano-Spherical Hybrid Linkage and Its Evolved Parallel Mechanism

[+] Author and Article Information
Ketao Zhang

Centre for Robotics Research,
Faculty of Natural and Mathematical Sciences,
King's College London,
University of London,
Strand, London WC2R 2LS, UK
e-mail: ketao.zhang@kcl.ac.uk

Jian S. Dai

Centre for Robotics Research,
Faculty of Natural and Mathematical Sciences,
King's College London,
University of London,
Strand, London WC2R 2LS, UK
e-mail: jian.dai@kcl.ac.uk

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received September 9, 2014; final manuscript received March 6, 2015; published online April 15, 2015. Assoc. Editor: Oscar Altuzarra.

J. Mech. Des 137(6), 062303 (Jun 01, 2015) (10 pages) Paper No: MD-14-1555; doi: 10.1115/1.4030015 History: Received September 09, 2014; Revised March 06, 2015; Online April 15, 2015

This paper presents the Bennett plano-spherical hybrid linkage and proposes a novel metamorphic parallel mechanism consisting of this plano-spherical linkage as part of limbs. In light of geometrical modeling of the Bennett plano-spherical linkage, and with the investigation of the motion-screw system, the paper reveals for the first time the reconfigurability property of this plano-spherical linkage and identifies the design parameters that lead to change of constraint equations, and subsequently to variation of the order of the motion-screw system. Arranging this linkage as part of limbs, the paper further investigates the reconfiguration property of the plano-spherical linkage evolved parallel mechanism. The analysis reveals that the platform constraint-screw system varies following both bifurcation and trifurcation with motion branch variation in the 6R linkage integrated limb structure. Consequently, this variation of the platform constraint-screw system leads to reconfiguration of the proposed metamorphic parallel mechanism. The paper presents a way of analyzing reconfigurability of kinematic structures based on the screw-system approach.

