Abstract
The method of intersection of surfaces generated by kinematic dyads is applied to obtain mechanisms that are able to shift from one mode of motion to another. Then a mobility analysis shows that the singularities of the generated surfaces can be used to obtain mechanisms which can change their number of degrees-of-freedom depending on its configuration. The generator dyads are connected as usually done by a spherical pair. However, in the cases shown in this contribution the three-degrees-of-freedom of the spherical pair are not all necessary to keep the kinematic chain closed and movable, and the spherical pair can be substituted by either a pair of intersecting revolute joints or a single revolute joint. This substitution can be obtained by means of two methods presented in this contribution.
Issue Section:
Research Papers
References
1.
Dai
, J.
, and Jones
, J. R.
, 1999
, “Mobility in Metamorphic Mechanisms of Foldable/Erectable Kinds
,” ASME J. Mech. Des.
, 121
(3
), pp. 375
–382
.2.
Dai
, J.
, Zoppi
, M.
, and Kong
, X.
, eds., 2012
, Advances in Reconfigurable Mechanisms and Robots I
, Springer Verlag
, London
.3.
Wohlhart
, K.
, 1996
, “Kinematotropic Linkages
,” in Recent Advances in Robot Kinematics
, J.
Lenarcic
, and V.
Parent-Castelli
, eds., Kluwer Academic, Portoroz, Slovenia; Dordrecht, The Netherlands
, pp. 359
–368
.4.
Galletti
, C.
, and Fanghella
, P.
, 2001
, “Single-Loop Kinematotropic Mechanisms
,” Mech. Mach. Theory
, 36
(3
), pp. 743
–761
.5.
Rafaat
, S.
, Hervé
, J.
, Nahavandi
, S.
, and Trinh
, H.
, 2007
, “Two-Mode Overconstrained Three-DOFs Rotational-Translational Linear-Motor-Based Parallel Kinematic Mechanism for Machine Tool Applications
,” Robotica
, 25
(4
), pp. 461
–466
.6.
Kong
, X.
, 2012
, “Type Synthesis of Variable Degrees-Of-Freedom Parallel Manipulators With Both Planar and 3T1R Operation Modes
,” ASME
Paper No. DETC2012-70621.7.
Kong
, X.
, 2014
, “Reconfiguration Analysis of a 3-DOF Parallel Mechanism Using Euler Parameter Quaternions and Algebraic Geometry Method
,” Mech. Mach. Theory
, 74
, pp. 188
–201
.8.
Kong
, X.
, and Huang
, C.
, 2009
, “Type Synthesis of Single-Dof Single-Loop Mechanisms With Two Operation Modes
,” ASME/IFToMM International Conference on Reconfigurable Mechanisms and Robots
, pp. 136
–141
.9.
Kong
, X.
, and Pfurner
, M.
, 2015
, “Type Synthesis and Reconfiguration Analysis of a Class of Variable-dof Single-Loop Mechanisms
,” Mech. Mach. Theory
, 85
, pp. 116
–128
.10.
Zhang
, K.
, and Dai
, J. S.
, 2015
, “Screw-System-Variation Enabled Reconfiguration of the Bennett Plano-Spherical Hybrid Linkage and its Evolved Parallel Mechanism
,” ASME J. Mech. Des.
, 137
(6
), pp. 1
–10
.11.
Gan
, D.
, Dai
, J. S.
, and Caldwell
, D.
, 2011
, “Constraint-Based Limb Synthesis and Mobility-Change-Aimed Mechanism Construction
,” ASME J. Mech. Des.
, 133
(5
), pp. 1
–9
.12.
Torfason
, L.
, and Crossley
, F.
, 1971
, “Use of the Intersection of Surfaces as a Method for Design of Spatial Mechanisms
,” 3rd World Congress for the Theory of Machines and Mechanisms
, Vol. B, Kupari, Yugoslavia, pp. 247
–258
, Paper No. B-20.13.
Shrivastava
, A.
, and Hunt
, K.
, 1973
, “Dwell Motion From Spatial Linkages
,” ASME J. Eng. Industry
, 95
(2
), pp. 511
–518
.14.
Su
, H.
, and McCarthy
, J.
, 2005
, “Dimensioning a Constrained Parallel Robot to Reach a Set of Task Positions
,” IEEE International Conference on Robotics and Automation
, Barcelona, Spain, pp. 4026
–4030
.15.
Lee
, C.
, and Hervé
, J.
, 2012
, “A Discontinuously Movable Constant Velocity Shaft Coupling of Koenigs Joint Type
,” in Advances in Reconfigurable Mechanisms and Robots I
, M.
Zoppi
, J. S.
Dai
, and X.
Kong
, eds., Springer-Verlag, London, pp. 35
–43
.16.
Müller
, A.
, 1998
, “Generic Mobility of Rigid Body Mechanisms,” Mech. Mach. Theory
, 44
(6), pp. 1240–1255.17.
Müller
, A.
