Autonomous Deployment of a Solar Panel Using Elastic Origami and Distributed Shape-Memory-Polymer Actuators

We introduce a metamaterial-based self-deployable system with a rotational periodicity. As a demonstration, we propose an autonomous solar panel array that is programmed to self-deploy in response to changes in the surrounding temperature. We achieve shape reconfiguration and structural stability by exploiting the physical properties in the constituting material and the architecture of the wedge-shaped unit cell. The unit cell consists of one arm of the elastic “flasher” origami and a pair of scissor mechanisms. First, kinematic analysis shows the difference between the theoretical behavior and behavior considering the physical dimensions. This is used to optimize the expansion ratio. Second, the deployment mechanics are enabled through the shape-memory effect inherent in the underlying polymer. A viscoelastic constitutive model is constructed to accurately predict the self-expanding behavior. Lastly, the collapsing and deployment dynamics are discussed. Bifurcation is observed during folding, leading to two different end states, a disk or a cone. By investigating the energy landscape of the system, an apparatus is introduced to enable the disk-shaped folding. A two-stage expansion is observed during deployment. The system first rotates and then expands radially. The resulting system is three-dimensionally (3D) printed, achieves an expansion ratio of 1000% in under 40 s, and shows excellent agreement with simulation prediction both in the collapsed and expanded configurations.

Figure 1

The schematic of collapsing and deployment from (a) to (b) of the proposed functional metamaterial. An outer ring acts as the primary actuator and structural support. An inner substrate forms the secondary actuator and provides the surface to carry the solar panels. Both components are fabricated using a SMP as the means of actuation.

Figure 2

A ring of self-deploying scissor mechanisms. A ring is extracted from the Hoberman-sphere toy and shown in both collapsed and expanded configurations. The definitions of a unit cell and of the articulated pin joints and rotational hubs are shown.

Figure 3

Parametric optimization of the scissor mechanisms accounting for physical dimensions. (a) Theoretical collapsed and expanded configurations of selected mechanisms. (b) Given a fixed maximum outer radius of 195 mm as dictated by the fabrication method, the expansion ratio as a function of $n$ is plotted for different member thicknesses, $w$. For member thickness $w=4$, the optimal expansion ratio occurs at $n=20$. The derivation is detailed in Appendix pp1.

Figure 4

An elastic “flasher” origami in both collapsed and expanded configurations, with the crease pattern indicated. A unit cell of the origami is defined by the angle of rotation $2\pi /n$.

Figure 5

Maximization of the number of flexible solar panels by changing the “flasher” origami crease pattern. Two variables—$n$, the number of unit cells, and $c$, the number of circumferential layers in the pattern—are optimized to fit the largest number of solar panels of a given dimension. The contour plot shows the number of solar panels that can fit for every pair of $(n,c)$.

Figure 6

A fabricated specimen of the scissor mechanisms and of the origami substrate in both collapsed and expanded configurations showing a 10 times change in area. The inset shows one unit cell of the functional metamaterial, consisting of a scissor mechanism and an arm of the origami.

Figure 7

The mechanics of a scissor mechanism and the relationship between the shape-memory hubs and the radial pressure. (a) A force-displacement plot of a single shape-memory hub from experiments and simulations. (b) The overall pressure produced by all the shape-memory joints of a $n=20$ ring as a function of the angle $\alpha$ in the scissor mechanism.

Figure 8

A schematic of the behavior of mountain and valley folds. The crease-line width $t_c$ is dimensioned such that valley folds can be accommodated without inducing unnecessary strain on the base layer.

Figure 9

Bifurcation during folding of the “flasher” origami as explained by the elastic energy within the fold lines. Two distinct folded shapes are observed during folding, both in experiment and in simulation. (a) A plot of the total height of the origami as a function of the fold angle (between $0$ and $\pi$). (b) A plot of the total elastic energy as a function of the fold angle. The resulting folded shapes (i.e., $\alpha =\pi$) is either a cone or a disk. (${\mathrm{c}}_{1\text{−}5}$) and (${\mathrm{d}}_{1\text{−}5}$) show different stages of the folding simulations that result in the two eventual shapes. Strain energy is shown as a color gradient.

Figure 10

The deployable solar-panel array. (a),(b) Physical specimens showing the collapsed and the expanded configurations.

Figure 11

The construction of the scissor mechanisms. The variables used in the derivation are shown.

Figure 12

If the arm lengths of the scissors are uniform, the physical outer radii will differ depending on whether the end of the scissor mechanism is a SMP hub or a pin joint. The variable $\xi$ is introduced to ensure that these two radii are identical.

Figure 13

A detailed analysis of the collapse motion of one scissor mechanism, with and without the outlining physical geometry.

Figure 14

The fully collapsed configuration, showing the variables needed to derived the collapsed outer radius.

Figure 15

The construction of a crease pattern of a “flasher” origami. The variables used in the derivation are shown.

Figure 16

One unit cell of the origami pattern, with variables used in the derivation of the optimization objective indicated. The details of the mountain and valley folds are shown in both the flat and the folded configurations.

Figure 17

The “programming” of the solar-panel array. (a),(c) The procedure starts with the deployed configuration. (b),(d) A center rotational core is installed and connected with the origami via flexible wires. (e) In a heated environment, the system is rotated and folded until it fits within a cylindrical mold. (f) After cooling within the mold, it is released and stable on its own.