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Merlet, J.-P., 2001, Parallel Robots, Kluwer Academic Publishers, Dordrecht, Netherlands.
Gosselin, C., and Angeles, J., 1989, “The Optimum Kinematic Design of a Spherical Three-Degree-of-Freedom Parallel Manipulator,” ASME J. Mech. Des., 111(2), pp. 202–207. [CrossRef]
Dasgupta, B., and Mruthyunjaya, T. S., 2000, “The Stewart Platform Manipulator: A Review,” Mech. Mach. Theory, 35(1), pp. 15–40. [CrossRef]
Gogu, G., 2008, Structural Synthesis of Parallel Robots, Springer, Dordrecht, Netherlands.
Briot, S., and Bonev, I. A., 2007, “Are Parallel Robots More Accurate Than Serial Robots,” Trans. Can. Soc. Mech. Eng., 31(4), pp. 445–455.
Lee, K. M., and Shah, D. K., 1988, “Dynamic Analysis of a Three-Degrees-Of-Freedom In-Parallel Actuated Manipulator,” IEEE J. Rob. Autom., 4(3), pp. 361–367. [CrossRef]
Pashkevich, A., Chablat, D., and Wenger, P., 2009, “Stiffness Analysis of Overconstrained Parallel Manipulators,” Mech. Mach. Theory, 44(5), pp. 966–982. [CrossRef]
Claver, R., 1988, “Delta, a Fast Robot With Parallel Geometry,” Proceedings of the International Symposium on Industrial Robot, Switzerland, pp. 91–100.
Tsai, L. W., Walsh, G. C., and Stamper, R. E., 1996, “Kinematics of a Novel Three DOF Translational Platform,” Proceedings of the 1996 IEEE International Conference on Robotics and Automation, Minneapolis, pp. 3446–3451.
Ceccarelli, M., 1997, “A New 3 D.O.F Spatial Parallel Mechanism,” Mech. Mach. Theory, 32(8), pp. 895–902. [CrossRef]
Pierrot, F., and Company, O., 1999, “H4: A New Family of 4-DOF Parallel Robots,” Proceedings of the 1999 IEEE/ASME International Conference on Advanced Intelligent Mechatronics, Atlanta, GA, pp. 508–513.
Gao, F., Li, W., Zhao, X., Jin, Z., and Zhao, H., 2002, “New Kinematic Structures for 2-, 3-, 4-, and 5-DOF Parallel Manipulator Designs,” Mech. Mach. Theory, 37(8), pp. 1395–1411. [CrossRef]
Liu, X., and Wang, J., 2003, “Some New Parallel Mechanisms Containing the Planar Four-Bar Parallelogram,” Int. J. Rob. Res., 22(9), pp. 717–732. [CrossRef]
Zhang, K., Fang, Y., Fang, H., and Dai, J. S., 2010, “Geometry and Constraint Analysis of the Three-Spherical Kinematic Chain Based Parallel Mechanism,” ASME J. Mech. Rob., 2(3), p. 031014. [CrossRef]
Zhao, T. S., Dai, J. S., and Huang, Z., 2002, “Geometric Synthesis of Spatial Parallel Manipulators With Fewer Than Six Degrees of Freedom,” Proc. IMechE, 216(12), pp. 1175–1185 [CrossRef].
Dai, J. S., and Caldwell, D. G., 2012, “Robotics and Automation for Packaging in the Confectionery Industry,” Robotics and Automation in the Food Industry: Current and Future Technologies, Woodhead Publishing, Cambridge, pp. 401–419.
Wurdemann, H., Aminzadeh, V., Dai, J. S., Reed, J., and Purnell, G., 2011, “Category-Based Food Ordering Processes,” Trends Food Sci. Technol., 22(1), pp. 14–20. [CrossRef]
Salerno, M., Zhang, K., Menciassi, A., and Dai, J. S., 2014, “A Novel 4-DOFs Origami Enabled, SMA Actuated, Robotic End-Effector for Minimally Invasive Surgery,” Proceedings of the IEEE International Conference on Robotics and Automation (ICRA2014), Hong Kong, pp. 2844–2849.
Kuo, C. H., and Dai, J. S., 2012, “Kinematics of a Fully-Decoupled Remote Center-Of-Motion Parallel Manipulator for Minimally Invasive Surgery,” ASME J. Med. Devices, 6(2), p. 021008. [CrossRef]
Dai, J. S., and Rees Jones, J., 1999, “Mobility in Metamorphic Mechanisms of Foldable/Erectable Kinds,” ASME J. Mech. Des., 121(3), pp. 375–382. [CrossRef]
Coppola, G., Zhang, D., and Liu, K., 2014, “A 6-DOF Reconfigurable Hybrid Parallel Manipulator,” Rob. Comput.-Integr. Manuf., 30(2), pp. 99–106. [CrossRef]
Zlatanov, D., Bonev, I. A., and Gosselin, C. M., 2002, “Constraint Singularities as C-Space Singularities,” Advances in Robot Kinematics, Kluwer, Dordrecht, Netherlands, pp. 183–192.
Kong, X., Gosselin, C. M., and Richard, P. L., 2007, “Type Synthesis of Parallel Mechanisms With Multiple Operation Modes,” ASME J. Mech. Des., 129(7), pp. 595–601. [CrossRef]
Kong, X., 2013, “Type Synthesis of 3-DOF Parallel Manipulators With Both a Planar Operation Mode and a Spatial Translational Operation Mode,” ASME J. Mech. Rob., 5(4), p. 041015. [CrossRef]
Gan, D. M., Dai, J. S., and Liao, Q. Z., 2009, “Mobility Change in Two Types of Metamorphic Parallel Mechanisms,” ASME J. Mech. Rob., 1(4), p. 041007. [CrossRef]
Carbonari, L., Callegari, M., Palmieri, G., and Palpacelli, M.-C., 2014, “A New Class of Reconfigurable Parallel Kinematic Machines,” Mech. Mach. Theory, 79, pp. 173–183. [CrossRef]
Gogu, G., 2009, “Branching Singularities in Kinematotropic Parallel Mechanisms,” Proceedings of the 5th International Workshop on Computational Kinematics, Duisburg, Germany, pp. 341–348.
Wohlhart, K., 1996, “Kinematotropic Linkages,” Recent Advances in Robot Kinematics, Kluwer Academic, Dordrecht, The Netherlands, pp. 359–368.
Zhang, K. T., Dai, J. S., and Fang, Y. F., 2009, “A New Metamorphic Mechanism With Ability for Platform Orientation Switch and Mobility Change,” Proceedings of the ASME/IFToMM International Conference on Reconfigurable Mechanisms and Robots, London, pp. 626–632.
