Research Papers

Unified Kinematics and Singularity Analysis of a Metamorphic Parallel Mechanism With Bifurcated Motion

[+] Author and Article Information
Dongming Gan

Robotics Institute,
Khalifa University of Science,
Technology and Research,
Abu Dhabi 127788, UAE
e-mail: dongming.gan@kustar.ac.ae

Jian S. Dai

School of Natural and Mathematical Sciences,
King's College London,
University of London,
London WC2R2LS, UK

Jorge Dias

Robotics Institute,
Khalifa University of Science,
Technology and Research,
Abu Dhabi 127788, UAE;
Faculty of Science and Technology,
University of Coimbra,
Coimbra 3000-315, Portugal

Lakmal Seneviratne

Robotics Institute,
Khalifa University of Science,
Technology and Research,
Abu Dhabi 127788, UAE;
School of Natural and Mathematical Sciences,
King's College London,
University of London,
London WC2R2LS, UK

1Corresponding author.

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANISMS AND ROBOTICS. Manuscript received July 18, 2012; final manuscript received March 28, 2013; published online June 10, 2013. Assoc. Editor: Qiaode Jeffrey Ge.

J. Mechanisms Robotics 5(3), 031004 (Jun 24, 2013) (11 pages) Paper No: JMR-12-1101; doi: 10.1115/1.4024292 History: Received July 18, 2012; Revised March 28, 2013

This paper introduces a new metamorphic parallel mechanism consisting of four reconfigurable rTPS limbs. Based on the reconfigurability of the reconfigurable Hooke (rT) joint, the rTPS limb has two phases while in one phase the limb has no constraint to the platform, in the other it constrains the spherical joint center to lie on a plane. This results in the mechanism to have ability of reconfiguration between different topologies with variable mobility. Geometric constraint equations of the platform rotation matrix and translation vector are set up based on the point-plane constraint, which reveals the bifurcated motion property in the topology with mobility 2 and the geometric condition with mobility change in altering to other mechanism topologies. Following this, a unified kinematics limb modeling is proposed considering the difference between the two phases of the reconfigurable rTPS limb. This is further applied for the mechanism modeling and both the inverse and forward kinematics is analytically solved by combining phases of the four limbs covering all the mechanism topologies. Based on these, a unified singularity modeling is proposed by defining the geometric constraint forces and actuation forces in the Jacobian matrix with their change in the variable topologies in terms of constraint screws. Analysis of workspace with singularity distribution is carried out using this model and corresponding singularity loci are obtained with special singular configurations illustrated.

