Note: Descriptions are shown in the official language in which they were submitted.
CA 02367090 2009-12-24
STRUCTURAL SYSTEM OF TORSION/TOROIDAL ELEMENTS AND
METHODS OF CONSTRUCTION THEREWITH
Technical Field
The patent classification system does not contain a classification for
structural systems as such,
the most appropriate description of the present invention, but does address
specific types of structures,
such as "static structures" (U.S. Class 52), "bridges" (U.S. Class 14),
"railway rolling stock" (U.S.
Class/Subclass 105/396+), "ships" (U.S. Class/Subclass 114/65+), "aeronautics"
(U.S. Class/Subclass
244/117+), "land vehicles: bodies and tops" (U.S. Class 296) etc. With respect
to torsion devices, no
structural classification could be found, the classifications being restricted
to springs (U.S. Class 267),
etc. Also, the present invention has elements that may be considered to be
covered generally by U.S
Class/Subclass 152/1-13, spring wheels and resilient tires and wheels, and
U.S. Class/Subclass
152/516-520, "run- flat" devices.
Background Art
A significant advance in basic structural systems for stationary structures
has not occurred since
the advent of prestressed and reinforced concrete, structural steel, and the
use of cable as a tensional
element. There have been some innovative engineering and architectural
advances, such as various
types of folding structures, tube and ball and other space trusses, and in the
field of vehicular structure,
such as formed sheet rigidification. However, none of these advances has
escaped the use of
conventional structural elements in compression, tension and flexion mode.
Although there have been
more recent developments in the field of vehicular structure, such as formed
sheet rigidification, the
fundamental methods have not changed significantly from the rigid rib,
stringer, and truss design. The
present invention is a significant advance in structural systems, both
stationary and moveable, with
respect to weight, strength, flexibility and magnitude.
There does not appear to be any prior art that this invention builds upon
except generally in the
field of structural engineering, none of which directly addresses structural
combinations of torsion
elements or toroidal elements.
There are some superficial graphic similarities involving shapes and forms to
be found in
certain patents that claim inventions involving dome or sphere structures
which utilize ring or circular
elements. One is the Ring Structure disclosed by United States Patent No.
4,128,104 which is "a
structural framework composed of ring members intersecting one another in a
particular manner". That
disclosure does not specify any utilization of torsion loading of the ring
members and requires
interlinking ("intersecting") of the ring members. The other is the Modular
Dome Structure, United
States Patent No. 3,959,937, which is comprised of "ring-shaped" elements of
equal size which form
a dome when connected in a particular manner. That disclosure involves
"improved building
construction for domes or other spherical frames", does not teach a universal
structural system, teaches
against the use of "thin rings of simple toroidal shape or other simple form"
because of perceived
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problematic strength, is limited to "elements of substantially the same size",
and does not specify any
utilization of torsional strength of materials or loading.
Summary of the Invention
In accordance with one aspect of the present invention, there is provided a
structural system
of torsion elements comprising: (a) a plurality of torsion elements which
function with torsion as the
principle load bearing mode; and (b) means for connecting the torsion
elements, including one or more
couplings which grip the torsion elements such that the torsional load on one
or more of the torsion
elements is transmitted to one or more of the other of the torsion elements to
which the one or more of
the torsion elements is connected, and so that the torsional load on the one
or more of the other of the
torsion elements is in the opposite direction to that of the one of the
torsion elements.
Brief Description of the Drawings
FIG. I is a plan view of two open rectangle torsion elements connected in the
same orientation
by two couplings.
FIG. 2 is an exploded view of the connection of the open rectangle torsion
elements shown in
FIG. 1.
FIG. 3 is a perspective view of the torsion elements in FIG. 1.
FIG. 4 is an exploded view of the connection of the open rectangle torsion
elements shown in
FIG. 3.
FIG. 5 is a plan view of two open rectangle torsion elements connected in
opposite orientation
via an intermediate torsion element by four couplings.
FIG. 6 is an exploded view of the connection of the open rectangle torsion
elements shown in
FIG. 5.
FIG. 7 is a perspective view of the torsion elements in FIG. 5.
FIG. 8 is an exploded view of the connection of the open rectangle torsion
elements shown in
FIG. 7.
FIG. 9 is a plan view of two'M'-shaped torsion elements connected in opposite
orientation via
an intermediate torsion element by four couplings.
FIG. 10 is a perspective view of the torsion elements in FIG. 9.
FIG. 1 I is a perspective view of two'U'-shaped open rectangle torsion
elements connected at
an angle in opposite orientation by two couplings.
FIG. 12 is a perspective view of two 'U'-shaped open rectangle torsion
elements connected at
an angle in opposite orientation by four couplings via an intermediate torsion
element.
FIG. 13 is a perspective view of 6 connected pairs of open rectangle torsion
elements connected
in a linear array, each pair being connected to one another at an angle by two
couplings.
FIG. 14 is a perspective view of 32 pairs of U-shaped torsion elements
connected at an angle
in opposite orientation by four couplings via an intermediate torsion element
connected in a circular
array forming a toroid.
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FIG. 15 is a perspective view of two toroidal torsion elements connected at an
angle by one
coupling.
FIG. 16 is a side view of the toroidal torsion elements in FIG. 15.
FIG. 17 is a plan view of the toroidal torsion elements shown in FIG. 15.
FIG. 18 is a bottom view of the toroidal torsion elements shown in FIG. 15.
FIG. 19 is a perspective view of 32 pairs of toroidal torsional elements shown
in FIGS. 15-18
connected in a circular array forming a toroid.
FIG. 20 is a perspective view of two toroidal torsion elements connected at an
angle without
an external coupling.
FIG. 21 is a side view of the toroidal torsion elements in FIG. 20.
FIG. 22 is a plan view of the toroidal torsion elements in FIG. 20.
FIG. 23 is a bottom view of the toroidal torsion elements in FIG. 20.
FIG. 24 is a plan view of 64 pairs of angularly connected toroidal torsional
elements connected
in a circular array forming a toroid.
FIG. 25 is a perspective view of the toroid shown in FIG. 24.
FIG. 26 a side view of two toroids such as the one shown in FIG. 24 connected
internally by
couplings connecting a plurality of the toroidal elements of one with
proximate toroidal elements of
the other.
FIG. 27 is a fragmentary view of the region of internal connection between the
toroids in
FIG. 26.
FIG. 28 is another side view of the two toroids shown in FIG. 26.
FIG. 29 is a fragmentary view of the region of internal connection between the
toroids in
FIGS. 20-23.
