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Research Papers: Design of Mechanisms and Robotic Systems

Motion/Force Transmission Analysis of Parallel Mechanisms With Planar Closed-Loop Subchains

[+] Author and Article Information
Kristan Marlow

Centre for Intelligent Systems Research,
Deakin University,
Geelong, Victoria 3217, Australia
e-mail: kristan.marlow@research.deakin.edu.au

Mats Isaksson

Department of Electrical and Computer
Engineering,
Colorado State University,
Fort Collins, CO 80523-1373
e-mail: mats.isaksson@gmail.com

Jian S. Dai

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

Saeid Nahavandi

Centre for Intelligent Systems Research,
Deakin University,
Geelong, Victoria 3217, Australia
e-mail: saeid.nahavandi@deakin.edu.au

1Corresponding author.

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received July 20, 2015; final manuscript received March 29, 2016; published online April 29, 2016. Assoc. Editor: Oscar Altuzarra.

J. Mech. Des 138(6), 062302 (Apr 29, 2016) (11 pages) Paper No: MD-15-1514; doi: 10.1115/1.4033338 History: Received July 20, 2015; Revised March 29, 2016

Singularities are one of the most important issues affecting the performance of parallel mechanisms. A parallel mechanism with less than six degrees of freedom (6DOF) is classed as having lower mobility. In addition to input–output singularities, such mechanisms potentially suffer from singularities among their constraints. Furthermore, the utilization of closed-loop subchains (CLSCs) may introduce additional singularities, which can strongly affect the motion/force transmission ability of the entire mechanism. In this paper, we propose a technique for the analysis of singularities occurring within planar CLSCs, along with a finite, dimensionless, frame invariant index, based on screw theory, for examining the closeness to these singularities. The integration of the proposed index with existing performance measures is discussed in detail and exemplified on a prototype industrial parallel mechanism.

