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As an ancient paper craft originating from Japan, origami has been naturally embedded and contextualized in a variety of applications in the fields of mathematics, engineering, food packaging, and biological design. The computational and manufacturing capabilities today urge us to develop significantly new forms of folding as well as different materials for folding. In this paper, by allowing line cuts with crease patterns and creating folded hinges across basic structural units (BSU), typically not done in origami, we achieve a new multiprimitive folding framework such as using tetrahedral, cuboidal, prismatic, and pyramidal components, called “Kinetogami.” “Kinetogami” enables one to fold up closed-loop(s) polyhedral mechanisms (linkages) with multi-degree-of-freedom and self-deployable characteristics in a single build. This paper discusses a set of mathematical and design theories to enable design of 3D structures and mechanisms all folded from preplanned printed sheet materials. We present prototypical exploration of folding polyhedral mechanisms in a hierarchical manner as well as their transformations through reconfiguration that reorients the material and structure. The explicit 2D fabrication layout and construction rules are visually parameterized for geometric properties to ensure a continuous folding motion free of intersection. As a demonstration artifact, a multimaterial sheet is 3D printed with elastomeric flexure hinges connecting the rigid plastic facets.

Origami affords the creation of diverse 3D objects through explicit folding processes from 2D sheets of material. Originally as a paper craft from 17th century AD, origami designs reveal the rudimentary characteristics of sheet folding: it is lightweight, inexpensive, compact and combinatorial. In this paper, we present "HexaMorph", a novel starfish-like hexapod robot designed for modularity, foldability and reconfigurability. Our folding scheme encompasses periodic foldable tetrahedral units, called "Basic Structural Units" (BSU), for constructing a family of closed-loop spatial mechanisms and robotic forms. The proposed hexapod robot is fabricated using single sheets of cardboard. The electronic and battery components for actuation are allowed to be preassembled on the flattened crease-cut pattern and enclosed inside when the tetrahedral modules are folded. The self-deploying characteristic and the mobility of the robot are investigated, and we discuss the motion planning and control strategies for its squirming locomotion. Our design and folding paradigm provides a novel approach for building reconfigurable robots using a range of lightweight foldable sheets.

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In recent times, Origami has received an increasing research interest because of its capability to produce foldable tessellations and structures. This paper describes a new modular tetrahedral representation called “Kinetogami”. We embed the cuts and joining patterns into the crease pattern and create folded hinges across basic structural units (BSU), typically not done in Origami. We demonstrate sets of explicit 2D fabrication lay-outs and construction rules in order to fold reconfigurable structures and mechanisms in 3D by using a single flat paper sheet. The structural and combinatorial characteristics of Kinetogamic derivatives are further explored in a hierarchical manner. Inspired by Kinetogami, we design a family of multi-limbed tetrahedral robotic form that reconfigures and adapts. The kinematic properties of individual limbs are investigated and multiple gaits involving flipping, squatting/rising, squirming and slithering are synthesized for a representative hexapod robot. Our newly developed folding design paradigm provides affordances for a novel generation of robotic motion actuation and transformable reconfiguration.