Zhang, K. T., Dai, J. S., and Fang, Y. F., 2010, “Topology and Constraint Analysis of Phase Change in the Metamorphic Chain and Its Evolved Mechanism,” ASME J. Mech. Des., 132(12), p. 121001. [CrossRef]
Zeng, Q., Fang, Y., and Ehmann, K. F., 2011, “Design of a Novel 4-DOF Kinematotropic Hybrid Parallel Manipulator,” ASME J. Mech. Des., 133(12), p. 121006. [CrossRef]
Ye, W., Fang, Y., Zhang, K., and Guo, S., 2014, “A New Family of Reconfigurable Parallel Mechanisms With Diamond Kinematotropic Chain,” Mech. Mach. Theory, 74, pp. 1–9. [CrossRef]
Dai, J. S., Huang, Z., and Lipkin, H., 2006, “Mobility of Overconstrained Parallel Mechanisms,” ASME J. Mech. Des., 128(1), pp. 220–229. [CrossRef]
Zhang, K., and Dai, J. S., 2014, “Trifurcation of the Evolved Sarrus-Motion Linkage Based on Parametric Constraints,” Advances in Robot Kinematics, Springer International Publishing, Switzerland, pp. 345–353.
Bennett, G. T., 1905, “The Parallel Motion of Sarrut and Some Allied Mechanisms,” Philosophy Magazine, 6th series, Vol. 9, Taylor & Francis, London, pp. 803–810.
Alizade, R. I., Kiper, G., Bağdadioğlu, B., and Dede, M. İ. C., 2014, “Function Synthesis of Bennett 6R Mechanisms Using Chebyshev Approximation,” Mech. Mach. Theory, 81, pp. 62–78. [CrossRef]
Chen, Y., 2003, Design of Structural Mechanisms, University of Oxford, Oxford.
Cui, L., and Dai, J. S., 2011, “Axis Constraint Analysis and Its Resultant 6R Double-Centered Overconstrained Mechanisms,” ASME J. Mech. Rob., 3(3), p. 031004. [CrossRef]
Baker, J. E., 2012, “The Six-Revolute Hybrids of Four-Revolute Loops and Their Single Reciprocal Screws,” Mech. Mach. Theory, 53, pp. 128–144. [CrossRef]
Denavit, J., and Hartenberg, R. S., 1955, “A Kinematic Notation for Lower-Pair Mechanisms Based on Matrices,” ASME J. Appl. Mech., 77, pp. 215–221.
Baker, J. E., 1980, “An Analysis of Bricard Linkages,” Mech. Mach. Theory, 15, pp. 267–286. [CrossRef]
Viquerat, A. D., Hutt, T., and Guest, S. D., 2013, “A Plane Symmetric 6R Foldable Ring,” Mech. Mach. Theory, 63, pp. 73–88. [CrossRef]
Dai, J. S., and Rees Jones, J., 2001, “Interrelationship Between Screw Systems and Corresponding Reciprocal Systems and Applications,” Mech. Mach. Theory, 36(5), pp. 633–651. [CrossRef]
Zhao, J. S., Feng, Z. J., Zhou, K., and Dong, J. X., 2005, “Analysis of the Singularity of Spatial Parallel Manipulator With Terminal Constraints,” Mech. Mach. Theory, 40(3), pp. 275–284. [CrossRef]
Fang, Y., and Tsai, L. W., 2002, “Structure Synthesis of a Class of 4-Degree of Freedom and 5-Degree of Freedom Parallel Manipulators With Identical Limb Structures,” Int. J. Rob. Res., 21(9), pp. 799–810. [CrossRef]
Huang, Z., and Li, Q. C., 2002, “General Methodology for Type Synthesis of Symmetrical Lower-Mobility Parallel Manipulators and Several Novel Manipulators,” Int. J. Rob. Res., 21(9), pp. 131–145. [CrossRef]
Merlet, J. P., 1989, “Singularity Configurations of Parallel Manipulators and Grassmann Geometry,” Int. J. Rob. Res., 8(9), pp. 45–56. [CrossRef]
Monsarrat, B., and Gosselin, C. M., 2001, “Singularity Analysis of a Three-Leg Six-Degree-of-Freedom Parallel Platform Mechanism Based on Grassmann Line Geometry,” Int. J. Rob. Res., 20(4), pp. 312–328. [CrossRef]
Amine, S., Masouleh, M. T., Caro, S., Wenger, P., and Gosselin, C. M., 2012, “Singularity Analysis of 3T2R Parallel Mechanisms Using Grassmann–Cayley Algebra and Grassmann Geometry,” Mech. Mach. Theory, 52, pp. 326–340 [CrossRef]
Gosselin, C. M., and Angeles, J., 1990, “Singularity Analysis of Closed-Loop Kinematic Chains,” IEEE Trans. Rob. Autom., 6(3), pp. 281–290. [CrossRef]
McCarthy, J. M., and Soh, G. S., 2010, Geometric Design of Linkages, Springer Science & Business Media, New York.
Angeles, J., 1998, “The Application of Dual Algebra to Kinematic Analysis,” Computational Methods in Mechanical Systems, Springer, Berlin, Heidelberg, pp. 3–32.
Cheng, H., Liu, G. F., Yiu, Y. K., Xiong, Z. H., and Li, Z. X., 2001, “Advantages and Dynamics of Parallel Manipulators With Redundant Actuation,” Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems, Maui, HI, pp. 171–176.
Tosi, D., Legnani, G., Pedrocchi, N., Righettini, P., and Giberti, H., 2010, “Cheope: A New Reconfigurable Redundant Manipulator,” Mech. Mach. Theory, 45(4), pp. 611–626. [CrossRef]
Moosavian, A., and Xi, F., 2014, “Design and Analysis of Reconfigurable Parallel Robots With Enhanced Stiffness,” Mech. Mach. Theory, 77, pp. 92–110. [CrossRef]
Merlet, J. P., 2000, “Parallel Robots: Open Problems,” Robotics Research-International Symposium, Vol. 9, pp. 27–32.
Tadokoro, S., and Kobayashi, S., 2002, “A Portable Parallel Motion Platform for Urban Search and Surveillance in Disasters,” Adv. Rob., 16(6), pp. 537–540. [CrossRef]
Zhang, K., Dai, J. S., and Fang, Y., 2013, “Geometric Constraint and Mobility Variation of Two 3SvPSv Metamorphic Parallel Mechanisms,” ASME J. Mech. Des., 135(1), p. 011001. [CrossRef]


