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Research Papers

A Contact-Aided Compliant Displacement-Delimited Gripper Manipulator

[+] Author and Article Information
Anupam Saxena

Indian Institute of Technology Kanpur, Kanpur,
Uttar Pradesh 208016, India

The form of such a mechanism is not yet conceived by the author.

Subscript c suggests that the variable is continuous; subscript b represents a binary variable.

Synthesis of the displacement-delimited gripper is performed using the matlabtm code developed by Nagendra Reddy [29].

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the Journal of Mechanisms and Robotics. Manuscript received February 21, 2012; final manuscript received March 28, 2013; published online July 22, 2013. Assoc. Editor: Jian S. Dai.

J. Mechanisms Robotics 5(4), 041005 (Jul 22, 2013) (12 pages) Paper No: JMR-12-1018; doi: 10.1115/1.4024728 History: Received February 21, 2012; Revised March 28, 2013

A novel, monolithic, contact-aided, displacement-delimited gripper is presented. It is designed to employ contact interactions between its deforming members to delimit the output displacement such that excessive forces on the soft, fragile work-pieces are thwarted. The mechanism is appropriated using the topology, shape, and size optimization algorithm which, in addition to yielding structural details, also determines the interacting members and nature of contact. The symmetric halves of this design can be actuated independently thus rendering it the manipulative capabilities in addition to gripping. A cantilevered flexible “U” structure when introduced between the gripper ports of this mechanism can yield additional benefits in terms of reduced gripping forces. Macroscale Teflon prototype of the mechanism is tested on various work-pieces having different stiffness properties. Using experimentally acquired vision data, reaction loads on the work-pieces and gripper ports are estimated probabilistically by solving a Dirichlet problem for continua undergoing large deformation.

Copyright © 2013 by ASME
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Figures

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Fig. 1

Representative design specifications for the contact-aided compliant displacement-delimited gripper

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Fig. 9

One beam of the “U” structure in Fig. 8. ∈1, ∈2, Δδ1, and Δδt are uncertainties in experimental measurements. F represents the force from the gripper port on the beam, while R represents that from the work-piece.

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Fig. 8

Double gripper: the displacement-delimited gripper interacting with a cantilevered flexible “U” structure. (a) Setup. (b) Different deformed stages of the double gripper (a work-piece is not used yet).

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Fig. 3

Design methodology for the displacement-delimited gripper. Stage I: vI is converted into the candidate design. For tb = 0, the member is absent while for tb = 1, the member is present. Only for members present, shape (sc1, sc2) and size (wc, tc) variables are used. Stage II: Large deformation contact analysis is performed and the path traced by the output port O is determined. To evaluate the objective φI, the prescribed and traced paths are closed using a specified point C so that they can be modeled as periodic curves. Fourier coefficients ak and bk, and the path lengths L are determined for prescribed and traced paths. φI compares the respective coefficients and lengths. Stage III: The design vI is mutated to vJ and the analysis and evaluation continues until N (number of cycles) > N* (prescribed cycles).

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Fig. 2

Design specifications for the displacement-delimited compliant gripper

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Fig. 4

Full design of the contact-aided compliant displacement-delimited gripper and its displaced positions. Paths traced are shown using dotted lines.

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Fig. 5

The displacement-delimited gripper fabricated using Teflon. (a)–(d) Four displaced configurations. The paths traced by the gripper ports are also depicted.

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Fig. 6

The displacement-delimited gripper interacting with a vinyl Eraser. (a)–(c) Initial, intermediate, and final gripping stages. Positions of the gripper ports shown with horizontal bars. The eraser does not translate downward until a sufficient gripping force is achieved (see Fig. 7). (d)–(f) Three configurations demonstrating the rotation of the work-piece through the independent actuation of the gripper halves.

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Fig. 7

Displacement of the eraser versus average input displacement key: A, start of actuation; G, gripping occurs; M, point after which the eraser starts to move; O, specified limit of eraser translation; N, the eraser is catapulted to this point after the gripper ports release it at O. Solid line: average output displacement over five trials. Dashed vertical lines: error bars. Five different marker types correspond to five different trials.

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Fig. 10

Estimation of force between the output port of the displacement-delimited gripper and the “U” beam using the small deformation assumption. Key: dashed lines: force prediction with no uncertainties. “□”: forces predicted when uncertainties in δ1, δt, and l1 are permitted. Solid line: average force with different Δδ1, Δδt, and ∈1 over 1000 trials. If ∈1 is relaxed, “□” will be spread over a larger region.

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Fig. 11

The Dirichlet’s elasticity problem

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Fig. 12

Force prediction and comparison with synthetic data. Key: hexagrams and diamonds: true values of loads F and R. Solid rectangles represent the range ΔF when noise in measurements is considered. Dotted rectangles represent the range ΔR. A set of solid and dotted rectangles denote a single attempt of force prediction. Five such attempts are made. Prediction for each set (F, R) is enclosed within a thick solid rectangle.

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Fig. 16

Squares and circles: Estimation of forces between the displacement-delimited gripper ports and the beams (F), and those between the beams and the elastic band (R). The squares represent predicted loads between the ports and beams when permitted combinations of uncertainties in measurements are generated in 3000 Dirichlet trials per attempt. The circles represent estimated forces between the beams and the band. Load estimation is performed in five attempts. Filled squares and circles: Best predictions for F and R. For each set (F, R), permitted error in displacements is given by a. Solid and dotted rectangles: uncertainties in F and R, respectively, for a single attempt for a load set. Hexagrams represent loads (F) between the gripper ports and the beams while the triangles depict forces (R) between the beams and the elastic band when no corrections in measurements are performed.

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Fig. 14

(a) Interaction between the “double gripper” and a rubber band and (b) various stages of gripping

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Fig. 15

Interaction between “double gripper” and a stiff circular disc. Various stages of swing manipulation.

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Fig. 13

Reaction force estimation when the displacement-delimited gripper interacts with the “U” structure. Key: hexagrams: forces when no corrections in measurements are made. Rectangles: uncertainty in forces estimated over 3000 trials when measurement corrections are permitted. Five attempts are performed for force prediction. (a) left beam, configurations (ii–v) in Figs. 8(b) and (b) right beam, configurations (i–v) in Fig. 8(b).

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