FIG. 30 is a view of the two toroids in the direction of the arrow in FIG. 28.
FIG. 31 is a fragmentary view of the region of internal connection between the
toroids in
FIG. 30.
FIG. 32 is a perspective view of the two toroids in the direction of the arrow
in FIG. 30.
FIG. 33 is a fragmentary view of the region of internal connection between the
toroids shown
in FIG. 32.
FIG. 34 is a perspective view of a toroid formed by two tubularly concentric
toroids, the outer
and the inner both being 32 pairs of toroidal torsional elements shown in
FIGS. 20-23 connected in a
circular array forming a toroid, but with different angular orientation of the
pairs of toroidal elements.
FIG. 35 is a plan view of 20 pairs of toroidal torsional elements as shown in
FIGS. 20-23
connected in a eliptical array forming a toroid.
FIG. 36 is a perspective view of the toroid formed by the eliptical array
shown in FIG. 35.
FIG. 37 is a perspective view of a toroidal element with a circular spiral
tube, the tube of which
is bordered by other coaxial toroidal elements of lesser tubular diameter
which are bonded, bound or
otherwise connected to the central toroidal element.
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FIG. 38 is a plan view of a toroidal element consisting of seven interlinked
toroidal elements,
the tubes of which may be bonded, bound or otherwise connected to one another.
FIG. 39 is a cross section of the toroidal element in FIG. 38.
FIG. 40 is a perspective view of the toroidal element in FIG. 38.
FIG. 41 is a side view of the toroidal element in FIG. 38.
FIG. 42 is a perspective view of a plurality of pairs of toroidal elements as
shown in FIGS.
20-23 connected in a linear array to form a straight cylindrical rod, post or
tube.
FIG. 43 is a perspective view of a plurality of pairs of toroidal elements
connected in a linear
array to form a straight cylindrical rod, post or tube, with a different
angular orientation from those
comprising the structure shown in FIG. 42.
FIG. 44 is a perspective view of the linear array shown in FIG. 42 which is
connected to and
coaxially encloses the linear array shown FIG. 43.
FIG. 45 is a perspective view of a toroidal element with two opposite semi-
eliptical sides and
two opposite straight sides.
FIGS. 46-49 show various connections between toroidal elements (even numbered
showing the
plan view and odd numbered showing a perspective view).
FIGS. 50, 51, and 52 are perspective views of a coupling with splined grips
showing for
connecting two elements showing, respectively, the coupling open, the
compression band, and the
coupling closed with the compression band applied.
FIGS. 53, 54, 55, and 56 are perspective views of a coupling with splined
grips for connecting
two axially askew toroidal elements showing, respectively, the coupling open,
the compression bands,
the coupling closed with compression bands applied, and the coupling with an
arbitrary angle between
the grip axes (also with compression bands applied).
FIGS. 57-58 are perspective views of toroidal elements with two spline collars
on opposite
sides of the element attached to the toroidal elements of which they are
comprised.
FIG. 59 is a side view of a structural module comprised of three toroidal
elements connected
to form a triangle.
FIG. 60 is a perspective view of the structural module shown in FIG. 59.
FIG. 61 is a side view linear array of 8 of the structural modules shown in
FIG. 59 forming the
structure of a post, beam or rod of triangular cross section.
FIG. 62 is a top view of the linear array shown in FIG. 61.
FIG. 63 is a perspective view of the linear array shown in FIG. 61.
FIG. 64 is a side view of a structural module comprised of six toroidal
elements connected to
form a rectangular box.
FIG. 65 is a perspective view of the structural module in FIG. 64.
FIG. 66 is a side view linear array of 8 of the structural modules shown in
FIG. 64 forming the
structure of a post, beam or rod of rectangular cross section.
FIG. 67 is a perspective view of the structure shown in FIG. 66.
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FIG. 68 is a perspective view of a double width of a 3 deep array of a linear
array of 8 of the
structural modules shown in FIG. 64 forming the structure of a joist or beam.
FIG. 69 is a perspective view of a triple width semicircular array of 45
rectangular structural
modules of toroidal torsion elements connected in a semicircular array to form
an arch.
FIG. 70 is a perspective view of 90 rectangular structural modules of toroidal
torsion elements
connected in a circular array.
FIG. 71 is a cutaway plan view of a hexagonal toroidal element with 2 sets of
3 rotationally
joined internal shafts, one in each opposing half of the hexagon.
FIG. 72 is a cutaway perspective view of the toroidal element in FIG. 71.
FIG. 73 is a cutaway side view of the toroidal element in FIG. 71.
FIG. 74 is a side view of two hexagonal toroidal elements shown in FIG. 71
angularly
connected by one coupling.
FIG. 75 is a plan view of the two toroidal elements in FIG. 74.
FIG. 76 is a bottom view of the two toroidal elements in FIG. 74.
FIG. 77 is a perspective view of the toroidal elements in FIG. 74.
FIG. 78 is a perspective view of a toroidal element as shown in FIG. 24
connected to a similar
concentric toroidal element within it, the radii of the toroidal elements
comprising the inner and outer
toroidal elements being equal.
FIG. 79 is a perspective view of a toroidal element formed by 32 pairs of
toroidal torsional
elements shown in FIG. 21 connected in a circular array connected to a
concentric inner toroidal
element formed by 32 pairs of the angularly connected toroidal torsional
elements oriented as shown
in FIG. 22 connected in a circular array.
FIGS. 80 through 81 show two types of concentric connections of two toroidal
elements at
different angles (even numbered showing the plan view and odd numbered showing
a perspective
view).
FIG. 82 is schematic elevation of a dome structure formed by successive
interleaved layers of
equal numbers of toroids ofupwardly diminishing diameter, each toroid
connected at six points to those
adjacent capped by a similar dome structure of lesser diameter to form a
compound dome structure.
FIG. 83 is a schematic elevation of a spherical structure formed by two dome
structures formed
by successive layers of equal numbers of toroidal elements of upwardly
diminishing diameter, each
toroidal element connected at four points to those adjacent, connected in
opposite polar orientation.
FIG. 84 is a side view of a spherical/dodecahedral structure comprised of
twenty connected
toroidal elements with the gaps bridged by toroidal elements of lesser
diameter, with a group of
elements as shown in FIG. 85 scaled to connect to the topmost toroidal I
element of the structure, with
a similar connection of a similar group similarly scaled to connect to the
topmost toroidal element of
the first group.
