Research Papers

A Design Tool for a Single Vertex Compliant-Facet Origami Mechanism Including Torsional Hinge Lines

[+] Author and Article Information
Jelle Rommers

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

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 February 1, 2017; final manuscript received September 9, 2017; published online October 19, 2017. Assoc. Editor: Jian S. Dai.

J. Mechanisms Robotics 9(6), 061015 (Oct 19, 2017) (6 pages) Paper No: JMR-17-1025; doi: 10.1115/1.4038008 History: Received February 01, 2017; Revised September 09, 2017

Principles from origami art are applied in the design of mechanisms and robotics increasingly frequent. A large part of the application driven research of these origami-like mechanisms focuses on devices where the creases (hinge lines) are actuated and the facets are constructed as stiff elements. In this paper, a design tool is proposed in which hinge lines with torsional stiffness and flexible facets are used to design passive, instead of active mechanisms. The design tool is an extension of a model of a single vertex compliant facet origami mechanism (SV-COFOM) and is used to approximate a desired moment curve by optimizing the design variables of the mechanism. Three example designs are presented: a constant moment joint (CMJ), a gravity compensating joint (GCJ) and a zero moment joint (ZMJ). The CMJ design has been evaluated experimentally, resulting in a root-mean-squared error (RMSE) of 6.4 × 10−2 N·m on a constant moment value of 0.39 N·m. This indicates that the design tool is suitable for a course estimation of the moment curve of the SV-COFOM in early stages of a design process.

Copyright © 2017 by ASME
Topics: Hinges , Design , Stiffness
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Fig. 1

The SV-COFOM acting as a joint with nonlinear torsional stiffness. The bottom of the mechanism is clamped, forcing the bottom facets to bend during joint movement. The goal is to approach a desired moment curve by altering the design. Figure from Ref. [3].

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Fig. 2

The PRB model of the SV-COFOM. Modified figure from Ref. [3]. Bending of the bottom facets is modeled by introducing virtual hinge lines (dashed) with an equivalent torsional stiffness, dividing the compliant facets into two rigid ones. Point Cm is constrained in the y-direction, creating a one-degree-of-freedom mechanism. By writing the angular rotations of the torsional hinge lines τA, τB, and τC as a function of θjoint, the moment curve of the mechanism can be constructed.

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Fig. 3

Including the torsional stiffness of the hinge lines in the spherical representation of the PRB model of Ref. [3]. Goal is to calculate the angular rotation of the hinge lines τA, τB and τC as a function of the joint angle θjoint of the SV-COFOM. Modified figure from Ref. [3].

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Fig. 4

Fabrication of the constant moment joint design. Hinge lines are created by applying Mylar© tape between two spring steel plates in an alternating pattern. Torsional stiffness is added by clamping spring steel wire (torsion bars) at both sides of the hinge lines.

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Fig. 5

Experimental setup used to measure the stiffness of the torsion bars providing torsional stiffness κA and κC

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Fig. 6

Experimental setup used to record the moment curve of the constant moment joint design

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Fig. 7

Design 1: constant moment joint and separate contributions of the hinge lines. The range is 77 deg with a maximum 3% error from its mean constant value of 0.45 N·m.

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Fig. 8

Design 2: gravity compensating joint. Range of 80 deg with a maximum deviation of 3% of the maximum moment of the mass (0.4 kg). The mechanism is tilted forward 27 deg (in the positive Y-direction in Fig. 1).

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Fig. 9

Design 3: zero moment joint. Range of 66 deg within 3% error of the minimum value of the κvirtual curve.

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Fig. 10

The constant moment joint design with the desired and measured torsion constants as input. The measured values are τA=0.1250 N·m/rad (desired was 0.1430 N·m/rad) and τC=0.3204 N·m/rad (desired was 0.2513 N·m/rad). The average constant value in the original constant region changed from 0.45 N·m to 0.39 N·m.

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Fig. 11

Empirical validation of the constant moment joint design. (1) is the mechanism with κA=κC=0. (2) is the complete mechanism with added torsional stiffness κA=0.1250 N⋅m/rad and κC=0.3204 N⋅m/rad. The RMSE between model and empirical data for the original constant range of the CMJ is 6.4 × 102 N·m.




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