The Milli-Motein: A self-folding chain of programmable matter with a one centimeter module pitch

The Milli-Motein (Millimeter-Scale Motorized Protein) is ca chain of programmable matter with a 1 cm pitch. It can fold itself into digitized approximations of arbitrary three-dimensional shapes. The small size of the Milli-Motein segments is enabled by the use of our new electropermanent wobble stepper motors, described in this paper, and by a highly integrated electronic and mechanical design. The chain is an interlocked series of connected motor rotors and stators, wrapped with a continuous flex circuit to provide communications, control, and power transmission capabilities. The Milli-Motein uses off-the-shelf electronic components and fasteners, and custom parts fabricated by conventional and electric discharge machining, assembled with screws, glue, and solder using tweezers under a microscope. We perform shape reconfiguration experiments using a four-segment Milli-Motein. It can switch from a straight line to a prescribed shape in 5 seconds, consuming 2.6 W power during reconfiguration. It can hold its shape indefinitely without power. During reconfiguration, a segment can lift the weight of one but not two segments as a horizontal cantilever.United States. Defense Advanced Research Projects Agency. Programmable Matter ProgramUnited States. Defense Advanced Research Projects Agency. Maximum Mobility and Manipulation (M3) ProgramUnited States. Army Research Office (Grant W911NF-08-1-0254)United States. Army Research Office (Grant W911NF-11-1-0096)Massachusetts Institute of Technology. Center for Bits and Atom

Locked and Unlocked Chains of Planar Shapes

We extend linkage unfolding results from the well-studied case of polygonal linkages to the more general case of linkages of polygons. More precisely, we consider chains of nonoverlapping rigid planar shapes (Jordan regions) that are hinged together sequentially at rotatable joints. Our goal is to characterize the families of planar shapes that admit locked chains, where some configurations cannot be reached by continuous reconfiguration without self-intersection, and which families of planar shapes guarantee universal foldability, where every chain is guaranteed to have a connected configuration space. Previously, only obtuse triangles were known to admit locked shapes, and only line segments were known to guarantee universal foldability. We show that a surprisingly general family of planar shapes, called slender adornments, guarantees universal foldability: roughly, the distance from each edge along the path along the boundary of the slender adornment to each hinge should be monotone. In contrast, we show that isosceles triangles with any desired apex angle less than 90 degrees admit locked chains, which is precisely the threshold beyond which the inward-normal property no longer holds.Comment: 23 pages, 25 figures, Latex; full journal version with all proof details. (Fixed crash-induced bugs in the abstract.

Hinged Dissections Exist

We prove that any finite collection of polygons of equal area has a common hinged dissection. That is, for any such collection of polygons there exists a chain of polygons hinged at vertices that can be folded in the plane continuously without self-intersection to form any polygon in the collection. This result settles the open problem about the existence of hinged dissections between pairs of polygons that goes back implicitly to 1864 and has been studied extensively in the past ten years. Our result generalizes and indeed builds upon the result from 1814 that polygons have common dissections (without hinges). We also extend our common dissection result to edge-hinged dissections of solid 3D polyhedra that have a common (unhinged) dissection, as determined by Dehn's 1900 solution to Hilbert's Third Problem. Our proofs are constructive, giving explicit algorithms in all cases. For a constant number of planar polygons, both the number of pieces and running time required by our construction are pseudopolynomial. This bound is the best possible, even for unhinged dissections. Hinged dissections have possible applications to reconfigurable robotics, programmable matter, and nanomanufacturing.Comment: 22 pages, 14 figure

Growing machines

Thesis (Ph. D.)--Massachusetts Institute of Technology, School of Architecture and Planning, Program in Media Arts and Sciences, 2004.Includes bibliographical references.construction is developed in three dimensions. It is similarly shown that right-angled tetrahedrons, when folded from an edge-connected string, can generate any three dimensional structure where the primitive pixel (or voxel) is a rhombic hexahedron. This construction also suggests a concept of 3D completeness for assembly, somewhat analogous to the concept of Turing completeness in computation. In combination, these pieces of work suggest that a manufacturing system based on four tiles, with seven states per tile, is capable of self-replication of arbitrary 3D structure by copying, then folding, bit strings of those tiles where the desired structure is encoded in the tile sequence.Biological systems are replete with examples of high complexity structures that have "self assembled," or more accurately, programmatically assembled from many smaller, simpler components. By comparison, the fabrication systems engineered by humans are typically top down, or subtractive, processes where systems of limited complexity are carved from bulk materials. Self-assembly to date has resembled crystallization more than it has the programmatic assembly of complex or useful structures--these systems are information limited. This thesis explores the programming of self-assembling systems by the introduction of small amounts of state to the sub-units of the assembly. A six-state, kinematic, conformational latching component is presented that is capable of self-replicating bit strings of two shape differentiated versions of the same component where the two variants represent the 0 and 1 bits. Individual units do not assemble until a string is introduced to the assembly environment to be copied. Electro-mechanical state machine emulators were constructed. Operating on an air table, the units demonstrated logic limited aggregation, or error-preventing assembly, as well as autonomous self-replication of bit strings. A new construction was developed that demonstrates that any two dimensional shape composed of square pixels can be deterministically folded from a linear string of vertex-connected square tiles. This non-intersecting series of folds implies a 'resolution' limit of four tiles per pixel. It is shown that four types of tiles, patterned magnetically, is sufficient to construct any shape given sequential folding. The construction was implemented to fold the letters 'M I T' from sequences of the 4 tile types. An analogousSaul Thomas Griffith.Ph.D

Enabling New Functionally Embedded Mechanical Systems Via Cutting, Folding, and 3D Printing

Traditional design tools and fabrication methods implicitly prevent mechanical engineers from encapsulating full functionalities such as mobility, transformation, sensing and actuation in the early design concept prototyping stage. Therefore, designers are forced to design, fabricate and assemble individual parts similar to conventional manufacturing, and iteratively create additional functionalities. This results in relatively high design iteration times and complex assembly strategies

Towards Developing Efficient Area Coverage Approach in Domestic Robots

東京電機大学201