Singularities are one of the most important issues affecting the performance of parallel mechanisms. Therefore, analysis of their locations and closeness is essential for the development of a high-performance mechanism. The screw theory based motion/force transmission analysis provides such a closeness measure in terms of the work performed between specific mechanism twists and wrenches. As such, this technique has been applied to many serial chain parallel mechanisms. However, the motion/force transmission performance of parallel mechanisms with mixed topology chains is yet to be examined. These chains include linkages in both series and parallel, where the parallel portion is termed a closed-loop subchain (CLSC). This paper provides an analysis of such chains, where the CLSC is a planar four-bar linkage. In order to completely define the motion/force transmission abilities of these mechanisms, adapted wrench definitions are introduced. The proposed methodology is applied to a family of two degrees-of-freedom planar axis-symmetric parallel mechanisms, each with a different CLSC configuration. The presented analysis provides the first complete motion/force transmission analysis of such mechanisms.
Issue Section:
Research Papers
References
1.
Reboulet
, C.
, 1996
, “Parallel-Structure Manipulator Device for Displacing and Orienting an Object in a Cylindrical Work Space
,” U.S. Patent No. 5,539,291.2.
Brogårdh
, T.
, and Hovland
, G.
, 2008
, “The Tau PKM Structures
,” Smart Devices and Machines for Advanced Manufacturing
, L.
Wang
, and J.
Xi
, eds., Springer
, London
, pp. 79
–109
.3.
Isaksson
, M.
, and Watson
, M.
, 2013
, “Workspace Analysis of a Novel Six-Degrees-of-Freedom Parallel Manipulator With Coaxial Actuated Arms
,” ASME J. Mech. Des.
, 135
(10
), p. 104501
.4.
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
(IROS 2004
), Chicago, IL, Sept. 14–18, pp. 1690
–1696
.5.
Gosselin
, C.
, Isaksson
, M.
, Marlow
, K.
, and Laliberte
, T.
, 2016
, “Workspace and Sensitivity Analysis of a Novel Non-Redundant Parallel Scara Robot Featuring Infinite Tool Rotation
,” IEEE Rob. Autom. Lett.
, 1
(2
), pp. 776
–783
.6.
Carretero
, J. A.
, Podhorodeski
, R. P.
, Nahon
, M. A.
, and Gosselin
, C. M.
, 1999
, “Kinematic Analysis and Optimization of a New Three Degree-of-Freedom Spatial Parallel Manipulator
,” ASME J. Mech. Des.
, 122
(1
), pp. 17
–24
.7.
Isaksson
, M.
, Eriksson
, A.
, and Nahavandi
, S.
, 2014
, “Analysis of the Inverse Kinematics Problem for 3-DOF Axis-Symmetric Parallel Manipulators With Parasitic Motion
,” IEEE International Conference on Robotics and Automation
(ICRA
), Hong Kong, May 31–June 7, pp. 5736
–5743
.8.
Clavel
, R.
, 1990
, “Device for the Movement and Positioning of an Element in Space
,” U.S. Patent No. 4,976,582.9.
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
.10.
Kock
, S.
, Oesterlein
, R.
, and Brogårdh
, T.
, 2003
, “Industrial Robot
,” WO Patent No. 03/066289 A1.11.
Choi
, H.
, Konno
, A.
, and Uchiyama
, M.
, 2003
, “Singularity Analysis of a Novel 4-DOFs Parallel Robot H4 by Using Screw Theory
,” ASME
Paper No. DETC2003/DAC-48822. 12.
Marlow
, K.
, Isaksson
, M.
, Dai
, J. S.
, and Nahavandi
, S.
, 2015
, “Motion/Force Transmission Analysis of Parallel Mechanisms With Closed-Loop Sub-Chains
,” ASME J. Mech. Des.
(submitted).13.
Huang
, Z.
, Li
, Q.
, and Ding
, H.
, 2013
, “Special Configuration of Mechanisms
,” Theory of Parallel Mechanisms
(Mechanisms and Machine Science), Springer
, Dordrecht, The Netherlands
, pp. 217
–287
.14.
Isaksson
, M.
, 2011
, “A Family of Planar Parallel Manipulators
,” IEEE International Conference on Robotics and Automation
(ICRA
), Shanghai, May 9–13, pp. 2737
–2744
.15.
Ball
, R. S.
, 1998
, A Treatise on the Theory of Screws
, Cambridge University Press
, Cambridge, UK
.16.
Hunt
, K. H.
, 1978
, Kinematic Geometry of Mechanisms
, Oxford University Press
, Oxford, UK
.17.
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
.18.
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
.19.
Joshi
, S. A.
, and Tsai
, L.
, 2002
, “Jacobian Analysis of Limited-DOF Parallel Manipulators
,” ASME
Paper No. DETC2002/MECH-3423. 20.
Leal
, E. R.
, and Dai
, J. S.
, 2007
, “From Origami to a New Class of Centralized 3-DOF Parallel Mechanisms
,” ASME
Paper No. DETC2007-35516.21.
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
.22.
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
.23.
Plücker
, J.
, 1868
, Neue Geometrie des Raumes: gegründet auf die Betrachtung der geraden Linie als Raumelement
, Vol. 1
, Teubner
, Leipzig, Germany
.24.
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
.25.
Sutherland
, G.
, and Roth
, B.
, 1973
, “A Transmission Index for Spatial Mechanisms
,” ASME J. Eng. Ind.
, 95
(2
), pp. 589
–597
.26.
Tsai
, M. J.
, and Lee
, H. W.
, 1994
, “The Transmissivity and Manipulability of Spatial Mechanisms
,” ASME J. Mech. Des.
, 116
(1
), pp. 137
–143
.27.
Chen
, C.
, and Angeles
, J.
, 2007
, “Generalized Transmission Index and Transmission Quality for Spatial Linkages
,” Mech. Mach. Theory
, 42
(9
), pp. 1225
–1237
.28.
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
.29.
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
.30.
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
.31.
Liu
, H.
, Wang
, M.
, Huang
, T.
, Chetwynd
, D. G.
, and Kecskeméthy
, A.
, 2015
, “A Dual Space Approach for Force/Motion Transmissibility Analysis of Lower Mobility Parallel Manipulators
,” ASME J. Mech. Rob.
, 7
(3
), p. 034504
.32.
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), Springer International Publishing
, Cham, Switzerland, pp. 35
–43
.33.
Gosselin
, C.
, and Angeles
, J.
, 1990
, “Singularity Analysis of Closed-Loop Kinematic Chains
,” IEEE Trans. Rob. Autom.
, 6
(3
), pp. 281
–290
.34.
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. 35.
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
.36.
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
.37.
Balli
, S. S.
, and Chand
, S.
, 2002
, “Transmission Angle in Mechanisms (Triangle in Mech)
,” Mech. Mach. Theory
, 37
(2
), pp. 175
–195
.38.
Alt
, V. H.
, 1932
, “Der uberstragungswinkel und seine bedeutung fur dar konstruieren periodischer getriebe
,” Werksstattstechnik
, 26
(4
), pp. 61
–65
.39.
Hall
, A. S.
, 1961
, Kinematics and Linkage Design
, Prentice-Hall
, Englewood Cliffs, NJ
.40.
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
.41.
Phakatkar
, H. G.
, 2006
, Theory of Machines and Mechanisms I.
, 4th ed., Nirali Prakashan
, Pune, India.42.
Chen
, X.
, Chen
, C.
, and Liu
, X.
, 2015
, “Evaluation of Force/Torque Transmission Quality for Parallel Manipulators
,” ASME J. Mech. Rob.
, 7
(4
), p. 041013
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