An approach for the force/motion transmissibility analysis of full mobility planar multiloop mechanisms (PMLM) is proposed in this paper by drawing on the duality of twist space and wrench space. By making a comparison study, it is concluded that the velocity model of a full mobility planar multiloop mechanism can be expressed in the same form as that of a full mobility planar parallel mechanism (PPM). Thereby, a set of dimensionally homogeneous transmission indices is proposed, which can be employed for precisely representing the closeness to different types of singularities as well as for dimensional optimization. A 3-RRR parallel mechanism and a full mobility planar multiloop mechanism for face-shovel excavation are taken as examples to demonstrate the validity and effectiveness of the proposed approach.
Issue Section:
Research Papers
Topics:
Mechanical admittance
References
1.
Davies
, T. H.
, and Crossley
, F. E.
, 1966
, “Structural Analysis of Plane Linkages by Franke's Condensed Notation
,” J. Mech.
, 1
(2
), pp. 171
–183
.2.
Sohn
, W. J.
, and Freudenstein
, F.
, 1986
, “An Application of Dual Graphs to the Automatic Generation of the Kinematic Structures of Mechanisms
,” ASME J. Mech., Transm. Autom. Des.
, 108
(3
), pp. 392
–398
.3.
Ding
, H.
, and Huang
, Z.
, 2007
, “The Establishment of the Canonical Perimeter Topological Graph of Kinematic Chains and Isomorphism Identification
,” ASME J. Mech. Des.
, 129
(9
), pp. 915
–923
.4.
Ding
, H.
, Huang
, Z.
, and Mu
, D.
, 2008
, “Computer-Aided Structure Decomposition Theory of Kinematic Chains and Its Applications
,” Mech. Mach. Theory
, 43
(12
), pp. 1596
–1609
.5.
Ding
, H.
, Zhao
, J.
, and Huang
, Z.
, 2010
, “Unified Structural Synthesis of Planar Simple and Multiple Joint Kinematic Chains
,” Mech. Mach. Theory
, 45
(4
), pp. 555
–568
.6.
Ding
, H.
, Kecskeméthy
, A.
, Huang
, Z.
, and Cao
, W.
, 2012
, “Complete Atlas Database of 2-DOF Kinematic Chains and Creative Design of Mechanisms
,” ASME J. Mech. Des.
, 124
(3
), p. 031006
.7.
Gosselin
, C. M.
, and Angeles
, J.
, 1990
, “Singularity Analysis of Closed-Loop Kinematic Chains
,” IEEE Trans. Rob. Autom.
, 6
(3
), pp. 281
–290
.8.
Gosselin
, C. M.
, 1990
, “Dexterity Indices for Planar and Spatial Robotic Manipulators
,” IEEE International Conference on Robotics and Automation
(ICRA
), Cincinnati, OH, May 13–18, pp. 650
–655
.9.
Sefrioui
, J.
, and Gosselin
, C. M.
, 1992
, “Singularity Analysis and Representation of Planar Parallel Manipulators
,” Rob. Auton. Syst.
, 10
(4
), pp. 209
–224
.10.
Sefrioui
, J.
, and Gosselin
, C. M.
, 1995
, “On the Quadratic Nature of the Singularity Curves of Planar Three-Degree-of-Freedom Parallel Manipulators
,” Mech. Mach. Theory
, 30
(4
), pp. 533
–551
.11.
Zlatanov
, D.
, Fenton
, R. G.
, and Benhabib
, B.
, 1994
, “Singularity Analysis of Mechanisms and Robots Via a Motion-Space Model of the Instantaneous Kinematics
,” IEEE International Conference on Robotics and Automation
(ICRA
), San Diego, CA, May 8–13, pp. 980
–985
.12.
Gao
, F.
, Liu
, X.-J.
, and William
, A. G.
, 1998
, “Performance Evaluation of Two-Degree-of-Freedom Planar Parallel Robots
,” Mech. Mach. Theory
, 33
(6
), pp. 661
–668
.13.
Liu
, X.-J.
, Wang
, J.
, and Pritschow
, G.
, 2006
, “Kinematics, Singularity and Workspace of Planar 5R Symmetrical Parallel Mechanisms
,” Mech. Mach. Theory
, 41
(2
), pp. 145
–169
.14.
Liu
, X.-J.
, Wang
, J.
, and Pritschow
, G.
, 2006
, “Performance Atlases and Optimum Design of Planar 5R Symmetrical Parallel Mechanisms
,” Mech. Mach. Theory
, 41
(2
), pp. 119
–144
.15.
Liu
, X.-J.
, Wang
, J.
, and Pritschow
, G.
