Research Papers

Reconfigurable Mechanisms From the Intersection of Surfaces

[+] Author and Article Information
P. C. López-Custodio

Mechanical Engineering Department,
Universidad de Guanajuato,
Salamanca, Guanajuato 36885, Mexico
e-mail: custodio825@gmail.com

J. M. Rico

Mechanical Engineering Department,
Universidad de Guanajuato,
Salamanca, Guanajuato 36885, Mexico
e-mail: jrico@ugto.mx

J. J. Cervantes-Sánchez

Mechanical Engineering Department,
Universidad de Guanajuato,
Salamanca, Guanajuato 36885, Mexico
e-mail: jecer@ugto.mx

G. I. Pérez-Soto

Facultad de Ingeniería,
Universidad Autónoma de Querétaro,
Campus San Juan del Río,
San Juan del Río, Querétaro 76807, Mexico
e-mail: gerardo_p_s@hotmail.com

1Corresponding author.

Manuscript received June 2, 2015; final manuscript received November 6, 2015; published online March 2, 2016. Assoc. Editor: David Dooner.

J. Mechanisms Robotics 8(2), 021029 (Mar 02, 2016) (18 pages) Paper No: JMR-15-1126; doi: 10.1115/1.4032097 History: Received June 02, 2015; Revised November 06, 2015

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.

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Dai, J. , and Jones, J. R. , 1999, “ Mobility in Metamorphic Mechanisms of Foldable/Erectable Kinds,” ASME J. Mech. Des., 121(3), pp. 375–382. [CrossRef]
Dai, J. , Zoppi, M. , and Kong, X. , eds., 2012, Advances in Reconfigurable Mechanisms and Robots I, Springer Verlag, London.
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.
Galletti, C. , and Fanghella, P. , 2001, “ Single-Loop Kinematotropic Mechanisms,” Mech. Mach. Theory, 36(3), pp. 743–761. [CrossRef]
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. [CrossRef]
Kong, X. , 2012, “ Type Synthesis of Variable Degrees-Of-Freedom Parallel Manipulators With Both Planar and 3T1R Operation Modes,” ASME Paper No. DETC2012-70621.
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. [CrossRef]
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.
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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.
Shrivastava, A. , and Hunt, K. , 1973, “ Dwell Motion From Spatial Linkages,” ASME J. Eng. Industry, 95(2), pp. 511–518. [CrossRef]
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.
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.
Müller, A. , 1998, “Generic Mobility of Rigid Body Mechanisms,” Mech. Mach. Theory, 44(6), pp. 1240–1255.
Müller, A. , 2015, “Representation of the Kinematic Topology of Mechanisms for Kinematic Analysis,” Mech. Sci., 6, pp. 137–146.
Crane, C. , and Duffy, J. , 1998, Kinematic Analysis of Robot Manipulators, Cambridge University, Cambridge.
Levin, J. , 1976, “ A Parametric Algorithm for Drawing Pictures of Solid Objects Composed of Quadric Surfaces,” Commun. ACM, 19(10), pp. 555–563. [CrossRef]
Levin, J. , 1979, “ Mathematical Models for Determining the Intersection of Quadric Surfaces,” Comput. Graph. Image Process., 11(1), pp. 73–87. [CrossRef]
Miller, J. R. , 1987, “ Geometric Approaches to Nonplanar Quadric Surface Intersection Curves,” ACM Trans. Graph., 6(4), pp. 274–307. [CrossRef]
Liu, Y. , and Zsombor-Murray, P. , 1995, “ Intersection Curves Between Quadric Surfaces of Revolution,” Trans. Can. Soc. Mech. Eng., 19(4), pp. 435–453.
Hervé, J. , 1978, “ Analyse structurelle des mécanismes par groupe des déplacements,” Mech. Mach. Theory, 13(4), pp. 437–450. [CrossRef]
Rico, J. , and Ravani, B. , 2003, “ On Mobility Analysis of Linkages Using Group Theory,” ASME J. Mech. Des., 125(1), pp. 70–80. [CrossRef]
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. [CrossRef]
Myard, F. , 1931, “ Contribution à la géométrie des systèmes articulés,” Bull. Soc. Math. France, 59, pp. 183–210.
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. [CrossRef]
Lerbet, J. , 1998, “ Analytic Geometry and Singularities of Mechanisms,” Z. Angew. Math. Mech., 78(10), pp. 687–694. [CrossRef]
Müller, A. , 2002, “ Local Analysis of Singular Configuration of Open and Closed Loop Manipulators,” Multibody Sys. Dyn., 8(3), pp. 297–326. [CrossRef]
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).
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.
Sommese, A. , and Wampler, II, C. W. , 2005, The Numerical Solution of Systems of Polynomials Arising in Engineering and Science, World Scientific, Cambridge.
Baker, J. , 1984, “ On 5-Revolute Linkages With Parallel Adjacent Joint Axes,” Mech. Mach. Theory, 19(6), pp. 467–475. [CrossRef]
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. [CrossRef]
Villarceau, Y. , 1848, “ Théorème sur le tore,” Nouv. Ann. Math., 7, pp. 345–347.
Fitcher, E. , and Hunt, K. , 1975, “ The Fecund Torus, its Bitangent-Circles and Derived Linkages,” Mech. Mach. Theory, 10(2), pp. 167–176.
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.
Phillips, J. , 1990, Freedom in Machinery, Vol. 2: Screw Theory Exemplified, Cambridge University, Cambridge.
Baker, J. , 1993, “ A Geometrico-Algebraic Exploration of Altmann's Linkage,” Mech. Mach. Theory, 28(2), pp. 249–260. [CrossRef]
Baker, J. , 2012, “ On the Closure Modes of a Generalised Altmann Linkage,” Mech. Mach. Theory, 52, pp. 243–247. [CrossRef]


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Fig. 1

Closed-loop kinematic chain resulting from merging two open kinematic chains

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Fig. 2

Open kinematic chain with n + 1 bodies connected by n kinematic joints

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Fig. 6

Branching of modes of motion for the mechanism of Case 1

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Fig. 8

Closed-loop mechanism from AT14,7,13π∩BAT(BT14,7,13π)

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Fig. 3

Surfaces of case 1: AKγA∩BAT(BYRB)

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Fig. 4

Closed-loop mechanism from AKγA∩BAT(BYRB): (a) with spherical joint and (b) with spherical joint reduced

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Fig. 5

Plot of qA2 versus qA1

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Fig. 7

Surfaces of case 2: AT2R,R,γ∩BAT(BT2R,R,γ)

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Fig. 10

(a) Overconstrained 5R mechanism in which X∈C2=C2, (b) overconstrained 5R mechanism in which X∈C3=C3, and (c) reconfigurable 6R mechanism in which X∈C2∪C3

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Fig. 11

Branching of modes of motion

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Fig. 12

Surfaces of case 3: ATLA,RA,12π∩BAT(BTRA,LA,β)

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Fig. 13

Closed-loop mechanism from AT10,5,12π∩BAT(BT5,10,16π)

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Fig. 19

Branching of the modes of motion for the kinematotropic linkage

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Fig. 14

The four curves for qA1(qA2)

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Fig. 9

The three curves for qA1(qA2)

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Fig. 16

Surfaces of case 1: ATR sin γ,R,π2∩BAT(BKγ)

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Fig. 17

Closed-loop mechanism from AT72,7,π2∩BAT(BKπ6)

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Fig. 18

The three modes of motion for the analyzed kinematotropic mechanism

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Fig. 15

Modes of motion branching for Case 3



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