FIG. 85 is a group of 6 connected toroidal elements which comprise the
frontmost section of
the spherical/dodecahedral structure in FIG. 84.
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FIG. 86 is a perspective view of a tower structure formed by a vertical array
of connected
prismatic structural modules of upwardly diminishing dimension.
FIG. 87 is a schematic elevation of a conical tower structure formed by
successive layers of
equal numbers of toroids of upwardly diminishing diameter, each toroid
connected at four points to
those adjacent.
FIG. 88 is a schematic elevation of a conical tower structure formed by
successive interleaved
layers of equal numbers of toroids of upwardly diminishing diameter, each
toroid connected at six
points to those adjacent.
FIGS. 89, 90, and 91 are perspective views of an actuated two element coupling
with spline
grips, the latter two being cutaway views showing the motors, transmissions
and drives for each of the
spline grips within the body of the coupling.
FIGS. 92 and 93 show a series of plan views of a toroidal element shifting
shape from that of
a circular array of 40 toroidal elements forming a circular toroid to that of
an eliptical array forming
an eliptical toroid.
FIGS. 94 through 98 show a series of schematic elevations of the shifting of
shape of a prolate
spherical structure to an oblate spherical structure in phases through
intermediate structures of lesser
volume.
FIG. 99 is a perspective view of a circular horizontal arch of 20 toroidal
members.
FIG. 100 is a perspective view of a structure formed from two interleaved
layers of circular
horizontal arches, as shown in FIG. 99.
FIG. 101 is a perspective view of a structure formed from three interleaved
layers of circular
horizontal arches, as shown in FIG. 99.
FIG. 102 is a perspective cutaway view of a toroidal wheel body framework
sheathed in a
casing.
FIG. 103 is a cutaway of a perspective view of a wheel and tire structure (the
lowest five
elements of which are shown in detail with the rest of the elements being
shown diagrammatically)
embedded in a matrix.
FIG. 104 is perspective view of a wheel and tire structure (the lowest five
elements of which
are shown in detail with the rest of the elements being shown
diagrammatically) supported by a
common band.
FIG. 105 is a perspective view of a tire with the wheel and tire structure
shown in FIG. 104
installed.
FIG. 106 is a mathematical diagram to demonstrate the relationships among the
angles and
lengths of a plan for construction of a toroidal element framework with
smaller toroidal elements
showing the dimensional quantities involved.
FIG. 107 is a perspective view of a schematic mathematical diagram of a dome
showing the
dimensional quantities to demonstrate the relationships among the angles and
lengths of a plan for
construction of a toroidal dome framework.
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FIG. 108 is an elevation of a schematic mathematical diagram of a dome showing
the
dimensional quantities to demonstrate the relationships among the angles and
lengths of a plan for
construction of a toroidal dome framework.
Disclosure of Invention
The present invention is a structural system that, in one embodiment, employs
elements that
are "toroidal" in shape, "toroidal elements", which are connected to form
structures; in another
embodiment, employs elements which function with torsion as the principal load
bearing mode,
"torsion elements", which are connected to foam structures; and in a preferred
embodiment, employs
"toroidal torsion elements", structural elements that are "toroidal" in shape
and function with torsion
as the principal load bearing mode, which are connected to form structures.
As used in this disclosure and the appended claims the term "torsion element"
means a
structural element that functions with torsion as its principal load bearing
mode.
As used in this disclosure and the appended claims the term "toroidal" means
of or pertaining
to a "toroid". The term "toroid" is not intended to limit the present
invention to employment of elements
that are in the shape of a torus, which is mathematically defined as a
surface, and the solid of rotation
thereby bounded, obtained by rotating a circle which defines the cross section
of the tube of the torus
about an axis in the plane of the circular cross section. As used in this
description and the appended
claims the term "toroid" means any form with the general features of a torus,
i.e. a tube, cylinder or
prism closed on itself, without regard to any regularity thereof, and further
means any tubular,
cylindrical or prismatic form which is closed on itself in the general
configuration of a torus, thus
completing a mechanical circuit forming the "tube" of a "toroid", regardless
of the shape of the cross
section thereof, which may even vary within a given "toroid". A toroid may be
formed by the
connection of cylindrical or prismatic sections, straight or curved, or by the
connection of straight and
curved sections in any combination or order; and may be of any shape which the
closed tube may form:
elliptical, circular, polygonal, whether regular or irregular, symmetrical,
partially symmetrical, or even
asymmetrical, whether convex or concave outward, partially or completely.
Moreover, as used in this
description and the appended claims, the term "toroid" applies to and
includes: (a) the continuous
surfaces of toroids, tube walls of finite thickness, the exterior of which are
bounded by the toroidal
surface, and the solids that are bounded by the toroidal surface; (b) any
framework of elements which
if sheathed would have the shape of a toroid; (c) any framework of elements
which lays in the locus
of a toroidal surface; (d) a bundle or coil of fibers, wires, threads, cables,
or hollow tubing that are,
bound, wound, woven, twisted, glued, welded, or otherwise bonded together in
such a manner as to
form in their plurality or individuality a toroidal shape. The principal
feature of a toroidal structural
element is that it has no non-toroidal conventional cross-bracing, diametrical
or chordal, within the
interior perimeter of its tube that functions by compression, tension or other
loading. However, a
toroidal element may be reinforced within the interior perimeter of its tube
by other toroidal elements,
as shown in FIGS. 78-8 1, which may be torsional, conventional or otherwise.
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As used in this disclosure and the appended claims the term "torsion/toroidal
element" means
a structural element that may be either a torsion element, or a toroidal
element, or a toroidal torsion
element, the term "torsion/toroidal element" thus encompassing all three
alternatives, Otherwise, when
any one of the foregoing alternative meanings are referred to, that
alternative shall be specifically
referred to by its proper description: torsion element; toroidal element; or
toroidal torsion element.
However, reference to a torsion element shall be taken to mean a torsion
element which may be toroidal
or non-toroidal; and reference to a toroidal element shall mean a toroidal
element which may be
torsional or non-torsional.
The structural system is comprised of a plurality of torsion/toroidal elements
connected
together so that there is no substantial unwanted movement of the
torsion/toroidal elements in relation
to one another in the connection. Two or more torsion/toroidal elements may be
connected in the same
connection. The connection of the torsion/toroidal elements is the means by
which loading is
transmitted between and distributed among the torsion/toroidal elements.