, 2015
, “Representation of the Kinematic Topology of Mechanisms for Kinematic Analysis,” Mech. Sci.
, 6
, pp. 137–146.18.
Crane
, C.
, and Duffy
, J.
, 1998
, Kinematic Analysis of Robot Manipulators
, Cambridge University
, Cambridge
.19.
Levin
, J.
, 1976
, “A Parametric Algorithm for Drawing Pictures of Solid Objects Composed of Quadric Surfaces
,” Commun. ACM
, 19
(10
), pp. 555
–563
.20.
Levin
, J.
, 1979
, “Mathematical Models for Determining the Intersection of Quadric Surfaces
,” Comput. Graph. Image Process.
, 11
(1
), pp. 73
–87
.21.
Miller
, J. R.
, 1987
, “Geometric Approaches to Nonplanar Quadric Surface Intersection Curves
,” ACM Trans. Graph.
, 6
(4
), pp. 274
–307
.22.
Liu
, Y.
, and Zsombor-Murray
, P.
, 1995
, “Intersection Curves Between Quadric Surfaces of Revolution
,” Trans. Can. Soc. Mech. Eng.
, 19
(4
), pp. 435
–453
.23.
Hervé
, J.
, 1978
, “Analyse structurelle des mécanismes par groupe des déplacements
,” Mech. Mach. Theory
, 13
(4
), pp. 437
–450
.24.
Rico
, J.
, and Ravani
, B.
, 2003
, “On Mobility Analysis of Linkages Using Group Theory
,” ASME J. Mech. Des.
, 125
(1
), pp. 70
–80
.25.
Rico
, J.
, Gallardo
, J.
, and Duffy
, J.
, 1999
, “Screw Theory and the Higher Order Kinematic Analysis of Serial and Closed Chains
,” Mech. Mach. Theory
, 34
(4
), pp. 559
–586
.26.
Myard
, F.
, 1931
, “Contribution à la géométrie des systèmes articulés
,” Bull. Soc. Math. France
, 59
, pp. 183
–210
.27.
Lee
, C.
, and Hervé
, J.
, 2014
, “Oblique Circular Torus, Villarceau Circles and Four Types of Bennett Linkages
,” Proc. Inst. Mech. Eng., Part C
, 228
(4
), pp. 742
–752
.28.
Lerbet
, J.
, 1998
, “Analytic Geometry and Singularities of Mechanisms
,” Z. Angew. Math. Mech.
, 78
(10
), pp. 687
–694
.29.
Müller
, A.
, 2002
, “Local Analysis of Singular Configuration of Open and Closed Loop Manipulators
,” Multibody Sys. Dyn.
, 8
(3
), pp. 297
–326
.30.
López-Custodio
, P.
, Rico
, J.
, Cervantes-Sánchez
, J.
, and Pérez-Soto
, G.
, 2014
, “Verification of the Higher Order Kinematic Analyses Equations
,” Eur. J. Mech. A/Solids (submitted).31.
Tadeo-Chávez
, A.
, Rico
, J.
, Cervantes-Sánchez
, J.
, Pérez-Soto
, G.
, and Muller
, A.
, 2011
, “Screw Systems Generated by Subalgebras: A Further Analysis
,” ASME
Paper No. DETC2011-48304.32.
Sommese
, A.
, and Wampler
, II, C. W.
, 2005
, The Numerical Solution of Systems of Polynomials Arising in Engineering and Science
, World Scientific
, Cambridge
.33.
Baker
, J.
, 1984
, “On 5-Revolute Linkages With Parallel Adjacent Joint Axes
,” Mech. Mach. Theory
, 19
(6
), pp. 467
–475
.34.
Torfason
, L.
, and Sharma
, A.
, 1973
, “Analysis of Spatial RRGRR Mechanisms by the Method of Generated Surfaces
,” ASME J. Eng. Ind.
, 95
(3
), pp. 704
–708
.35.
Villarceau
, Y.
, 1848
, “Théorème sur le tore
,” Nouv. Ann. Math.
, 7
, pp. 345
–347
.36.
Fitcher
, E.
, and Hunt
, K.
, 1975
, “The Fecund Torus, its Bitangent-Circles and Derived Linkages
,” Mech. Mach. Theory
, 10
(2
), pp. 167
–176
.37.
Altmann
, F.
, 1954
, “Communication to Grodzinski P. and M'Ewen, E., Link Mechanisms in Modern Kinematics'
,” Proc. Inst. Mech. Eng., Part E
, 168
(37
), pp. 877
–896
.38.
Phillips
, J.
, 1990
, Freedom in Machinery, Vol. 2: Screw Theory Exemplified
, Cambridge University
, Cambridge
.39.
Baker
, J.
, 1993
, “A Geometrico-Algebraic Exploration of Altmann's Linkage
,” Mech. Mach. Theory
, 28
(2
), pp. 249
–260
.40.
Baker
, J.
, 2012
, “On the Closure Modes of a Generalised Altmann Linkage
,” Mech. Mach. Theory
, 52
, pp. 243
–247
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