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References

Brogårdh, T. , 2002, “ PKM Research-Important Issues, as Seen From a Product Development Perspective at ABB Robotics,” Workshop on Fundamental Issues and Future Research Directions for Parallel Mechanisms and Manipulators, Quebec, Canada.
Marlow, K. , Isaksson, M. , Abdi, H. , and Nahavandi, S. , 2014, “ Workspace Analysis of Two Similar 3-DOF Axis-Symmetric Parallel Manipulators,” IEEE/RSJ International Conference on Intelligent Robots and Systems, Chicago, IL, Sept. 14–18, pp. 1690–1696.
Zhang, K. , Dai, J. S. , and Fang, Y. , 2012, “ Constraint Analysis and Bifurcated Motion of the 3PUP Parallel Mechanism,” Mech. Mach. Theory, 49, pp. 256–269. [CrossRef]
Zoppi, M. , Zlatanov, D. , and Molfino, R. , 2010, “ Kinematics Analysis of the Exechon Tripod,” ASME Paper No. DETC2010-28668.
Marlow, K. , 2015, “ Motion/Force Transmission Analysis of Axis-Symmetric Parallel Mechanisms With Closed-Loop Sub-Chains,” Ph.D. thesis, Deakin University, Geelong, Australia.
Clavel, R. , 1990, “ Device for the Movement and Positioning of an Element in Space,” U.S. Patent No. 4,976,582.
Exechon, A. B. , 2015, “ Exechon,” Last accessed June 2015, www.exechon.com/
PKM TRICEPT, S. L. , 2015, “ Tricept T9000,” Last accessed June, 2015, www.pkmtricept.com/
Pierrot, F. , and Company, O. , 1999, “ H4: A New Family of 4-DOF Parallel Robots,” IEEE/ASME International Conference on Advanced Intelligent Mechatronics, Atlanta, GA, pp. 508–513.
Kock, S. , Oesterlein, R. , and Brogårdh, T. , 2003, “ Industrial Robot,” WO Patent Application 03/066289 A1.
Wenger, P. , and Chablat, D. , 2000, “ Kinematic Analysis of a New Parallel Machine Tool: The Orthoglide,” Advances in Robot Kinematics, Springer, Dordrecht, The Netherlands, pp. 305–314.
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. , Bonev, I. , and Gosselin, C. , 2002, “ Constraint Singularities of Parallel Mechanisms,” IEEE International Conference on Robotics and Automation (ICRA’02), Vol. 1, pp. 496–502.
Amine, S. , Masouleh, M. T. , Caro, S. , Wenger, P. , and Gosselin, C. , 2012, “ Singularity Conditions of 3T1R Parallel Manipulators With Identical Limb Structures,” ASME J. Mech. Rob., 4(1), p. 011011. [CrossRef]
Tsai, L. , 1998, “ The Jacobian Analysis of a Parallel Manipulator Using Reciprocal Screws,” Advances in Robot Kinematics: Analysis and Control, Springer, Dordrecht, The Netherlands, pp. 327–336.
Joshi, S. A. , and Tsai, L. , 2002, “ Jacobian Analysis of Limited-DOF Parallel Manipulators,” ASME Paper No. DETC2002/MECH-34238.
Leal, E. R. , and Dai, J. S. , 2007, “ From Origami to a New Class of Centralized 3-DOF Parallel Mechanisms,” ASME Paper No. DETC2007-35516.
Ball, R. S. , 1998, A Treatise on the Theory of Screws, Cambridge University Press, Cambridge, UK.
Hunt, K. H. , 1978, Kinematic Geometry of Mechanisms, Oxford University Press, Oxford, UK.
Sutherland, G. , and Roth, B. , 1973, “ A Transmission Index for Spatial Mechanisms,” ASME J. Eng. Ind., 95(2), pp. 589–597. [CrossRef]
Tsai, M. J. , and Lee, H. W. , 1994, “ The Transmissivity and Manipulability of Spatial Mechanisms,” ASME J. Mech. Des., 116(1), pp. 137–143. [CrossRef]
Chen, C. , and Angeles, J. , 2007, “ Generalized Transmission Index and Transmission Quality for Spatial Linkages,” Mech. Mach. Theory, 42(9), pp. 1225–1237. [CrossRef]
Wang, J. , Wu, C. , and Liu, X. , 2010, “ Performance Evaluation of Parallel Manipulators: Motion/Force Transmissibility and Its Index,” Mech. Mach. Theory, 45(10), pp. 1462–1476. [CrossRef]
Liu, X.-J. , Wu, C. , and Wang, J. , 2012, “ A New Approach for Singularity Analysis and Closeness Measurement to Singularities of Parallel Manipulators,” ASME J. Mech. Rob., 4(4), p. 041001. [CrossRef]
Amine, S. , Kanaan, D. , Caro, S. , and Wenger, P. , 2010, “ Constraint and Singularity Analysis of Lower-Mobility Parallel Manipulators With Parallelogram Joints,” ASME Paper No. DETC2010-28483.
Fang, H. , Fang, Y. , and Zhang, K. , 2012, “ Reciprocal Screw Theory Based Singularity Analysis of a Novel 3-DOF Parallel Manipulator,” Chin. J. Mech. Eng., 25(4), pp. 647–653. [CrossRef]
Davidson, J. K. , and Hunt, K. H. , 2004, Robots and Screw Theory: Applications of Kinematics and Statics to Robotics, Oxford University Press, New York.
Plücker, J. , 1868, Neue Geometrie des Raumes: gegründet auf die Betrachtung der geraden Linie als Raumelement, Vol. 1. Teubner, Leipzig, Germany.
Dai, J. S. , and Jones, J. R. , 2002, “ Null-Space Construction Using Cofactors From a Screw-Algebra Context,” Proc. R. Soc. London, Ser. A, 458(2024), pp. 1845–1866. [CrossRef]
Zhao, J. , Li, B. , Yang, X. , and Yu, H. , 2009, “ Geometrical Method to Determine the Reciprocal Screws and Applications to Parallel Manipulators,” Robotica, 27(6), pp. 929–940. [CrossRef]
Dai, J. S. , and Jones, J. R. , 2001, “ Interrelationship Between Screw Systems and Corresponding Reciprocal Systems and Applications,” Mech. Mach. Theory, 36(5), pp. 633–651. [CrossRef]
Huang, Z. , and Li, Q. , 2002, “ General Methodology for Type Synthesis of Symmetrical Lower-Mobility Parallel Manipulators and Several Novel Manipulators,” Int. J. Rob. Res., 21(2), pp. 131–145. [CrossRef]
Zhao, T. S. , Dai, J. S. , and Huang, Z. , 2002, “ Geometric Analysis of Overconstrained Parallel Manipulators With Three and Four Degrees of Freedom,” JSME Int. J., Ser. C, 45(3), pp. 730–740. [CrossRef]
Clavel, R. , 1988. “ Delta: A Fast Robot With Parallel Geometry,” 18th International Symposium on Industrial Robots, Lausanne, Switzerland, pp. 91–100.
Liu, X.-J. , Chen, X. , and Nahon, M. , 2014, “ Motion/Force Constrainability Analysis of Lower-Mobility Parallel Manipulators,” ASME J. Mech. Rob., 6(3), p. 031006. [CrossRef]
Xie, F. , Liu, X. , and Li, J. , 2014, “ Performance Indices for Parallel Robots Considering Motion/Force Transmissibility,” Intelligent Robotics and Applications (Lecture Notes in Computer Science), Vol. 8917, Springer International Publishing, Cham, Switzerland, pp. 35–43.
Balli, S. S. , and Chand, S. , 2002, “ Transmission Angle in Mechanisms (Triangle in Mech),” Mech. Mach. Theory, 37(2), pp. 175–195. [CrossRef]
Alt, V. H. , 1932, “ Der uberstragungswinkel und seine bedeutung fur dar konstruieren periodischer getriebe,” Werksstattstechnik, 26(4), pp. 61–65.
Hall, A. S. , 1961, Kinematics and Linkage Design, Prentice-Hall, Englewood Cliffs, NJ.
Cui, H. , Zhu, Z. , Gan, Z. , and Brogårdh, T. , 2005, “ Kinematic Analysis and Error Modeling of TAU Parallel Robot,” Rob. Comput.-Integr. Manuf., 21(6), pp. 497–505. [CrossRef]
Zhu, Z. , Li, J. , Gan, Z. , and Zhang, H. , 2005, “ Kinematic and Dynamic Modelling for Real-Time Control of Tau Parallel Robot,” Mech. Mach. Theory, 40(9), pp. 1051–1067. [CrossRef]
Isaksson, M. , Brogårdh, T. , Lundberg, I. , and Nahavandi, S. , 2010, “ Improving the Kinematic Performance of the SCARA-Tau PKM,” IEEE International Conference on Robotics and Automation (ICRA), Anchorage, AK, May 3–7, pp. 4683–4690.
Isaksson, M. , Brogårdh, T. , and Nahavandi, S. , 2012, “ Parallel Manipulators With a Rotation-Symmetric Arm System,” ASME J. Mech. Des., 134(11), p. 114503. [CrossRef]
Isaksson, M. , Eriksson, A. , Watson, M. , Brogårdh, T. , and Nahavandi, S. , 2015, “ A Method for Extending Planar Axis-Symmetric Parallel Manipulators to Spatial Mechanisms,” Mech. Mach. Theory, 83, pp. 1–13. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

