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Research Papers: Design Automation

Origami Actuator Design and Networking Through Crease Topology Optimization

[+] Author and Article Information
Kazuko Fuchi

Mem. ASME
Wright State Research Institute,
4035 Colonel Glenn Highway,
Suite 200,
Beavercreek, OH 45431
e-mail: kazuko.fuchi@wright.edu

Philip R. Buskohl

Air Force Research Laboratory,
2941 Hobson Way,
Wright-Patterson AFB, OH 45433
e-mail: philip.buskohl.1@us.af.mil

Giorgio Bazzan

UES, Inc.,
4401 Dayton Xenia Road,
Beavercreek, OH 45432
e-mail: giorgio.bazzan.1.ctr@us.af.mil

Michael F. Durstock

Air Force Research Laboratory,
2941 Hobson Way,
Wright-Patterson AFB, OH 45433
e-mail: michael.durstock@us.af.mil

Gregory W. Reich

Mem. ASME
Air Force Research Laboratory,
2210 Eighth Street,
Wright-Patterson AFB, OH 45433
e-mail: gregory.reich.1@us.af.mil

Richard A. Vaia

Air Force Research Laboratory,
2179 12th Street,
Wright-Patterson AFB, OH 45433
e-mail: richard.vaia@us.af.mil

James J. Joo

Mem. ASME
Air Force Research Laboratory,
2210 Eighth Street,
Wright-Patterson AFB, OH 45433
e-mail: james.joo.1@us.af.mil

1Corresponding author.

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received November 30, 2014; final manuscript received June 8, 2015; published online July 10, 2015. Assoc. Editor: James K. Guest.

J. Mech. Des 137(9), 091401 (Jul 10, 2015) (10 pages) Paper No: MD-14-1761; doi: 10.1115/1.4030876 History: Received November 30, 2014

Origami structures morph between 2D and 3D conformations along predetermined fold lines that efficiently program the form of the structure and show potential for many engineering applications. However, the enormity of the design space and the complex relationship between origami-based geometries and engineering metrics place a severe limitation on design strategies based on intuition. The presented work proposes a systematic design method using topology optimization to distribute foldline properties within a reference crease pattern, adding or removing folds through optimization, for a mechanism design. Optimization techniques and mechanical analysis are co-utilized to identify an action origami building block and determine the optimal network connectivity between multiple actuators. Foldable structures are modeled as pin-joint truss structures with additional constraints on fold, or dihedral, angles. A continuous tuning of foldline stiffness leads to a rigid-to-compliant transformation of the local foldline property, the combination of which results in origami crease design optimization. The performance of a designed origami mechanism is evaluated in 3D by applying prescribed forces and finding displacements at set locations. A constraint on the number of foldlines is used to tune design complexity, highlighting the value-add of an optimization approach. Together, these results underscore that the optimization of function, in addition to shape, is a promising approach to origami design and motivates the further development of function-based origami design tools.

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Figures

Grahic Jump Location
Fig. 1

Fold angle definition and stiffness assignment during optimization. Local node numbering and the dihedral angle θ.

Grahic Jump Location
Fig. 2

Fold stiffness interpolation scheme in a log scale. Darker gray color refers to smaller α and Gj. Inset: two-fold structure with equal applied forces, but different fold stiffness values resulting in different dihedral angles.

Grahic Jump Location
Fig. 3

Flow chart of the optimization process. The stiffness matrix (K) and fold line constraint are evaluated at the onset of each design iteration. The displacement field (u) feeds into the design objective, which informs the gradient-based optimizer's choice of fold stiffnesses for the next iteration. MMA—Method of moving asymptotes.

Grahic Jump Location
Fig. 4

Optimal design for the Chomper design problem. (a) Reference crease pattern with BCs: fixed nodes (triangles), input forces (squares), and out-of-plane displacement objective (circles). (b) Optimized crease pattern and (c) deformed configuration (l0 = 0.5 and f = −0.74).

Grahic Jump Location
Fig. 5

Iteration history for minimizing f for the Chomper design problem. Insets: deformed configuration and fold line patterns for (a) initial search (iteration 2), (b) entering well (iteration 7), (c) approaching convergence (iteration 11), and (d) converged solution (iteration 25).

Grahic Jump Location
Fig. 6

Action origami with the same working principle as the optimal design (Shafer's Chomper design [14]). (a) Unloaded paper Chomper with artistic flange. (b) Loaded paper Chomper with highlighted mechanism. (c) Graph of coupled spherical 4-bar mechanism shown from view in (b) and from top view. Solid—valley, large dash—mountain, and short dash—hidden valley.

Grahic Jump Location
Fig. 7

Coupled spherical 4-bar mechanism is conserved as the design solution across reference grids. (a) Refined triangular grid (l0 = 0.5 and f = −0.38), (b) rectangular grid with diagonal discretization (l0 = 0.5 and f = −0.47), (c) conventional ground structure for topology optimization (l0 = 0.2 and f = −0.22), and (d) rectangular grid without closed Chomper solution available (l0 = 0.5 and f = −0.25).

Grahic Jump Location
Fig. 8

Pareto front depicting the trade-off between actuator deflection and allowable foldline fraction l0, which serves as a measure of fold pattern complexity. Insets: deformed configurations with increasingly more complex solutions. Gray region—threshold of minimum number of fold lines needed for coupled spherical mechanism.

Grahic Jump Location
Fig. 9

Chomper design is sensitive to changes in BCs. Reference grids with original BCs (a) and modified BCs (e). Optimal solutions for each configuration are shown as the fold pattern ((b) and (f)) and deformed configuration ((c) l0 = 0.2 and f = −0.23 and (g) l0 = 0.2 and f = −0.34). The solution with five fixed nodes uses two spherical 4-bar mechanisms (d); the solution with three fixed nodes uses four spherical 4-bar mechanisms coupled through a 6-bar mechanism (h). Reducing the number of fixed nodes increased the design performance by 48% (f = −0.23 versus f = −0.34). Simulation details: l0 = 0.2 and |F|  = 500.

Grahic Jump Location
Fig. 10

Comparison of actuating mechanisms via prototypes made from PP sheeting (Grafix Plastics, Cleveland, OH). Fold patterns were laser machined into matte and smooth finish PP sheets of thickness ranging from 400 to 1100 μm. Scoring was performed on an laser engraver epilog helix 24 using a laser intensity of 30 W and speed of 35 mm/s. (a) and (b) Coupled spherical 4-bar Chomper and (c) and (d) four spherical 4-bar coupled through a 6-bar mechanism.

Grahic Jump Location
Fig. 11

Comparison of solutions obtained using linear and nonlinear analyses. The problem specification (a) and the optimal solution using linear analysis (b). Designs involving twist motion are obtained using multiple load steps (c). The objective function surface plot (d) indicates a significant change in the slope over the fold evolution when twist is involved.

Grahic Jump Location
Fig. 12

Optimized fold line connectivity for networked actuation. The optimized fold pattern, 3D rendering of deformed configuration, and PP prototype for (a) max center displacement, (b) max centerline displacement, and (c) max rotated actuation. Simulation details: square reference grid, l0 = 0.4, and |F| = 500.

Grahic Jump Location
Fig. 13

Additional details of max center displacement case study. Solution in Fig. 12(a) is flat foldable if fold directions are reoriented, with fold area only 25% of unfolded. (b) and (c) Additional views of flat-foldable pattern in intermediate folding configurations.

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