Grahic Jump Location
Fig. 1

The plane-symmetric Bennett plano-spherical hybrid linkage and its geometrical model (a) kinematic model and (b) geometric model

Grahic Jump Location
Fig. 2

The singular configurations of the Bennett plano-spherical hybrid linkage (a) case (i): r  >  ldg, (b) case (ii): r  <  ldg, and (c) case (iii): r = ldg

Grahic Jump Location
Fig. 3

The metamorphic parallel mechanism composed of Bennett plano-spherical hybrid linkages

Grahic Jump Location
Fig. 4

The hybrid limb with closed loop subchain working in overconstrained 6R linkage motion branch (a) kinematic model of the hybrid limb, (b) the equivalent RvRvRvRR kinematic chain

Grahic Jump Location
Fig. 5

The hybrid limb with closed loop subchain in spherical 4R motion branch (a) kinematic model of the hybrid limb, (b) the equivalent RvRvRR kinematic chain

Grahic Jump Location
Fig. 6

The hybrid limb with closed loop subchain in planar 4R motion branch (a) kinematic model of the hybrid limb and (b) the equivalent RvPvRR kinematic chain

Grahic Jump Location
Fig. 7

The motion branch of the parallel mechanism implementing 3DOF spherical motion

Grahic Jump Location
Fig. 8

The motion branch of the parallel mechanism implementing 1DOF pure translation




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