As used in this disclosure and the appended claims the term "connected" means,
in addition to
its ordinary meaning, being in a "connection" with torsion/toroidal elements;
and the term "connection"
as used in this disclosure includes, in addition to its ordinary meaning, any
combination of components
and processes that results in two or more structural elements being connected,
and further includes the
space actually occupied by such components, the objects resulting from such
processes, and the parts
of the structural elements connected by contact with such components or
objects; but both the terms
"connected" and "connection" exclude interlinking ( "intersection") of
structural elements as a means
for connecting toroidal elements.
Although the structural system of connected torsion elements may be utilized
for constructions
without the employment of toroidal elements, and the structural system of
connected toroidal elements
may be utilized for constructions without the employment of torsion elements,
the preferred
embodiment and the best mode is in combination with the other, a structural
system of connected
toroidal torsion elements. Thus, although the structural system of torsion
elements and the structural
system of toroidal elements are each operative separately (without combination
with the other), they
are joined in the inventive concept of the structural system of toroidal
torsion elements by the
complementary characteristics of the toroidal shape with torsion load bearing.
The present invention includes a method of construction with the structural
system in its
various modes, as well as a method of construction of toroidal torsion
elements in a process of
replication, and the construction of certain advanced structures possible with
the system.
Torsion/toroidal elements use the strength of materials more effectively and
have the capacity
to redistribute the loads distributed to them by the connections of the
structural system of which they
are a part. The structural system effectively distributes most compression,
tension, flexion and torsion
loading among the connected torsion/toroidal elements of constructions. Thus
the construction is
distinguished from conventional constructions employing elements which
function only in compression,
tension or flexion, such as beams, struts, joists, decks, trusses, etc.
However, when elements which
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function in compression, tension or flexion are constructed using the present
invention, the same
structural benefit of load distribution applies.
The preferred embodiment of the present invention employs toroidal elements
that are
constructed with the use of torsion elements which are toroidal in shape.
Torsion elements use the
torsional strength of materials and have the capacity to bear the torsion
loads distributed to them by the
connections of the structural system of which they are a part. The preferred
embodiment using toroidal
torsion elements converts most compression, tension and flexion loading of
constructions using the
system to torsional loading of the torsion elements of which the constructions
are comprised. The use
of toroidal torsion elements also contributes to construction of toroids which
are self-supporting.
The present invention contemplates that torsion/toroidal elements may be
constructed of yet
other torsion/toroidal elements, so that a given torsion/toroidal element so
constructed functions to bear
loads by the bearing of structural loads by its constituent substructures.
Such substructures may be
structural elements, torsion/toroidal, conventional or otherwise, which are
part of a combination of
structural elements of a scale similar to the given toroidal element, or
structural elements of a scale
significantly smaller than the given torsion/toroidal element and
fundamentally underlying the bearing
capacity of the given torsion/toroidal element. In the latter case the
structure of a given torsion/toroidal
element may be the replication of small substructures of torsion/toroidal
elements, which in turn may
be replications of still smaller substructures of torsion/toroidal elements.
This process of structural
replication can be continued to microscopic, and even molecular, levels of
smallness.
The system also includes the construction of conventional elements using
torsion/toroidal
elements which may be used in combination with other torsion/toroidal
structures in constructions.
Moreover, it is one of the features of the present system that conventional
elements, such as beams,
joists, decks, trusses, etc., constructed using torsion/toroidal elements may
be engineered with arching
camber and prestressing. Although such constructions may bear resemblance to
conventional trusses,
the structural integrity and strength of torsion elements is ultimately
dependent on torsion/toroidal
elements which may be bearing torsion loads, and is not fundamentally (in the
sense of originally
underlying) or necessarily dependent on elements such as linear chords and
struts bearing loads in
compression, tension or flexion.
Torsion/toroidal elements can be made of virtually any material suitable for
the loads to which
the structure may be subjected and for the environment in which the structure
may be utilized.
It is the fundamental principle of the structural system which is the present
invention that
torsion elements bear as torsional load the greatest part of the load placed
on the structures of which
they are a part, excepting localized forces existing in the connection of the
torsion elements, and evenly
distribute such loading amongthe connected torsion elements of which the
structures are ultimately and
fundamentally constructed.
The present invention contemplates that structures constructed of connected
torsion/toroidal
elements may be incorporated in yet other structures together with
conventional structural elements in
order to bear compression, tension and flexion loads with such
torsion/toroidal structures.
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Torsion elements may have virtually any shape that allows them to be connected
and thereby
function by torsional loading. However, the preferred embodiment of the
present invention employs
torsion elements which are toroidal in shape. Such toroidal torsion elements
may be used to create a
variety of new structural forms for both stationary and moveable structures.
The toroidal shape
facilitates replication of structured toroidal torsion elements to produce
larger and larger toroidal
torsion elements which may be suitable for the dimension of the ultimate
structural application.
A large variety of structures made feasible by origination of the replication
process with
torsion/toroidal elements on the order of nanostructures or larger may
themselves be considered as
materials which can be utilized in conventional structures, such as decking,
plates, skins, and sheeting
of arbitrary curvature.
Torsion/toroidal elements may be used to create new structural forms for both
stationary and
moveable structures. The toroidal shape allows for replication of toroidal
elements to produce larger
and larger toroidal elements which may be suitable to the dimensions of the
structural application. A
large variety of structures made feasible by origination of the replication
process with toroidal elements
on the order of nanostructures or larger may themselves be considered as
materials which can be
utilized in conventional structures such as decking, plates, skins, and
sheeting of arbitrary curvature.
Erection of structural frames using the present invention requires only
connection of the
torsion/toroidal elements, and may use connectors which are prepositioned and
even integrated in the
design of the torsion/toroidal elements.
Torsion/toroidal elements may be connected by any means that does not permit
unwanted
movement in the connection. Such means may be any type of joining, such as
welding, gluing, fusing,
or with the use of fasteners, such as pins, screws and clamps. However, the
preferred means for
connection is by use of a "coupling". The term "coupling" is used in this
disclosure to mean a device
which connects two or more torsion elements by holding them in a desired
position relative to one
another, so that when the desired positions of the torsion/toroidal elements
are achieved, the
torsion/toroidal elements will not be able to unwantedly move relative to each
other within the
coupling. The coupling may itself be constructed of torsion/toroidal elements,
or may be solid or have
some other structure. The term "coupling" also includes a device which
connects a torsion/toroidal
element to a conventional structural element by holding both the
torsion/toroidal element and the
conventional structural element in the desired position, so that the
structural elements will not be able
to unwantedly move relative to each other within the coupling. Although, the
function of couplings is
to hold torsion/toroidal elements in position in relation to each other, there
may be motion of the
torsion/toroidal elements outside the connection associated with the
structural loading of the elements,
including rotation of the elements with respect to each other about the axis
defined by the grip within
the coupling, and sliding of the elements through the grip of the coupling.
