# Sculpting the Vertex: Manipulating the Configuration Space Topography and Topology of Origami Vertices to Design Mechanical Robustness

## TL;DR

This paper introduces a novel method for designing origami-based mechanisms by heterogeneously combining high-degree-of-freedom vertices to control the configuration space, enhancing robustness and functional constraints in micro and nano-scale machines.

## Contribution

It presents a technique to manipulate the configuration space of origami vertices, enabling robust, constrained mechanisms without tight fabrication tolerances.

## Key findings

- Mapped the configuration space of a modified degree-6 Miura-ori vertex.
- Demonstrated mechanisms that isolate deformations and constrain neighboring vertices.
- Achieved sequential bistable folding in origami sheets.

## Abstract

The geometric, aesthetic, and mathematical elegance of origami is being recognized as a powerful pathway to self-assembly of micro and nano-scale machines with programmable mechanical properties. The typical approach to designing the mechanical response of an ideal origami machine is to include mechanisms where mechanical constraints transform applied forces into a desired motion along a narrow set of degrees of freedom. In fact, to date, most design approaches focus on building up complex mechanisms from simple ones in ways that preserve each individual mechanism's degree of freedom (DOF), with examples ranging from simple robotic arms to homogenous arrays of identical vertices, such as the well-known Miura-ori. However, such approaches typically require tight fabrication tolerances, and often suffer from parasitic compliance. In this work, we demonstrate a technique in which high-degree-of-freedom mechanisms associated with single vertices are heterogeneously combined so that the coupled phase spaces of neighboring vertices are pared down to a controlled range of motions. This approach has the advantage that it produces mechanisms that retain the DOF at each vertex, are robust against fabrication tolerances and parasitic compliance, but nevertheless effectively constrain the range of motion of the entire machine. We demonstrate the utility of this approach by mapping out the configuration space for the modified Miura-ori vertex of degree 6, and show that when strung together, their combined configuration spaces create mechanisms that isolate deformations, constrain the configuration topology of neighboring vertices, or lead to sequential bistable folding throughout the entire origami sheet.