342 research outputs found
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.
Locked and unlocked smooth embeddings of surfaces
We study the continuous motion of smooth isometric embeddings of a planar
surface in three-dimensional Euclidean space, and two related discrete
analogues of these embeddings, polygonal embeddings and flat foldings without
interior vertices, under continuous changes of the embedding or folding. We
show that every star-shaped or spiral-shaped domain is unlocked: a continuous
motion unfolds it to a flat embedding. However, disks with two holes can have
locked embeddings that are topologically equivalent to a flat embedding but
cannot reach a flat embedding by continuous motion.Comment: 8 pages, 8 figures. To appear in 34th Canadian Conference on
Computational Geometr
Force-Guiding Particle Chains for Shape-Shifting Displays
We present design and implementation of a chain of particles that can be
programmed to fold the chain into a given curve. The particles guide an
external force to fold, therefore the particles are simple and amenable for
miniaturization. A chain can consist of a large number of such particles. Using
multiple of these chains, a shape-shifting display can be constructed that
folds its initially flat surface to approximate a given 3D shape that can be
touched and modified by users, for example, enabling architects to
interactively view, touch, and modify a 3D model of a building.Comment: 6 pages, 5 figure, submitted to IROS 201
The GR2 gripper: an underactuated hand for open-loop in-hand planar manipulation
Performing dexterous manipulation of unknown objects with robot grippers without using high-fidelity contact sensors, active/sliding surfaces, or a priori workspace exploration is still an open problem in robot manipulation and a necessity for many robotics applications. In this paper, we present a two-fingered gripper topology that enables an enhanced predefined in-hand manipulation primitive controlled without knowing the size, shape, or other particularities of the grasped object. The in-hand manipulation behavior, namely, the planar manipulation of the grasped body, is predefined thanks to a simple hybrid low-level control scheme and has an increased range of motion due to the introduction of an elastic pivot joint between the two fingers. Experimental results with a prototype clearly show the advantages and benefits of the proposed concept. Given the generality of the topology and in-hand manipulation principle, researchers and designers working on multiple areas of robotics can benefit from the findings
Fun with Fonts: Algorithmic Typography
Over the past decade, we have designed six typefaces based on mathematical
theorems and open problems, specifically computational geometry. These
typefaces expose the general public in a unique way to intriguing results and
hard problems in hinged dissections, geometric tours, origami design,
computer-aided glass design, physical simulation, and protein folding. In
particular, most of these typefaces include puzzle fonts, where reading the
intended message requires solving a series of puzzles which illustrate the
challenge of the underlying algorithmic problem.Comment: 14 pages, 12 figures. Revised paper with new glass cane font.
Original version in Proceedings of the 7th International Conference on Fun
with Algorithm
An Algorithmic Study of Manufacturing Paperclips and Other Folded Structures
We study algorithmic aspects of bending wires and sheet metal into a
specified structure. Problems of this type are closely related to the question
of deciding whether a simple non-self-intersecting wire structure (a
carpenter's ruler) can be straightened, a problem that was open for several
years and has only recently been solved in the affirmative.
If we impose some of the constraints that are imposed by the manufacturing
process, we obtain quite different results. In particular, we study the variant
of the carpenter's ruler problem in which there is a restriction that only one
joint can be modified at a time. For a linkage that does not self-intersect or
self-touch, the recent results of Connelly et al. and Streinu imply that it can
always be straightened, modifying one joint at a time. However, we show that
for a linkage with even a single vertex degeneracy, it becomes NP-hard to
decide if it can be straightened while altering only one joint at a time. If we
add the restriction that each joint can be altered at most once, we show that
the problem is NP-complete even without vertex degeneracies.
In the special case, arising in wire forming manufacturing, that each joint
can be altered at most once, and must be done sequentially from one or both
ends of the linkage, we give an efficient algorithm to determine if a linkage
can be straightened.Comment: 28 pages, 14 figures, Latex, to appear in Computational Geometry -
Theory and Application
Complexity of Interlocking Polyominoes
Polyominoes are a subset of polygons which can be constructed from
integer-length squares fused at their edges. A system of polygons P is
interlocked if no subset of the polygons in P can be removed arbitrarily far
away from the rest. It is already known that polyominoes with four or fewer
squares cannot interlock. It is also known that determining the interlockedness
of polyominoes with an arbitrary number of squares is PSPACE hard. Here, we
prove that a system of polyominoes with five or fewer squares cannot interlock,
and that determining interlockedness of a system of polyominoes including
hexominoes (polyominoes with six squares) or larger polyominoes is PSPACE hard.Comment: 18 pages, 15 figure
Tuning vortex fluctuations and the resistive transition in superconducting films with a thin overlayer
It is shown that the temperature of the resistive transition of a
superconducting film can be increased by a thin superconducting or normal
overlayer. For instance, deposition of a highly conductive thin overlayer onto
a dirty superconducting film can give rise to an "anti-proximity effect" which
manifests itself in an initial increase of with the overlayer
thickness followed by a decrease of at larger . Such a
nonmonotonic thickness dependence of results from the interplay of
the increase of a net superfluid density mitigating phase fluctuations and the
suppression of the critical temperature due to the conventional proximity
effect. This behavior of is obtained by solving the Usadel equations
to calculate the temperature of the Berezinskii-Kosterletz-Thouless transition,
and the temperature of the resistive transition due to thermally-activated
hopping of single vortices in dirty bilayers. The theory incorporates relevant
materials parameters such as thicknesses and conductivities of the layers,
interface contact resistance between them and the subgap quasiparticle states
which affect both phase fluctuations and the proximity effect suppression of
. The transition temperature can be optimized by tuning the
overlayer parameters, which can significantly weaken vortex fluctuations and
nearly restore the mean-field critical temperature. The calculated behavior of
may explain the nonmonotonic dependence of observed on
(Ag, Au, Mg, Zn)-coated Bi films, Ag-coated Ga and Pb films or NbN and NbTiN
films on AlN buffer layers. These results suggest that bilayers can be used as
model systems for systematic investigations of optimization of fluctuations in
superconductors
- …