Such motion is expected and
appropriate for the distribution of stress among the elements of a given
torsion/toroidal structure.
The function of couplings in holding structural elements in position may be
combined with
prior positional adjustment and actuation of such adjustment. In this respect
the position of
torsion/toroidal elements connected by a coupling with respect to one another
may be changed or
CA 02367090 2009-12-24
adjusted and then held in the desired position. Accordingly, the coupling must
be designed to have the
capability for and even to perform such adjustment, and may also be designed
to have such adjustment
actuated by some motive power. Such actuation may implement dynamic
distribution of loading among
the structural elements affected or implement dynamic shape shifting, or both.
This can be achieved
by making one or more connections of the structure adjustable, with or without
the use of actuation.
Moreover, such powered actuation of adjustable coupled connections may be
computer controlled in
order to precisely determine the shape changes and structural effects desired.
The function of such a
coupling, therefore, is to adjust the coupled connections, with or without the
use of such controlled
actuation, so that a torsion/toroidal element may be moved within a connection
in relation to other
structural elements connected therein, and then firmly held by the connection
in the position resulting
from such movement so that the torsion/toroidal element will not have
substantial movement within
the connection in relation to any other structural element in the connection
unless deliberately moved
again by the coupling.
To present the details of the system, the function of its elements, and the
method by which
structures are constructed using the system, reference is made to the
drawings.
FIGS. 1-4 show an embodiment which demonstrates the fundamental principles of
the torsional
aspect of the structural system. In FIGS. 1-4 two torsion elements 3, 4 are
connected by two couplings
1, 6 to form a torsional structural module. The torsion elements 3 and 4 are
shown as open rectangles
with a circular cross section to demonstrate the principle, but any cross
sectional shape and any element
shape may be used with couplings having compatible openings. The couplings
shown 1, 6 have
cylindrical openings, coupling 6 having bearings 7 which allow for free
rotational movement of the
torsion elements within the coupling, and coupling I having spline grips 2 to
engage the spline ends
5 of the torsion elements 3, 4. The purpose of the spline ends 5 being engaged
by corresponding spline
grips 2 is to hold the torsion element firmly in relation to the coupling I so
as to prevent movement of
the torsion element within the coupling. The purpose of the couplings 6 with
bearings is to constrain
the arms of the torsion elements 3 and 4 to be in alignment under the action
of the forces. Thus, when
the torsion element 3 is subjected to a force which attempts to rotate the arm
of torsion element 3 about
its axis in relation to the coupling 1 within which it is engaged, the force
will result in a torsion load
on the arm where the position of coupling 1 is fixed. Where the position of
coupling I is not fixed, such
an attempt to change the orientation of the torsion element 3 will also result
in a rotation of the coupling
I with torsion element 3 in relation to the torsion arm of the other torsion
element 4 which is also
engaged within coupling 1. This attempt to rotate the coupling 1, the spline
grip 2 of which is engaged
to the spline 5 of torsion element 4, will result in a torsion load on the arm
of the other torsion element
4 where the position of torsion element 4 is fixed. Thus any change in the
position of one torsion
element 3 connected to another 4 by an engaged coupling I will result in
transmission of the torsion
load on one torsion element 3 to the other 4. The role of coupling 6 is to
assist in maintaining the
alignment of the arms of the torsion elements 3 and 4.
Another embodiment which demonstrates the principle is shown in FIGS. 5- 8. In
this variation
the orientation of the torsion elements is opposing, but with the transmission
of torque loading
11
CA 02367090 2009-12-24
accomplished with couplings 21, 26 similar to those in FIGS. 1-4 through the
addition of an
intermediate torsion element 28, in this case a cylindrical bar. Again the
purpose of the splines 25 is
to engage the spline grips 22 of the couplings 2 1, thus fixing their rotation
with that of the torsion
elements 23, 24, and the purpose of the couplings 26 with bearings 27 is to
constrain the movement of
the arms of the torsion elements 23, 24 and the intermediate torsion element
28 to rotation in alignment
with each other. In this variation the intermediate torsion element 28 is
acted upon with opposing torque
by connection at its opposite ends with couplings 21 that transmit the load on
the torsion elements 23
and 24. The transmission of load to the intermediate torsion element 28 occurs
in the same manner as
the transmission of load between the torsion elements 3 and 4 of the module
shown in FIGS. 1-4.
Therefore, the load transmitted to the intermediate torsion element 28 by one
torsion element 23 is
opposite to the torsional load transmitted from the other torsion element 24.
In this way the intermediate
element 28 provides for additional capacity for bearing of torsional loading
by the structural module.
Although a means for connection between torsion elements 23 and 24 via a
single intermediate
torsion element 28 is shown in FIGS. 5-8, the connection between torsion
elements 23 and 24 as shown
in FIGS. 5-8 may be accomplished using more than one intermediate torsion
element and the
appropriate combination and placement of couplings.
In both of the foregoing variations torsional load is distributed equally
among the connected
torsion elements by their action upon each other as understood with Newton's
third law, which may be
stated in part as: "To every action there is always opposed an equal
reaction".
The spline grip couplings and the corresponding spline ends of torsion
elements shown in
FIGS. 1-4 and FIGS. 5-8 are not the only means contemplated for achieving
fixed connections between
torsion elements and couplings. Indeed all means for fixing a coupling to a
torsion element, such as
welding, gluing, fusing, pinning, screwing, clamping, and the mating of the
coupling with a torsion
element of any non-circular cross section, are contemplated as appropriate in
order for a coupling
connecting torsion elements to transmit torsional loading.
The modules shown in FIGS. 1-4 and 5-8 may themselves be similarly connected
in linear
arrays and different types of modules shown may be connected to form arrays
which may have any
shape, and may be closed, circular, or asymmetrical and irregular.
Closed arrays of connected torsion modules have no terminus for the
transmission of loading,
as do linear arrays. Thus, any torsional load placed on a torsion element in a
closed array will be
transmitted to and distributed among all of the torsion elements in the array.
As previously indicated the torsion elements may be of virtually any shape so
long as they may
be connected in a way similar to that as shown in FIGS. 1-4 and 5-8, thus
providing for the bearing and
transmission of torsional loading. An example of another torsion element shape
is shown in FIGS. 9
and 10, connected in the various ways shown in FIGS. 5-8.