CLSC in a parallel mechanism

Grahic Jump Location
Fig. 2

Representation of a wrench of actuation for a common RSS (RUS, RUU, RRR, etc.) serial chain

Grahic Jump Location
Fig. 3

(a) The vectors associated with the wrenches of the (SS)2 four-bar closed-loop and (b) the common R(SS)2 chain with various (SS)2 orientations

Grahic Jump Location
Fig. 4

(a) The physical prototype of the SCARA-Tau parallel mechanism and (b) its kinematic parameters

Grahic Jump Location
Fig. 5

ITI distribution throughout the SCARA-Tau's workspace. Shaded from dark at singular locations to light when furthest from singular locations according to (a). (a) Index mapping, (b) ITI1, (c) ITI2, (d) ITI3, and (e) min(ITI1,ITI2,ITI3).

Grahic Jump Location
Fig. 6

OTI distribution throughout the SCARA-Tau's workspace. Shaded as per Fig. 5(a), ranging from dark at singular locations to light when furthest from singular locations. (a) OTI1, (b) OTI2, (c) OTI3, and (d) min(OTI1,OTI2,OTI3).

Grahic Jump Location
Fig. 7

OTI overall minimum distribution for the SCARA-Tau with a poor parameter choice, where h3,1 = 0.400, while the other parameters are identical to those in Table 1. Shaded as per Fig. 5(a), ranging from dark at singular locations to light when furthest from singular locations.

Grahic Jump Location
Fig. 8

CTI distribution throughout the SCARA-Tau's workspace. Shaded as per Fig. 5(a), ranging from dark at singular locations to light when furthest from singular locations. (a) CTI1,1, (b) CTI2,1, (c) CTI2,2, and (d) min(CTI1,1,CTI2,1,CTI2,2).

Grahic Jump Location
Fig. 9

ICCI distribution throughout the SCARA-Tau's workspace. Shaded as per Fig. 5(a), ranging from dark at singular locations to light when furthest from singular locations. (a) ICCI1,11, (b) ICCI2,11, (c) ICCI2,21, and (d) min(ICCI1,11,ICCI2,11,ICCI2,21).

Grahic Jump Location
Fig. 10

The SCARA-Tau mechanism in a singularity free location, [x, y, z] = [1.4, 0, 0], from (a) an angled and (b) top view and close to an ICCS of the yaw constraining parallelogram at point [x, y, z] = [0.5, 0, 0], from (c) an angled and (d) top view. The point of analysis is indicated by the cross.

Grahic Jump Location
Fig. 11

(a) The OSI distribution throughout the SCARA-Tau's workspace and (b) with a lower acceptable bound on the ICCI of 0.64 applied. Shaded as per Fig. 5(a), ranging from dark at singular locations to light when furthest from singular locations.

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