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Research Papers

Reconfigurable Mechanisms From the Intersection of Surfaces

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

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

J. M. Rico

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

J. J. Cervantes-Sánchez

Mechanical Engineering Department,
DICIS,
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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Figures

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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. 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. 6

Branching of modes of motion for the mechanism of Case 1

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Fig. 7

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

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Fig. 8

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

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Fig. 9

The three curves for qA1(qA2)

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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. 14

The four curves for qA1(qA2)

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Fig. 15

Modes of motion branching for Case 3

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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. 19

Branching of the modes of motion for the kinematotropic linkage

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