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Mathematics and computation

Mathematics and computation

Kirigami cubes make a novel mechanical computer

09 Aug 2024 Isabelle Dumé
Image showing the mechanical, kirigami-inspired cube computer in three states: a neutral flat state, a state with some of the cubes pushed up, and a state with cubes pushed to higher levels, like a pyramid
Pop up bits: A kirigami-inspired mechanical computer uses a complex structure of rigid, interconnected polymer cubes to store, retrieve and erase data without relying on electronic components. (Courtesy: Yanbin Li, NC State University)

A new mechanical computer made from an array of rigid, interconnected plastic cubes can store, retrieve and erase data simply by stretching the array and manipulating the position of the cubes. The device’s construction is inspired by the ancient Japanese art of paper cutting, or kirigami, and its designers at North Carolina State University in the US say that more advanced versions could be used in stable, high-density memory and logic computing; in information encryption and decryption; and to create displays based on three-dimensional units called voxels.

Mechanical computers were first developed in the 19th century and do not contain any electronic components. Instead, they perform calculations with levers and gears. We don’t often hear about such contraptions these days, but researchers led by NC State mechanical and aerospace engineer Jie Yin are attempting to bring them back due to their stability and their capacity for storing complex information.

A periodic array of computing cubes

The NC State team’s computer comprises a periodic array, or metastructure, of 64 interconnected polymer cubes, each measuring 1 cm on a side and grouped into blocks. These cubes are connected by thin hinges of elastic tape that can be used to move the cubes either physically or by means of a magnetic plate attached to the cubes’ top surfaces. When the array is stretched in one direction, it enters a multi-stable state in which cubes can be pushed up or down, representing a binary 1 and 0 respectively. Thus, while the unit cells are interconnected, each cell acts as an independent switch with two possible states – in other words, as a “bit” familiar from electronic computing.

If the array is then compressed, the cubes lock in place, fixing them in the 0 or 1 state and allowing information to be stored in a stable way. To change these stored bits, the three-dimensional structure can be re-stretched, returning it to the multi-stable state in which each unit cell becomes editable.

Ancient inspiration

The new device was inspired by Yin and colleagues’ previous work, which saw them apply kirigami principles to shape-morphing matter. “We cut a thick plate of plastic into connected cubes,” Yin explains. “The cubes can be connected in multiple ways in a closed loop so that they can transform from 2D plates to versatile 3D voxelated structures.”

These transformations, he continues, were based on rigid rotations – that is, ones in which neither the cubes nor the hinges deform. “We were originally thinking of storing elastic energy in the hinges so that they could lead to different shape changes,” he says. “With this came the bistable unit cell idea.”

Yin says that one of the main challenges involved in turning the earlier shape-morphing system into a mechanical computer was to work out how to construct and connect the unit cells. “In our previous work, we made use of an ad-hoc design, but we could not directly extend this to this new work,” he tells Physics World. “We finally came up with the solution of using four cubes as a base unit and [assembling] them in a hierarchical way.”

While the platform has several possible applications, Yin says one of the most interesting would be in three-dimensional displays. “Each pop-up cube acts as a voxel with a certain volume and can independently be pushed up and remain stable,” he says. “These properties are useful for interactive displays or haptic devices for virtual reality.”

Computing beyond binary code

The current version of the device is still far from being a working mechanical computer, with many improvements needed to perform even simple mathematical operations. However, team member Yanbin Li, a postdoctoral researcher at NC State and first author of a Science Advances paper on the work, points out that the density of information it can store is relatively high. “Using a binary framework – where cubes are either up or down – a simple metastructure of nine functional units has more than 362 000 possible configurations,” he explains.

A further advantage is that a functional unit of 64 cubes can take on a wide variety of architectures, with up to five cubes stacked on top of each other. These novel configurations would allow for the development of computing that goes well beyond binary code, Li says.

In the nearer term, Li suggests that the cube array could allow users to create three-dimensional versions of mechanical encryption or decryption. “For example, a specific configuration of functional units could serve as a 3D password,” he says.

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