Papers by Denise Halverson
Design projects in childcare settings present unique design challenges because of their function,... more Design projects in childcare settings present unique design challenges because of their function, size, and specific safety concerns. In selecting effective childcare furniture, stowage space, safety, and ease of access for childcare furniture are important considerations. Origami-inspired design can be useful in addressing these issues in an innovative way by introducing flat-foldability and deployability into childcare furniture. Fundamental design considerations for childcare furniture and mechanical design principles for deployable furniture are examined in order to understand how to make safe and functional furniture pieces. Childcare furniture must be very child-safe. This means that origami principles used must not add safety concerns like decreased stability or pinch points. Nonhazardous, durable, and comfortable materials must be used. Extra precaution must be taken when designing folding structures for use in a childcare environment. Mechanical principles for such systems, including folding methods and thickness accommodation, are examined in the context of childcare spaces. Various types of joints are also examined and the M-LET compliant joint is shown as a potential replacement for rigid hinges in folding furniture. Using this understanding, this work presents two simple flat-folding techniques and a compliant joint suitable for a childcare setting and demonstrates these principles through functional “safe space” furniture.
Journal of Mechanisms and Robotics, Mar 12, 2021
We demonstrate analytically that it is possible to construct a developable mechanism on a cone th... more We demonstrate analytically that it is possible to construct a developable mechanism on a cone that has rigid motion. We solve for the paths of rigid motion and analyze the properties of this motion. In particular, we provide an analytical method for predicting the behavior of the mechanism with respect to the conical surface. Moreover, we observe that the conical developable mechanisms specified in this article have motion paths that necessarily contain bifurcation points, which lead to an unbounded array of motion paths in the parameterization plane.
Mediterranean Journal of Mathematics, Jun 23, 2012
We show that if G is an upper semicontinuous decomposition of R n , n ≥ 4, into convex sets, then... more We show that if G is an upper semicontinuous decomposition of R n , n ≥ 4, into convex sets, then the quotient space R n /G is a codimension one manifold factor. In particular, we show that R n /G has the disjoint arc-disk property.
Topology and its Applications, May 1, 2007
We prove recognition theorems for codimension one manifold factors of dimension n ≥ 4. In particu... more We prove recognition theorems for codimension one manifold factors of dimension n ≥ 4. In particular, we formalize topographical methods and introduce three ribbons properties: the crinkled ribbons property, the twisted crinkled ribbons property, and the fuzzy ribbons property. We show that X × R is a manifold in the cases when X is a resolvable generalized manifold of finite dimension n ≥ 3 with either: (1) the crinkled ribbons property; (2) the twisted crinkled ribbons property and the disjoint point disk property; or (3) the fuzzy ribbons property.
We demonstrate analytically that it is possible to construct a developable mechanism on a cone th... more We demonstrate analytically that it is possible to construct a developable mechanism on a cone that has rigid motion. We solve for the paths of rigid motion and analyze the properties of this motion. In particular, we provide an analytical method for predicting the behavior of the mechanism with respect to the conical surface. Moreover, we observe that the conical developable mechanisms specified in this paper have motion paths that necessarily contain bifurcation points which lead to an unbounded array of motion paths in the parameterization plane.
Differential Geometry and Its Applications, Jun 1, 2011
We present short proofs of all known topological properties of general Busemann G-spaces (at pres... more We present short proofs of all known topological properties of general Busemann G-spaces (at present no other property is known for dimensions more than four). We prove that all small metric spheres in locally G-homogeneous Busemann G-spaces are homeomorphic and strongly topologically homogeneous. This is a key result in the context of the classical Busemann conjecture concerning the characterization of topological manifolds, which asserts that every n-dimensional Busemann G-space is a topological nmanifold. We also prove that every Busemann G-space which is uniformly locally G-homogeneous on an orbal subset must be finite-dimensional.
Geometry and Topology Monographs, Apr 22, 2006
We present a new property, the Disjoint Path Concordances Property, of an ENR homology manifold X... more We present a new property, the Disjoint Path Concordances Property, of an ENR homology manifold X which precisely characterizes when X ޒ has the Disjoint Disks Property. As a consequence, X ޒ is a manifold if and only if X is resolvable and it possesses this Disjoint Path Concordances Property.