Torsion elements may be angularly connected to produce angular torsion modules
and
structures and form linear arrays thereof as shown in the example of FIG. 13.
The same characteristics
of transmission of torsional loading exist in this type of configuration as in
the structures shown and
discussed earlier. Angular connections are possible for virtually any type of
torsion element as shown
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CA 02367090 2009-12-24
in the examples of FIGS. I I and 12. Moreover, any type of connection may be
used for angular
connection of torsion elements.
Angularly connected torsion elements may also be connected in closed arrays as
shown in FIG.
14. The angular connection between elements allows for the inclusion of more
torsion elements in the
array within the same length, thereby providing for a greater capacity of the
array to absorb torsional
stress. Although only circular arrays have been shown, any closed array is
possible and will share the
same characteristics of distribution of torsional loads as circular arrays.
The symmetry of an array and
the manner in which it is loaded will determine the evenness of the
distribution of torsional stress,
whether the array is open or closed. Also as can be seen from FIG. 14, a
closed symmetrical array of
torsion elements forms a toroid, the shape of the preferred embodiments of the
invention.
Structural modules of torsion elements, and arrays thereof, connected by one
coupling are also
possible, as shown in FIGS. 15-18 where the torsion elements are toroidal.
Smoothly curved torsion
elements absorb torsion stress variably along the length of the toroidal tube.
Torque applied to any
point on such a torsion element along its tube length which tends to twist the
body of the torsion
element is transmitted along the body of the torsion element as determined by
the structure of the
torsion element, the capacity of the material used to absorb torsional stress,
and the curvature of the
torsion element. Nevertheless, the load on one curved torsion element fixedly
connected with one
coupling to another curved torsion element as shown in FIGS. 15- 18 will be
transmitted to the other
in the same manner as for the connected torsion elements shown in FIGS. 1-4.
As with all other torsional elements, toroidal torsional elements can be
connected in closed
arrays as shown in FIG. 19, which may form the framework of largertoroidal
elements having torsional
strength characteristics. Indeed, it is contemplated by this invention that
the self-similarity of toroidal
torsion elements constructed from smaller toroidal torsion elements can be
extended to precisely
control all of the structural characteristics of such toroidal torsion
elements.
Through FIG. 19 all of the connections between torsion/toroidal elements have
been shown in
the figures as "external", i.e. achieved with an "external" coupling applied
to the exterior surfaces of
torsion/toroidal elements. Such connections shall be continued to be referred
to as "external", as
opposed to "internal" connections, which include all means for connecting
torsion/toroidal elements
without the use of a coupling or other intermediate device. Torsion/toroidal
elements in an internally
connected combination of torsion elements is shown in the various views in
FIGS, 20-23.
For the purpose of the figures of this disclosure, it shall be understood that
all of the closely
proximate torsion/toroidal elements shown are connected in the region of their
closest proximity by
internal connection, unless otherwise indicated such as by connection with
couplings. Furthermore, for
the purpose of the rest of this disclosure, the lack of the appearance of an
external coupling at the point
of closest proximity of two torsion/toroidal elements shall not be taken to
mean that such elements are
not connectable by couplings, unless otherwise indicated. All connections thus
shown in the figures
may be internal or external as required by the application, even though not
indicated as such in a
particular figure. This convention is used in the examples of closed arrays
shown in FIGS. 24 and 25,
where the structural modules shown in FIGS. 20-23, form the framework of
toroidal torsion elements.
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By the convention herein established the circular array shown in FIGS. 24 and
25 is comprised
of toroidal torsion elements that are internally connected. However,
observation of an internal
connection, shown in the various views of FIGS. 26-33 between two toroids
formed as shown in FIGS.
24 and 25, demonstrates that internal connections between toroidal elements
may be achieved by the
use of external connections between their constituent toroidal elements. This
internal connection, rather
than being accomplished by coupling of the constituent toroidal elements of
the toroids, could have
been accomplished by internal connections between the torsion elements of
which the constituent
toroidal elements are constructed. Such internal connection may also be
mediated by additional
elements, torsional or otherwise. Furthermore, this process may be continually
replicated in a
self-similar manner on a smaller and smaller scale, down to a fundamental
torsion/toroidal element,
which may be a construction itself, but not necessarily by formation from a
circular array.
Arrays of angularly connected torsion/toroidal elements that themselves form
toroids may be
elliptical, as shown in FIGS. 35 and 36, or of any other shape, and have
various directional
characteristics, such as where lateral flexion of the resulting
torsion/toroidal element is converted to
torsional loading of its constituent toroidal torsion elements. Such varying
constructions of
torsion/toroidal elements may be combined as needed to meet extrinsic
structural requirements by
tubularly concentric connection between such torsion/torsion elements as shown
in FIG. 34.
Constructions from linear arrays of connected torsion/toroidal elements may
also be used to
form structural members such as rods, tubes, poles or posts, examples of which
are shown in FIGS. 42
and 43. These constructions may also have directional characteristics similar
to that of the circular
arrays discussed above, and may be included in compound tubularly concentric
constructions as shown
in FIG. 44.
Fundamental torsion/toroidal elements may be fabricated from what can be
considered solid
material, such as metal, polymers, foams, wood, or tubes of such material.
Such fundamental
torsion/toroidal elements may even be molded as torsion elements connected in
modules, partial or
whole, in the form of a framework of a torsion/toroidal element. Fabrication
of fundamental
torsion/toroidal elements may proceed from any standard manufacturing method,
such as winding,
extrusion, injection molding, layering of resins and fabrics, and fiber
compositing.
Torsion/toroidal elements may also be constructed from other torsion/toroidal
elements without
the use of connected arrays, such as the interlinkage shown in FIGS. 38-4 1,
formed by an apparent
braid of six toroids about a central axial toroid, all of which are identical
in dimension. The principal
characteristic of this type of torsion/toroidal element is that the apparent
braid of toroids rotates freely
about its circular axis impeded only by the internal friction of the toroids
in the braid and the frictional
forces between them.
It is possible to construct a torsion/toroidal element with a tube defined by
a closed spiral as
shown in FIG. 37. The principal characteristic of this type of toroidal
element is that the spiral tube
rotates freely about its axis, which is the curved line within and at the
center of the tube, impeded only
by internal friction. Such a toroidal tubular spiral can transmit torque about
the axis of the tube to any
point around the tube, and thereby distribute torsion stress throughout the
tubular spiral. Such a toroidal
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CA 02367090 2009-12-24
tubular spiral can be stabilized by torsion/toroidal elements connected to the
periphery of the tube as
shown in FIG. 37, so that the rotation of the spiral about its tubular axis is
regulated by the peripheral
torsion/toroidal elements. The spiral may itself be a array of connected
torsion/toroidal elements.
