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Research Papers

Pseudo-Rigid-Body Modeling of a Single Vertex Compliant-Facet Origami Mechanism

[+] Author and Article Information
Jelle Rommers

Department of Precision and
Microsystems Engineering,
Delft University of Technology,
Delft 2628 CD, The Netherlands
e-mail: jellerommers@gmail.com

Giuseppe Radaelli

Department of Precision and
Microsystems Engineering,
Delft University of Technology,
Delft 2628 CD, The Netherlands
e-mail: g.radaelli@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

Manuscript received October 16, 2016; final manuscript received January 16, 2017; published online March 22, 2017. Assoc. Editor: Larry L Howell.

J. Mechanisms Robotics 9(3), 031009 (Mar 22, 2017) (7 pages) Paper No: JMR-16-1312; doi: 10.1115/1.4035881 History: Received October 16, 2016; Revised January 16, 2017

Recently, there has been an increased interest in origami art from a mechanism design perspective. The deployable nature and the planar fabrication method inherent to origami provide potential for space and cost-efficient mechanisms. In this paper, a novel type of origami mechanisms is proposed in which the compliance of the facets is used to incorporate the spring behavior: compliant facet origami mechanisms (COFOMs). A simple model that computes the moment characteristic of a single vertex COFOM has been proposed, using a semispatial version of the pseudo-rigid-body (PRB) theory to model bending of the facets. The PRB model has been evaluated numerically and experimentally, showing good performance. The PRB model is a potential starting point for a design tool which would provide an intuitive way of designing this type of mechanisms including their spring behavior, with very low computational cost.

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References

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Figures

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Fig. 1

Single vertex compliant facet origami mechanism (SV-COFOM). The mechanism exists out of a plate material with hinge lines, which act as a surrogate for creases in paper. The hinges lines are assumed to have zero torsional stiffness.

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Fig. 2

The SV-COFOM clamped at the bottom at an angle θfoot. The bottom facets are forced to bend during movement, acting as springs and causing a bi-stable behavior. The mechanism can be viewed as a joint with angle θjoint with a nonlinear torsional stiffness.

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Fig. 3

PRB model of the clamped SV-COFOM. Bending of the bottom facets is modeled by introducing virtual hinge lines (dashed lines) with a torsion spring, dividing both compliant facets into two rigid ones. Point Cm is constrained to lie in the XZ-plane, creating a 1dof mechanism. By writing the angular rotation of the torsional springs τB as a function of θjoint, the moment curve of the mechanism can be constructed.

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Fig. 4

Spherical representation of the PRB model. Only the right half of the facets is drawn, as indicated in the inserted figure in the top right. Goal is to calculate the angular rotation of the virtual hinge line τB as a function of θjoint.

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Fig. 5

Fabrication of the SV-COFOM. Hinge lines are created by applying Mylar© tape between two spring steel plates in an alternating pattern.

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Fig. 6

Experimental setup. The moment curve of the clamped SV-COFOM is recorded using a load cell and a potentiometer.

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Fig. 7

Reaction moment curve of the standard design of the SV-COFOM. The PRB model is fitted on the FEM data, resulting in model parameter values ξ1=0.994 m−1 and ξ2=16.9 deg, RMSE = 1.0 × 10−2 N·m.

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Fig. 8

Prediction performance of the PRB model with the earlier obtained model parameters. The PRB model has not been refitted: (a) varying θA from the standard value of 50 deg, (b) varying θfoot from the standard value of 60 deg, (c) varying width w from the standard value of 150 mm, and (d) varying the thickness t from the standard value of 0.3 mm.

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Fig. 9

Effect of changing the height of the SV-COFOM. RMSE values between the PRB model and FEM data are 2.3 × 10−2 N·m and 1.7 × 10−2 N·m, for h = 200 and h = 400, respectively. Note that the PRB model is independent of the height parameter.

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Fig. 10

Effect of the cutout radius (FEM data). In this paper, the cutout radius is chosen to be fixed at 15 mm.

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Fig. 11

Empirical validation of the FE model for the standard design of the SV-COFOM. The RMSE is 4.5 × 10−2 N·m.

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