Open Mathematics, 2013
We show that all finite-dimensional resolvable generalized manifolds with the piecewise disjoint ... more We show that all finite-dimensional resolvable generalized manifolds with the piecewise disjoint arc-disk property are codimension one manifold factors. We then show how the piecewise disjoint arc-disk property and other general position properties that detect codimension one manifold factors are related. We also note that in every example presently known to the authors of a codimension one manifold factor of dimension ≥ 4 determined by general position properties, the piecewise disjoint arc-disk property is satisfied.
Journal of Applied Mechanics, Apr 12, 2019
Of the many valid configurations that a curved fold may assume, it is of particular interest to i... more Of the many valid configurations that a curved fold may assume, it is of particular interest to identify natural-or lowest energy-configurations that physical models will preferentially assume. We present normalized coordinate equations-equations that relate fold surface properties to their edge of regression-to simplify curved-fold relationships. An energy method based on these normalized coordinate equations is developed to identify natural configurations of general curved folds. While it has been noted that natural configurations have nearly planar creases for curved folds, we show that non-planar behavior near the crease ends substantially reduces the energy of a fold.
Journal of Applied Mechanics, Feb 10, 2016
Analyzing the Stability Properties of Kaleidocycles Kaleidocycles are continuously rotating n-joi... more Analyzing the Stability Properties of Kaleidocycles Kaleidocycles are continuously rotating n-jointed linkages. We consider a certain class of six-jointed kaleidocycles which have a spring at each joint. For this class of kaleidocycles, stored energy varies throughout the rotation process in a nonconstant, cyclic pattern. The purpose of this paper is to model and provide an analysis of the stored energy of a kaleidocycle throughout its motion. In particular, we will solve analytically for the number of stable equilibrium states for any kaleidocycle in this class.
Pacific Journal of Mathematics, Jun 1, 2003
Sufficient conditions for which a minimal graph over a nonconvex domain is area-minimizing are pr... more Sufficient conditions for which a minimal graph over a nonconvex domain is area-minimizing are presented. The conditions are shown to hold for subsurfaces of Enneper's surface, the singly periodic Scherk surface, and the associated surfaces of the doubly periodic Scherk surface which previously were unknown to be area-minimizing. In particular these surfaces are graphs over (angularly accessible) domains which have a nice complementary set of rays. A computer assisted method for proving polynomial inequalities with rational coefficients is also presented. This method is then applied to prove more general inequalities.
Topology and its Applications, Nov 1, 2009
We prove recognition theorems for codimension one manifold factors of dimension n ≥ 4. In particu... more We prove recognition theorems for codimension one manifold factors of dimension n ≥ 4. In particular, we formalize topographical methods and introduce three ribbons properties: the crinkled ribbons property, the twisted crinkled ribbons property, and the fuzzy ribbons property. We show that X × R is a manifold in the cases when X is a resolvable generalized manifold of finite dimension n ≥ 3 with either: (1) the crinkled ribbons property; (2) the twisted crinkled ribbons property and the disjoint point disk property; or (3) the fuzzy ribbons property.
Cmc-computers Materials & Continua, 2010
... Dustin D. Gerrard1, David T. Fullwood1, Denise M. Halverson2 and Stephen R. Niezgoda3 ... and... more ... Dustin D. Gerrard1, David T. Fullwood1, Denise M. Halverson2 and Stephen R. Niezgoda3 ... and Zabaras (2006), Torquato (2002)], and simple topolog-ical measures such as the Euler characteristic [Mecke (1996), Mecke and Sofonea (1997), Mendoza, Thornton, Savin and ...
Topology and its Applications, Feb 1, 2002
Codimension one manifold factors are spaces which have the property that their product with R is ... more Codimension one manifold factors are spaces which have the property that their product with R is a manifold. In this paper, the disjoint homotopies property (DHP) is introduced and it is shown that resolvable generalized manifolds with DHP are codimension one manifold factors. For generalized manifolds of dimensions n 4 it is shown that DHP is implied by the plentiful 2-manifolds property, a property satisfied by many examples. Furthermore, a new class of codimension one manifold factors, the k-ghastly spaces for k > 2, is constructed.
arXiv (Cornell University), Nov 6, 2008
We present two classical conjectures concerning the characterization of manifolds: the Bing Borsu... more We present two classical conjectures concerning the characterization of manifolds: the Bing Borsuk Conjecture asserts that every n-dimensional homogeneous ANR is a topological n-manifold, whereas the Busemann Conjecture asserts that every n-dimensional G-space is a topological n-manifold. The key object in both cases are so-called generalized manifolds, i.e. ENR homology manifolds. We look at the history, from the early beginnings to the present day. We also list several open problems and related conjectures.
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Papers by Denise Halverson