Virtually any shape of torsion/toroidal element is possible, as shown in FIG.
45, and may be
constructed by either appropriately shaped arrays of torsion/toroidal
elements, or fabricated as
fundamental torsion/toroidal elements.
The combination and orientations in which structural modules may be
constructed of
torsion/toroidal elements with the use of couplings is exemplified by the
categories shown in FIGS.
46-49. Examples ofcoupl ings that can be used to achieve such combinations and
orientations are shown
in FIGS. 50-52 for two-element connections, as shown in FIGS. 1-4 and 5-8; and
FIGS. 53-56 for the
types of connections shown in FIGS. 46-49.
The spline grip couplings and the corresponding spline collars of
torsion/toroidal elements are
among several other means contemplated for achieving fixed connections between
torsion/toroidal
elements and connecting couplings to transmit torsional loading. Examples of
such other means are
welding, gluing, fusing; the use of fasteners, such as pins, screws and
clamps; and the mating of the
coupling with a torsion/toroidal element of non-circular cross section.
Couplings may also be designed with various mechanical devices for integrated
securing
against movement of the torsion/toroidal element held. Some examples of such a
coupling is shown in
FIGS. 50-52, a split block coupling in which each of the parts of the block,
61 and 63 are fitted with
spline grips 62. The manner in which the coupling effects the connection is to
close the block sections
61, 63 around the spline collars of the torsion/toroidal elements to be
connected, and bind the block
with the compression band 65 tightened into the band groove 64 with a
tightening device 66, such as
a ratcheted roller on which the compression band is wound.
The coupling shown in FIGS. 53-56 is an open-end coupling in which each of the
end caps 83
and 87 and the main body of the coupling 81 are fitted with spline grips 82,
also demonstrating the type
of connection shown in FIG. 46. The manner in which the coupling effects the
connection is to close
end caps 83 and 87 around the spline collars of the torsion elements to be
connected, and bind the caps
to the main body block with the compression bands 85, which are locked to the
main body by the lock
pins 88 and tightened into the band grooves 84 with the tightening devices 86.
Torsion/toroidal elements shown in FIGS. 57 and 58 as 102, 104 with spline
collars 101, 103
are connectable by the couplings which have spline grips. The spline collars
may be integral to the
torsion/toroidal element, or may be attached by a means for bonding the spline
collar to the
torsion/toroidal elements or their components, by means fora mechanical
linkage within the spline
collar, or by or attachment or fastening to the spline collar. If a structural
element does not have spline
collars attached, other forms of connection are possible, such as with a
coupling with form grips, or by
internal connection with torsion/toroidal elements constituting such
structural elements.
A split-block coupling with form grips that uses structural foam that cures to
a permanent shape
after being compressed about the torsion/toroidal element, or a resilient
elastic cushion that grips the
torsion/toroidal element, is similar to that shown in FIGS. 50-52 where the
form grips would occupy
CA 02367090 2009-12-24
the location of the spline grips. The block sections of the coupling are then
locked in place by either
compression bands, as used on the split-block coupling shown in FIGS. 50-52,
or other means for
fastening the block together, such as screws or bolts.
The formation of structures using the system may proceed from constructions
which may be
referred to as "structural modules". One basic form of structural module is a
connected triangular array
of torsion/toroidal elements shown in FIGS. 59 and 60. One type of connected
linear array of the
triangular structural module is shown in FIGS. 61-63 which forms a rod, beam,
or post structure.
Connected arrays of such modules can form plate or deck structures. Another
basic structural module
is the connected cubic array of torsion/toroidal elements which is shown in
FIGS. 64 and 65, with a
connected linear array shown in FIGS. 66 and 67 forming rod, beam or post
structures. Connected
arrays of these structures can form plate, deck and joist structures as shown
in FIG. 68. A wide variety
of such structural modules is possible.
FIG. 69 is an example of the more complex structures, such as arches or
fibbing, formed when
the structural modules shown are connected in arrays. The closed circular
array in FIG. 70 may also
be another form of torsion/toroidal element.
Structures may also be formed from polygonal torsion/toroidal elements. The
preferred use of
such forms is as a body for a complex toroidal torsion element having internal
shafts for the absorption
of torsion stress, as shown in FIGS. 71-73 in one variation of which torsion
stress is absorbed by
multiple internal shafts 112. The shafts 112 are the point region of
connection with other structural
elements where they are not enclosed by the polygonal toroidal body I1 1 of
the toroidal torsion
element. The shafts 112 rotate on bearings 114 which are positioned by bearing
mounts 113 which are
fixedly attached to the body I11. A torque applied to turn the shaft 112 at
its point of connection will
induce a stress in the shaft 112 if the rotation of the shaft is restricted in
some way. In the polygonal
toroidal torsion element shown the shaft 112 to which the torque applied is
connected at both ends to
other shafts 112 by means of a universal joint 115 which transmits the torque
to the other shafts 112.
If the rotational motion of any of the shafts 112 are restricted, a torque on
the shaft 112 will induce a
torsional stress in the shaft 112, and the loading will be transmitted to
adjacent shafts 112 by means of
the universal joint 1 1 5 which connects them. Restriction of motion of a
shaft 112 can be provided for
by a rotation block 116, which is a means of fixing the end of a shaft 112 to
the body I I 1 or of
otherwise resisting rotation so that the end of the shaft 112 will not rotate
freely. Such a rotation block
116 may be applied to the ends of a shaft 112 to which the torque may be
applied where it is exposed
for connection to other structural elements. If there are no rotational blocks
the shafts will be free to
rotate. If such free shafts are further connected by universal joints around
the sides of the element, the
torque will transmitted from the region of application to the other region of
connection. Thus rotation
induced at one side of the element will be transmitted to the other side of
the element without
substantial constraint within the element. However, if the movement of the
shafts on one side of the
element are restricted, as by connection to another torsion structural
element, a torsional load will result
and transmitted equally along the connected shafts and torsion stress will be
induced therein.