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Merlet, J. P., 2008, Parallel Robots, 2nd ed., Springer, New York.
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, p. 041007. [CrossRef]
Dai, J. S., and Rees, J. J., 1999, “Mobility in Metamorphic Mechanisms of Foldable/Erectable Kinds,” ASME J. Mech. Des., 121(3), pp. 375–382. [CrossRef]
Wohlhart, K., 1996, “Kinematotropic Linkages,” Advances in Robot Kinematics, J.Lenarcic and V.Parenti-Castelli, eds., Kluwer, Dordrecht, pp. 359–368.
Parise, J. J., Howell, L. L., and Magleby, S. P., 2000, “Ortho-Planar Mechanisms,” Proceedings of 26th Biennial Mechanisms and Robotics Conference, Baltimore, MD, Sept., Paper No. DETC2000/MECH-14193.
Chen, I. M., Li, S. H., and Cathala, A., 2003, “Mechatronic Design and Locomotion of Amoebot—A Metamorphic Underwater Vehicle,” J. Rob. Syst., 20(6), pp. 307–314. [CrossRef]
Liu, C., and Yang, T., 2004, “Essence and Characteristics of Metamorphic Mechanisms and Their Metamorphic Ways,” Proceedings of 11th World Congress in Mechanism and Machine Science, Tianjing, China, April, pp. 1285–1288.
Dai, J. S., and Rees, J. J., 2005, “Matrix Representation of Topological Changes in Metamorphic Mechanisms,” ASME J. Mech. Des., 127(4), pp. 837–840. [CrossRef]
Yan, H. S., and Kuo, C. H., 2006, “Topological Representations and Characteristics of Variable Kinematic Joints,” ASME J. Mech. Des., 128(2), pp. 384–391. [CrossRef]
Kuo, C. H., and Yan, H. S., 2007, “On the Mobility and Configuration Singularity of Mechanisms With Variable Topologies,” ASME J. Mech. Des., 129, pp. 617–624. [CrossRef]
Fanghella, P., Galletti, C., and Giannotti, E., 2006, “Parallel Robots that Change Their Group of Motion,” Advances in Robot Kinematics, Springer, New York, pp. 49–56.
Xi, F., Xu, Y., and Xiong, G., 2006, “Design and Analysis of a Re-Configurable Parallel Robot,” Mech. Mach. Theory, 41, pp. 191–211. [CrossRef]
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]
Dai, J. S., and Wang, D., 2007, “Geometric Analysis and Synthesis of the Metamorphic Robotic Hand,” ASME J. Mech. Des., 129(11), pp. 1191–1197. [CrossRef]
Zhang, L. P., Wang, D. L., and Dai, J. S., 2008, “Biological Modeling and Evolution Based Synthesis of Metamorphic Mechanisms,” ASME J. Mech. Des., 130, p. 072303. [CrossRef]
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]
Gan, D. M., Dai, J. S., and Liao, Q. Z., 2010, “Constraint Analysis on Mobility Change of a Novel Metamorphic Parallel Mechanism,” Mech. Mach. Theory, 45(12), pp. 1864–1876. [CrossRef]
Gan, D. M., Dai, J. S., and Caldwell, D. G., 2011, “Constraint-Based Limb Synthesis and Mobility-Change Aimed Mechanism Construction,” ASME J. Mech. Des., 133(5), 051001. [CrossRef]
Wampler, C. W., 2006, “On a Rigid Body Subject to Point-Plane Constraints,” ASME J. Mech. Des., 128(1), pp. 151–158. [CrossRef]
Selig, J. M., 2011, “On the Geometry of Point-Plane Constraints on Rigid-Body Displacements,” Acta Appl. Math., 116(2), pp. 133–155. [CrossRef]
Karouia, M., and Hervé, J. M., 2002, “A Family of Novel Orientational 3-DOF Parallel Robots,” Proceedings of 14th CISM-IFToMM RoManSy, Springer, pp. 359–368.
Lee, C. C., and Hervé, J. M., 2009, “Uncoupled 6-DOF Tripods Via Group Theory,” Proceedings of the 5th International Workshop on Computational Kinematics, A.Kecskeméthy and A.Müller, eds. Springer, pp. 201–208.
Li, Q., and Hervé, J. M., 2010, “1T2R Parallel Mechanisms Without Parasitic Motion,” IEEE Trans. Rob. Autom., 26(3), pp. 401–410. [CrossRef]
Li, Q., and Hervé, J. M., 2009, “Parallel Mechanisms With Bifurcation of Schoenflies Motion,” IEEE Trans. Rob. Autom., 25(1), pp. 158–164. [CrossRef]
Gogu, G., 2011, “Maximally Regular T2R1-Type Parallel Manipulators With Bifurcated Spatial Motion,” ASME J. Mech. Rob., 3(1), p. 011010. [CrossRef]
