Mechanisms' instantaneous kinematics is modeled by linear and homogeneous mappings whose coefficient matrices are also meaningful to understand their static behavior through the virtual work principle. The analysis of these models is a mandatory step during design. The superposition principle can be used for building and studying linear and homogeneous models. Here, multi-degree-of-freedom (multi-DOF) spherical mechanisms are considered. Their instantaneous-kinematics model is written by exploiting instantaneous-pole-axes' (IPA) properties and the superposition principle. Then, this general model is analyzed and an exhaustive analytic and geometric technique to identify all their singular configurations is deduced. Eventually, the effectiveness of the deduced technique is shown with two relevant case studies.
Issue Section:
Research Papers
References
1.
Davies
, T. H.
, 1981
, “Kirchhoff Circulation Law Applied to Multi-Loop Kinematic Chains
,” Mech. Mach. Theory
, 16
(3
), pp. 171
–183
.10.1016/0094-114X(81)90033-12.
Zlatanov
, D.
, Fenton
, R. G.
, and Benhabib
, B.
, 1995
, “A Unifying Framework for Classification and Interpretation of Mechanism Singularities
,” ASME J. Mech. Des.
, 117
(4
), pp. 566
–572
.10.1115/1.28267203.
Hunt
, K. H.
, 1978
, Kinematic Geometry of Mechanisms
, Claredon Press
, Oxford, UK
.4.
Davidson
, J. K.
, and Hunt
, K. H.
, 2007
, Robots and Screw Theory
, Oxford University Press
, New York
.5.
Gosselin
, C. M.
, and Angeles
, J.
, 1990
, “Singularity Analysis of Closed-Loop Kinematic Chains
,” IEEE Tran. Rob. Autom.
, 6
(3
), pp. 281
–290
.10.1109/70.566606.
Ma
, O.
, and Angeles
, J.
, 1991
, “Architecture Singularities of Platform Manipulators
,” IEEE International Conference on Robotics and Automation
(ICRA 1991
), Sacramento, CA
, Apr. 9–11, pp. 1542
–1547
.10.1109/ROBOT.1991.1318357.
Di Gregorio
, R.
, 2011
, “A General Algorithm for Analytically Determining all the Instantaneous Pole Axis Locations in Single-DOF Spherical Mechanisms
,” Proc. Inst. Mech. Eng., Part C: J. Mech. Eng. Sci.
, 225
(9
), pp. 2062
–2075
.10.1177/09544062114048948.
Di Gregorio
, R.
, 2013
, “Analytical Method for the Singularity Analysis and Eenumeration of the Singularity Conditions in Single-Degree-of-Freedom Spherical Mechanisms
,” Proc. Inst. Mech. Eng., Part C: J. Mech. Eng. Sci.
, 227
(8
), pp. 1830
–1840
.10.1177/09544062124693289.
Lerner
, D.
, 2007
, Lecture Notes on Linear Algebra, Department of Mathematics, University of Kansas
, Lawrence, KS
, p. 27
(Sec. 5.4), available at: http://www.math.ku.edu/open/LinearAlgebraNotes-Lerner/LANotes.pdf10.
Chiang
, C. H.
, 1988
, Kinematics of Spherical Mechanisms
, Cambridge University Press
, New York
.11.
Gosselin
, C. M.
, 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
.10.1115/1.325898412.
Gosselin
, C. M.
, Sefrioui
, J.
, and Richard
, M. J.
, 1994
, “On the Direct Kinematics of Spherical Three-Degree-of-Freedom Parallel Manipulators of General Architecture
,” ASME J. Mech. Des.
, 116
(2
), pp. 594
–598
.10.1115/1.291941913.
Gosselin
, C.
, and Hamel
, J.-F.
, 1994
, “The Agile Eye: A High-Performance Three-Degree-of-Freedom Camera-Orienting Device
,” IEEE International Conference on Robotics and Automation
(ICRA 1994
), San Diego, CA, May 8–13, pp. 781
–786
.10.1109/ROBOT.1994.35139314.
Alizade
, R. I.
, Tagiyiev
, N. R.
, and Duffy
, J.
, 1994
, “A Forward and Reverse Displacement Analysis of an In-Parallel Spherical Manipulator
,” Mech. Mach. Theory
, 29
(1
), pp. 125
–137
.10.1016/0094-114X(94)90025-615.
Gosselin
, C. M.
, Perreault
, L.
, and Vaillancourt
, C.
, 1995
, “Simulation and Computer-Aided Kinematic Design of Three-Degree-of-Freedom Spherical Parallel Manipulators
,” J. Rob. Systems
, 12
(12
), pp. 857
–869
.10.1002/rob.462012120916.
Primrose
, E.
, Freudenstein
, F.
, and Roth
, B.
, 1967
, “Six-Bar Motion. II. The Stepenson-1 and Stephenson-2 Mechanism
,” Arch. Ration. Mech. Anal.
, 24
(1
), pp. 42
–72
.17.
Hernandez
, S.
, Bai
, S.
, and Angeles
, J.
, 2006
, “The Design of a Chain of Spherical Stephenson Mechanisms for a Gearless Robotic Pitch-Roll Wrist
,” ASME J. Mech. Des.
, 128
(3
), pp. 422
–429
.10.1115/1.216765318.
Ting
, K. L.
, Xue
, C.
, Wang
, J
, and Currie
, K.
, 2010
, “Full Rotatability and Singularity of Six-Bar and Geared Five-Bar Linkages
,” J. Mech. Rob.
, 2
(1
), p. 011011
.10.1115/1.400051719.
McCarthy
, J. M.
, and Soh
, G. S.
, 2011
, “Multiloop Spherical Linkages
,” Geometric Design of Linkages
, Springer
, New York
, pp. 231
–251
.10.1007/978-1-4419-7892-920.
Gosselin
, C. M.
, and Wang
, J.
, 2002
, “Singularity Loci of a Special Class of Spherical Three-Degree-of-Freedom Parallel Mechanisms With Revolute Actuators
,” Int. J. Rob. Res.
, 21
(7
), pp. 649
–659
.10.1177/02783640232202323121.
Bonev
, I. A.
, and Gosselin
, C.
, 2005
, “Singularity Loci of Spherical Parallel Mechanisms
,” IEEE International Conference on Robotics and Automation
(ICRA 2005
), Barcelona, Spain
, April 18–22, pp. 2968
–2973
.10.1109/ROBOT.2005.157056322.
Di Gregorio
, R.
, 2013
, “Parallel Wrists: Limb Types, Singularities and New Perspectives
,” Interdisciplinary Mechatronics
, M. K.
Habib
and J. P.
Davim
, eds., Wiley-ISTE
, Hoboken, NJ
, pp. 113
–144
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