# Geometric Design of Print-and-Fold Robots via Composition

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Goal: to enable automated design of print-and-fold robots, given the desired kinematics

Print-and-fold promises a rapid and inexpensive method for manufacturing robots. However, progress on this front is complicated by a lack of understanding of what types of motions can actually be produced by folding. In mechanism design not restricted to folding, the joints and links that are used to produce motion are readily available and can straightforwardly be connected together, making methods for automated mechanism design and analysis possible. Our approach is to enable such mechanism design tools to be used with folded structures by providing: 1) a library of foldable joints and rigid bodies, and 2) composition algorithms that allow the fold patterns of these library components to be connected together automatically.

## Foldable Joints

Pattern for a 6-sided hinge joint with 180 deg. range of motion

Our fold patterns for basic revolute and prismatic joints are parameterized to achieve user-specified sizes and ranges of motion. The joints can be composed with each other (see below) to achieve joints with higher degrees of freedom or with rigid bodies to produce foldable linkage mechanisms. They also provide natural placement of actuators. We have created a system that allows users to specify a type of joint and the desired joint limits and that automatically produces the corresponding fold pattern, and we have used this system to generate and fabricate multiple joints.

## Edge Composition of Unfoldings

Example composition of insect and gripper

To enable on-demand customization of printable machines, we are currently working on automatic composition of their fold patterns. So far, we have considered edge-compositions, compositions involving two surfaces connected at one edge. Our algorithm produces a one-piece, non-self-intersecting unfolding of the composite surface by attaching the unfoldings of the two original surfaces using a bridge of linking material. The algorithm is provably correct and has been tested on multiple surfaces. Future work includes other types of compositions, such as merging of faces. We are also investigating heuristics to minimize the total amount of wasteful linking material added to an unfolding.

## Composition of Foldable Robots and Mechanisms

We have implemented our composition algorithm in our system. In addition to generating joints, users can also input custom patterns for folded structures as a vector file. Users specify the edges or faces on separate folded structures that they wish to connect, and the system will generate a single-sheet fold pattern for the complete structure. The system provides views of both the at fold pattern and its folded state in 3-D so that users can visually verify that the composition is correct.

Foldable robot emulating the kinematics of a manufacturing crane

Using this system, we have designed several novel foldable mechanisms and robots. Print-and-fold manufacturing provides a natural method for incorporating actuation, sensing, and computation into a robot, specifically by printing circuitry and mounting components directly onto the fold pattern before folding. Using this method, we have produced fully functional robots that emulate the kinematics of the equivalent linkages built using standard machining techniques.

## Publications

Cynthia Sung, Daniela Rus. Foldable Joints for Foldable Robots. Journal of Mechanisms and Robotics. Vol. 7, No.2, May 2015. Article 021012.

Cynthia Sung, Daniela Rus. Foldable Joints for Foldable Robots. 2014 International Symposium on Experimental Robotics. Marrakech/Essaouira, Morocco. June 2014.

Cynthia Sung, Erik D. Demaine, Martin L. Demaine, Daniela Rus. Edge-Compositions of 3D Surfaces. Journal of Mechanical Design. Vol. 135, No.11, November 2013. Article 111001.

Cynthia Sung, Erik D. Demaine, Martin L. Demaine, Daniela Rus. Joining Unfoldings of 3-D Surfaces. ASME 2013 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference. Portland, OR, USA. August 2013.

## People

Cynthia Sung (crsung at mit dot edu)

Daniela Rus