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The geometric, aesthetic, and mathematical elegance of origami is beingrecognized as a powerful pathway to self-assembly of micro and nano-scalemachines with programmable mechanical properties. The typical approach todesigning the mechanical response of an ideal origami machine is to includemechanisms where mechanical constraints transform applied forces into a desiredmotion along a narrow set of degrees of freedom. In fact, to date, most designapproaches focus on building up complex mechanisms from simple ones in waysthat preserve each individual mechanism's degree of freedom (DOF), withexamples ranging from simple robotic arms to homogenous arrays of identicalvertices, such as the well-known Miura-ori. However, such approaches typicallyrequire tight fabrication tolerances, and often suffer from parasiticcompliance. In this work, we demonstrate a technique in whichhigh-degree-of-freedom mechanisms associated with single vertices areheterogeneously combined so that the coupled phase spaces of neighboringvertices are pared down to a controlled range of motions. This approach has theadvantage that it produces mechanisms that retain the DOF at each vertex, arerobust against fabrication tolerances and parasitic compliance, butnevertheless effectively constrain the range of motion of the entire machine.We demonstrate the utility of this approach by mapping out the configurationspace for the modified Miura-ori vertex of degree 6, and show that when strungtogether, their combined configuration spaces create mechanisms that isolatedeformations, constrain the configuration topology of neighboring vertices, orlead to sequential bistable folding throughout the entire origami sheet.

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