6 research outputs found
A class of spherical folding subdivisions
The classification of the dihedral folding tesselations of the sphere whose prototiles are a kite and an equilateral or isosceles triangle was obtained in recent papers. In this paper we extend this classification to scalene triangles, presenting all the dihedral folding tesselations of the sphere by kites and scalene triangles in which the longest side of the kite is equal to the lower side of the triangle
Spherical folding tessellations by kites and isosceles triangles: a case of adjacency
The classification of dihedral folding tessellations of the sphere and the plane whose prototiles are a kite and an equilateral triangle are obtained in a recent paper, [1]. In this paper, we extend this classification presenting all the dihedral folding tessellations of
the sphere by kites and isosceles triangles in a particular case of adjacency. A list containing these tilings including its combinatorial structure is presented in Table 1
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7th International Meshing Roundtable '98
The goal of the 7th International Meshing Roundtable is to bring together researchers and developers from industry, academia, and government labs in a stimulating, open environment for the exchange of technical information related to the meshing process. In the past, the Roundtable has enjoyed significant participation from each of these groups from a wide variety of countries
The Application of Auxetic Structures for Rugby Shoulder Padding
Auxetic materials have a negative Poisson’s ratio (NPR), they laterally expand under
stretch, laterally shrink under compression and conform to curved surfaces through
the formation of synclastic curvature. It was identified that these qualities could
enhance the current standard of personal protective equipment (PPE) often
embedded within sports apparel (sPPE) at regions of the body exposed to soft tissue
injury through collision, fall or impact. Current pads can inhibit movement,
breathability and wicking, whilst moulded pads are prone to saddling; segmentation
techniques including vacuum moulding and cut segmenting are applied to improve
the conformability of padding. It is unclear as to whether the impact performance of
auxetic sPPE is affected under a state of synclastic curvature or biaxial expansion and
as such sPPE applications are limited to date. User-centred design strategies for
functional clothing have not yet been established for sPPE with auxetic elements, this
could improve accessibility for implementation by pad designers. Therefore, this
research set out to determine strategies for the application of auxetic sPPE with
enhanced conformability.
In order to achieve the overall aims of this research a multi-method research strategy
was employed investigating the problem first through the user and product. A
quantitative survey was designed to assess user perceptions of commercial rugby
shoulder padding comfort. Commercial rugby shoulder padding featuring different
segmentation types were assessed for conformability to the shoulder region through
fit and pressure comfort measurements. Following this the research investigated
how auxetic structures of different geometries could enhance the conformability of
rugby shoulder padding. Data collection included pressure comfort assessments,
impact tests over curved surfaces and lateral expansion of pads through tensile
displacement and fitting pads to a mannequin.
A user-perception survey of commercial rugby shoulder pads found that fit and
protection were the most important of six realms of respondents perceived comfort.
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Current regulations for rugby shoulder padding suggest that pads must not hinder
comfort and mobility yet only stipulate test methods for impact protection. The
commercial rugby pads provided poor pressure comfort and conformability across
the different types of segmentation and segment (unit cell) shapes. It was also
identified that poor conformability was of detriment to product function where pads
moved out of position. The findings from the survey and product analysis showed
that the main cause of poor fit and pressure comfort was padding bulkiness caused
by larger circumferences and less conforming segmentation techniques. Cutsegmented pads provided the best route to conformability but none of the pads
provided the ideal pressure comfort range identified for this research.
Rugby shoulder pads were cut-segmented with different auxetic structures and
following this manipulation of an auxetic geometry was investigated. It was found
that sPPE with auxetic elements conformed to curvatures and expanded laterally
compared to the non-auxetic alternative. Parameters for use were identified
including that opening consistency of the individual auxetic geometries had potential
to affect sPPE function. Auxetic geometries in an arrangement of singular cuts had
the most consistent opening mechanism throughout the pad when subject to a
tensile load. Additionally, the manipulation of an auxetic geometry showed that
anisotropy can be applied to offer higher displacement in specific directions, which
may have use for sPPE not subject to rotational forces such as knee pads. It was also
found that increasing the difference between rib (unit cell wall) length and separation
between ribs led to the auxetic structure opening out less, which could be applied at
specific regions of a pad that require restriction.
The findings of this research showed that auxetic structures could be manipulated
for different sPPE applications. A recommended strategy for development of sPPE
with auxetic elements was presented, influenced by user-centred design strategies.
The first stage of the strategy focused on defining the problem via the user, sport,
body region and product. Ideation of possible solutions formed the second stage, by
assessing manipulations of auxetic geometry in relation to requirements of the user,
product, sport and body region, and was repeated until the product was found to
provide a solution to the defined problem; implementation completed stage 3