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Research Papers

A Linear Multiport Network Approach for Elastically Coupled Underactuated Grippers

[+] Author and Article Information
Michael J. Martell

Department of Mechanical Engineering,
The University of Tulsa,
Tulsa, OK 74104
e-mail: michael-martell@utulsa.edu

J. C. Díaz

Tandy School of Computer Science,
The University of Tulsa,
Tulsa, OK 74104
e-mail: diaz@utulsa.edu

Joshua A. Schultz

Department of Mechanical Engineering,
The University of Tulsa,
Tulsa, OK 74104
e-mail: joshua-schultz@utulsa.edu

1Corresponding author.

Manuscript received January 9, 2017; final manuscript received July 21, 2017; published online August 23, 2017. Assoc. Editor: K. H. Low.

J. Mechanisms Robotics 9(5), 051012 (Aug 23, 2017) (10 pages) Paper No: JMR-17-1007; doi: 10.1115/1.4037566 History: Received January 09, 2017; Revised July 21, 2017

This paper presents a framework based on multiport network theory for modeling underactuated grippers where the actuators produce finger motion by deforming an elastic transmission mechanism. If the transmission is synthesized from compliant components joined together with series (equal force) or parallel (equal displacement) connections, the resulting multiport immittance (stiffness) matrix for the entire transmission can be used to deduce how the object will behave in the grasp. To illustrate this, a three-fingered gripper is presented in which each finger is driven by one of two linear two-port spring networks. The multiport approach predicts contact force distribution with good fidelity even with asymmetric objects. The parallel-connected configuration exhibited object rotation and was more prone to object ejection than the series-connected case, which balanced the contact forces evenly.

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Figures

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Fig. 1

Illustration of various underactuation schemes used to couple fingers to a small number of actuators: (a) tendon branch—equal displacement, (b) tendon circuit—equal force, and (c) tendons joined by a flexible web

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Fig. 2

A compliant mechanism with a simple multiport model, like the whiffletree on the left, can be combined with other compliant mechanisms to synthesize an elastic transmission web (center). This web (or interconnected webs) can map the actions of a small number of actuators to a larger number of fingers as shown in the anthropomorphic robot hand concept on the right.

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Fig. 3

Diagram of a general multiport network with n ports

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Fig. 4

Diagram of the internetwork parallel connection of multiport networks 1 and 2

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Fig. 5

Diagram of the internetwork series connection of multiport networks 1 and 2

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Fig. 6

Photographs of the grasping device in its parallel (a) and series (b) configurations

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Fig. 7

Force–displacement profiles and photographs showing differing behavior between the series- and parallel-configured three-fingered gripper. (a) Plot of digit forces versus actuator displacement while digits are in contact with an object in a grasping test (parallel configuration). (b) Pictures of an acrylic cutout of the U.S. state of Oklahoma in stages of a grasping test (parallel configuration). A line is drawn along the Oklahoma–Kansas border to better visualize the rotation. (c) Plot of digit forces versus actuator displacement while digits are in contact with an object in a grasping test (series configuration). (d) Pictures of an acrylic cutout of the U.S. state of Oklahoma in stages of a grasping test (series configuration). A line is drawn along the Oklahoma–Kansas border to better visualize the rotation.

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