, 2006
, “On the Optimal Kinematic Design of the PRRRP 2-DoF Parallel Mechanism
,” Mech. Mach. Theory
, 41
(9
), pp. 1111
–1130
.16.
Flores
, F. G.
, Kecskeméthy
, A.
, and Pöttker
, A.
, 2007
, “Workspace Analysis and Maximal Force Calculation of a Face-Shovel Excavator Using Kinematical Transformers
,” 12th World Congress in Mechanism and Machine Science
, Besancon, France, June 18–21, pp. 1–6.17.
Merlet
, J.-P.
, 2006
, “Jacobian, Manipulability, Condition Number, and Accuracy of Parallel Robots
,” ASME J. Mech. Des.
, 128
(1
), pp. 199
–206
.18.
Merlet
, J.-P.
, 2006
, Parallel Robots
, 2nd ed., Springer
, Dordrecht, The Netherlands
.19.
Merlet
, J.-P.
, and Gosselin
, C. M.
, 2008
, “Parallel Mechanisms and Robots
,” Springer Handbook of Robotics
, S.
Bruno
and K.
Oussama
, eds., Springer-Verlag
, Berlin, pp. 269
–285
.20.
Balli
, S. S.
, and Satish
, C.
, 2002
, “Transmission Angle in Mechanisms
,” Mech. Mach. Theory
, 37
(2
), pp. 175
–195
.21.
Balli
, S. S.
, and Satish
, C.
, 2004
, “Synthesis of a Five-Bar Mechanism of Variable Topology Type With Transmission Angle Control
,” ASME J. Mech. Des.
, 126
(1
), pp. 128
–134
.22.
Dresner
, T. L.
, and Buffinton
, K. W.
, 1991
, “Definition of Pressure and Transmission Angles Applicable to Multi-Input Mechanisms
,” ASME J. Mech. Des.
, 113
(4
), pp. 495
–499
.23.
Bonev
, A. I.
, Zlatanov
, D.
, and Gosselin
, C. M.
, 2003
, “Singularity Analysis of 3-DOF Planar Parallel Mechanisms Via Screw Theory
,” ASME J. Mech. Des.
, 125
(3
), pp. 573
–581
.24.
Lin
, C.-C.
, and Chang
, W.-T.
, 2002
, “The Force Transmissibility Index of Planar Linkage Mechanisms
,” Mech. Mach. Theory
, 37
(12
), pp. 1465
–1485
.25.
Chang
, W.-T.
, Lin
, C.-C.
, and Lee
, J.-J.
, 2003
, “Force Transmissibility Performance of Parallel Manipulators
,” J. Rob. Syst.
, 20
(11
), pp. 659
–670
.26.
Sutherland
, G.
, and Roth
, B.
, 1973
, “A Transmission Index for Spatial Mechanisms
,” ASME J. Eng. Ind.
, 95
(2
), pp. 589
–597
.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.
Liu
, X.-J.
, Wu
, C.
, and Wang
, J. S.
, 2012
, “A New Approach for Singularity Analysis and Closeness Measurement to Singularities of Parallel Manipulators
,” ASME J. Mech. Rob.
, 4
(4
), p. 041001
.29.
Chen
, X.
, Liu
, X.-J.
, and Xie
, F.
, 2015
, “Screw Theory Based Singularity Analysis of Lower-Mobility Parallel Robots Considering the Motion/Force Transmissibility and Constrainability
,” Math. Probl. Eng.
, 2015
(2015
), p. 487956
.30.
Wang
, J.-S.
, Wu
, C.
, and Liu
, X.-J.
, 2010
, “Performance Evaluation of Parallel Manipulators: Motion/Force Transmissibility and Its Index
,” Mech. Mach. Theory
, 45
(10
), pp. 1462
–1476
.31.
Huang
, T.
, Wang
, M.
, Yang
, S.
, Sun
, T.
, Chetwynd
, D. G.
, and Xie
, F.
, 2014
, “Force/Motion Transmissibility Analysis of Six Degree of Freedom Parallel Mechanisms
,” ASME J. Mech. Rob.
, 6
(3
), p. 031010
.32.
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
.33.
Liu
, H.
, Huang
, T.
, Kecskeméthy
, A.
, and Chetwynd
, D. G.
, 2014
, “A Generalized Approach for Computing the Transmission Index of Parallel Mechanisms
,” Mech. Mach. Theory
, 74
, pp. 245
–256
.34.
Ball
, R. S.
, 1900
, A Treatise on the Theory of Screws
, Cambridge University Press
, Cambridge, UK.35.
Hall
, A.
, and McAree
, P. R.
, 2005
, “Robust Bucket Position Tracking for a Large Hydraulic Excavator
,” Mech. Mach. Theory
, 40
(1
), pp. 1
–16
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