Zlatanov, D., Bonev, I. A., and Gosselin, C. M., 2002, “Constraint Singularities of Parallel Mechanisms,” Proceedings of IEEE International Conference on Robotics and Automation, Washington, D.C., pp. 496–502.
Zlatanov, D., Bonev, I. A., and Gosselin, C. M., 2002, “Constraint Singularities as C-Space Singularities,” Advances in Robot Kinematics, J.Lenarcic and F.Thomas, eds., Kluwer, Dordrecht, pp. 183–192.
Jeong, Y. K., Lee, D. J., Kim, K. H., and Park, J. O., 2000, “A Wearable Robotic Arm With High Force-Reflection Capability,” Proceedings of the 2000 IEEE International Workshop on Robot and Human Interactive Communication, Sept. 27–29, Osaka, Japan, pp. 411–416.
Grosch, P., Di Gregorio, R., López, J., and Thomas, F., 2010, “Motion Planning for a Novel Reconfigurable Parallel Manipulator With Lockable Revolute Joints,” Proceedings of the 2010 IEEE International Conference on Robotics and Automation, Anchorage, Alaska, May 3–8.
Liao, Q. Z., Seneviratne, L. D., and Earles, S. W. E., 1995, “Forward Positional Analysis for the General 4–6 In-Parallel Platform,” Proc. Inst. Mech. Eng., Part C: Mech. Eng. Sci., 209(1), pp. 55–67. [CrossRef]
Gan, D. M., Liao, Q. Z., Dai, J. S., Wei, S. M., and Seneviratne, L. D., 2009, “Forward Displacement Analysis of the General 6-6 Stewart Mechanism Using Grobner Bases,” Mech. Mach. Theory, 44(9), pp. 1640–1647. [CrossRef]
Gosselin, C., and Angeles, J., 1990, “Singularity Analysis of Closed-Loop Kinematic Chains,” IEEE Trans. Rob. Autom., 6(3), pp. 281–290. [CrossRef]
Zlatanov, D., Fenton, R. G., and Benhabib, B., 1995, “A Unifying Framework for Classification and Interpretation of Mechanism Singularities,” ASME J. Mech. Des., 117, pp. 566–572. [CrossRef]
Merlet, J. P., 2007, “A Formal-Numerical Approach for Robust In-Workspace Singularity Detection,” IEEE Trans. Rob. Autom., 23(3), pp. 393–402. [CrossRef]
Kong, X., and Gosselin, C., 2001, “Uncertainty Singularity Analysis of Parallel Manipulators Based on the Instability Analysis of Structures,” Int. J. Robot. Res., 20(11), pp. 847–856. [CrossRef]
Tsai, L. W., 1998, “The Jacobian Analysis of a Parallel Manipulator Using Reciprocal Screws,” Adv. Robot Kinematics, J. Lenarčič, M. L. Husty, eds., Kluwer, Dordrecht, pp. 327–336.
Hao, F., and McCarthy, J. M., 1998, “Conditions for Line-Based Singularities in Spatial Platform Manipulators,” J. Rob. Syst., 15(1), pp. 43–55. [CrossRef]
Merlet, J. P., 1989, “Singular Configurations of Parallel Manipulators and Grassmann Geometry,” Int. J. Robot. Res., 8(5), pp. 45–56. [CrossRef]
Ben-Horin, P., and Shoham, M., 2006, “Singularity Condition of Six-Degree-of-Freedom Three-Legged Parallel Robots Based on Grassmann–Cayley Algebra,” IEEE Tran. Robotics, 22(4), pp. 577–590. [CrossRef]
Bottema, O., and Roth, B., 1979, Theoretical Kinematics, North-Holland, New York.


Grahic Jump Location
Fig. 1

Two phases of the rTPS limb (a) (rT)1PS and (b) (rT)2PS

Grahic Jump Location
Fig. 2

The 4(rT)2PS MPM with bifurcated motion

Grahic Jump Location
Fig. 3

Variable topologies of the 4(rT)PS MPM (a) 3(rT)2PS-1(rT)1PS (1T2R), (b) 2(rT)2PS-2(rT)1PS (2T2R), (c) 1(rT)2PS-3(rT)1PS (2T3R), and (d) 4(rT)1PS (3T3R)

Grahic Jump Location
Fig. 4

Unified limb modeling

Grahic Jump Location
Fig. 5

Workspace and singular configurations of 4(rT)2PS (2DOF) (a) workspace with singularity distribution, (b) singularity 1, (c) singularity 2, and (d) singularity 3

Grahic Jump Location
Fig. 6

Workspace and singularity locus of the 3(rT)2PS-1(rT)1PS (3DOF) (a) workspace with singularities (3D view), (b) workspace with singularities (top view), (c) singularity locus, (d) singularity 4

Grahic Jump Location
Fig. 8

Singularity 6 in two different configurations (a) home position (b) a general configuration (px = −4, py = 2, and pz = 8)



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