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Research Papers

Unified Stiffness Characterization of Nonlinear Compliant Shell Mechanisms

[+] Author and Article Information
Joost R. Leemans

Department of Precision and
Microsystems Engineering,
Delft University of Technology,
Delft 2628 CD, The Netherlands
e-mail: J.R.Leemans@student.tudelft.nl

Charles J. Kim

Department of Mechanical Engineering,
Bucknell University,
Lewisburg, PA 17837
e-mail: charles.kim@bucknell.edu

Werner W .P. J. van de Sande

Department of Precision and
Microsystems Engineering,
Delft University of Technology,
Delft 2628 CD, The Netherlands
e-mail: w.w.p.j.vandeSande@tudelft.nl

Just L. Herder

Department of Precision and
Microsystems Engineering,
Delft University of Technology,
Delft 2628 CD, The Netherlands
e-mail: J.L.Herder@tudelft.nl

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANISMS AND ROBOTICS. Manuscript received February 5, 2018; final manuscript received October 8, 2018; published online December 10, 2018. Assoc. Editor: Hai-Jun Su.

J. Mechanisms Robotics 11(1), 011011 (Dec 10, 2018) (11 pages) Paper No: JMR-18-1035; doi: 10.1115/1.4041785 History: Received February 05, 2018; Revised October 08, 2018

Compliant shell mechanisms utilize spatially curved thin-walled structures to transfer or transmit force, motion, or energy through elastic deformation. To design spatial mechanisms, designers need comprehensive nonlinear characterization methods, while the existing methods fall short of meaningful comparisons between rotational and translational degrees-of-freedom. This paper presents two approaches, both of which are based on the principle of virtual loads and potential energy, utilizing properties of screw theory, Plücker coordinates, and an eigen-decomposition. This leads to two unification lengths that can be used to compare and visualize all six degrees-of-freedom directions and magnitudes in a nonarbitrary, physically meaningful manner for mechanisms exhibiting geometrically nonlinear behavior.

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References

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Figures

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Fig. 1

Visual representation of the Plücker axis coordinates in vector form

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Fig. 2

Visual representation eigen-decomposition: (a) twist axes, (b) wrench axes, (c) twist compliance vectors, and (d) wrench compliance vectors

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Fig. 3

Equivalent translation geometry

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Fig. 4

Equivalent virtual force geometry

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Fig. 5

Principal compliance directions of the cross pivot flexure mechanism

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Fig. 6

Unified compliance vectors of the cross pivot flexure mechanism

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Fig. 7

Principal compliance directions of the double parallel flexure mechanism

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Fig. 8

Unified compliance vectors of the double parallel flexure mechanism

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Fig. 9

Unified compliance vectors along a rotation of the point of interest around the y-axis range of motion

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Fig. 10

Unified compliance vectors single corrugated shell

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Fig. 11

Unified compliance vectors single corrugated shell along displacement

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Fig. 12

Magnitude plot unified compliance over range of motion of the single corrugated shell

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Fig. 13

Unified compliance vectors of the spiral shell mechanism

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Fig. 14

Unified compliance vectors of the spiral shell mechanism during motion

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Fig. 15

Magnitude graph unified compliance over range of motion of the spiral shell mechanism

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Fig. 16

Measurement setup

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Fig. 17

Location vector offset bracket

Tables

Errata

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