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CA 02367090 2009-12-24
As with other torsion/toroidal elements, polygonal torsion/toroidal elements
may be connected
in an array to forma structural module as shown in FIGS. 74-77. The couplings
used maybe of the split
block type shown in FIGS. 50-52. Also as with other torsion/toroidal elements
a wide variation in form
and combination is possible with polygonal torsion/toroidal elements.
Polygonal torsion/toroidal
elements may range from the pentagonal to the nonogonal, with the number of
sides limited only by
the application. Polygonal torsion/toroidal elements may be combined with
other torsion/toroidal
elements to form complex torsion/toroidal elements with structural features
that can be tailored to any
structural application.
In addition to the connections between torsion/toroidal elements in which the
torsion/toroidal
elements remain outside of the peripheral tube of the other, previously
demonstrated in FIG. 34,
connections between torsion/toroidal elements where one element is within the
space surrounded by
the tube of another are a useful structural alternative to combination by
constructing torsion/toroidal
elements with coaxial tubes. Such a variation is shown in FIGS. 78 and 79
where the torsion/toroidal
elements are coaxial, and in FIGS. 80 and 81 where the axes of the
torsion/toroidal elements are
angulated with each other.
Certain basic structural forms that are difficult to achieve without
significant structural
disadvantage using conventional structural systems, are natural using the
present invention with no
structural disadvantages. Among these are spherical frameworks, as shown in
FIG. 84, and framework
towers, as shown in FIG. 86. Other examples of structures for which
torsion/toroidal elements are
similarly suitable are shown in FIGS. 82, 84, 85, 83, 87 and 88. All of the
structural forms demonstrated
are also useful in combination with each other, for reinforcement, aesthetics,
as well as in the design
of complex structures.
Fundamental to some of these structural forms is a structure in which the
horizontally
compressive support of its torsion/toroidal elements by each other results
from the application of
vertically downward loading on such torsion/toroidal elements. The structure,
which may be described
as a "horizontal arch", is formed by a plurality of torsion/toroidal elements
which are connected
side-to-side on or in an arc of a curve in the horizontal plane, with adjacent
members leaning together
toward the center of curvature of the arc, as shown in FIG. 99. The positions
of the bottom of such
torsion/toroidal elements are fixed at their base along the horizontal are
which describes the overall
shape of the horizontal arch. Said positions are determined by the placement
of each torsion/toroidal
element so that the sides thereof are in contact, directly, or indirectly
within a connection, above and
within the perimeter of said arc of the horizontal arch. The torsion/toroidal
members of the horizontal
arch are thus forced together horizontally under the application of vertically
downward loading near
the top of each of the compression members.
The horizontal arch may be employed as a part of successively vertically
layered constructions
as exemplified in FIGS. 100 and 101, in which each layer subjects the next
layer below to vertically
downward loading, such as in towers and multi-story buildings. The vertical
loading of the "horizontal
arch" layers forces the torsion/toroidal elements in each layer together
horizontally, and adds to the
horizontal cohesiveness of the structure, thus increasing its vertical load
bearing strength.
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CA 02367090 2009-12-24
With regard to spherical frameworks, an example of which is shown in FIG. 84,
another useful
structural form is possible with the replication of a section as shown in FIG.
85, and then connecting
it in an appropriate scale to a torsion/toroidal element forming the spherical
surface shown in FIG. 84.
The replication of the spherical section shown in FIG. 85 is applied once 141
and then again in smaller
scale 142 to the first. This application of the spherical section shown in
FIG. 85 can be made in
replication to all of the torsion/toroidal elements that form the sphere, and
yet again and again to all of
the torsion/toroidal elements that form successive replications, until a
practical limit is reached beyond
which the process has no structural efficacy. Such a replicated spherical
framework can be utilized as
an implosion resistant pressure vessel, in which pressures interior to the
vessel may be maintained at
a lower level than the pressure outside the vessel.
The use of torsion/toroidal elements may also be applied to create structures
which are
dynamic, with the constituent elements capable of movement by design, not only
by deflection as a
result of loading, but also by the active management of structural stresses.
Torsion/toroidal elements
may also be varied in shape dynamically so as to achieve alteration of the
shape, size and volume of
the structure of which they are constituent.
Generally, structures such as buildings, bridges, even automobiles, seacraft,
airframes and
spaceframes are considered to be static structures in accordance with their
manner of performance. That
is, the expectation of performance for such structures is that they respond to
the loads to which they
are subjected by adequate management of the stress on the materials used and
the means by which the
materials are connected to comprise the structure. There are some structures
that are built with moving
parts, such as a roof that opens by sliding or some other aperture that is
created by actuation, manual
or otherwise, as in the housing of an astronomical observatory. The present
invention contemplates its
application to create a dynamic structure, a structure in which the stress of
the materials and their
connections are managed by automated actuation of the coupling of
torsion/toroidal elements and the
shifting of the size and shape of structures by actuation of couplings.
An example of an actuated coupling which can perform a fundamental shifting of
shape is
shown in FIGS. 89-91, in which a motor 135 rotates a bearing 133 supported
spline grip 132 by the
rotational power it delivers to the drive 136 through the use of a
transmission 134. When the motor 135
is powered, the spline grips 132 are driven, in a controlled manner to rotate
and thus rotate a torsion
element held in a grip in relation to the body 131 of the coupling, as well as
any other torsion/toroidal
element held in the other spline grip 132. The manner in which the change in
shape of a 20 element
array can be effected using such actuated couplings is demonstrated in FIGS.
92 and 93. Couplings such
as those described above and shown in FIGS. 89-91 (but not shown in FIGS. 92
and 93) would connect
the torsion/toroidal elements, in the region of closest proximity of the
elements, and would cause the
angulation of the elements to change with sufficient precision so as to
achieve the exact shape and size
of the resulting structure required. Such a change of shape or size could be
directed to take place in an
organized way for all of the torsion/toroidal elements of the structure,
including replicated
substructures, which would result in a change of shape or size of the entire
structure. An example of
such an operation is shown in the schematic series of FIGS. 94-98, where the
frame of the surface of
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CA 02367090 2009-12-24
the prolate spheroid (FIG. 94) is transformed in stages (FIGS. 95-97) to the
frame of the surface of a
sphere (FIG. 98) by the changing of the shape of the constituent connected
eliptical torsion/toroidal
elements comprising the frame of the surface of the prolate sphere to more
circular torsion/toroidal
elements. This transformation results in a reduction of the volume bounded by
the framework. Other
transformations are possible, such as where the frame of surface of the sphere
is transformed to the
frame of the surface of an oblate spheroid, by the changing of the shape of
the constituent connected
torsion/toroidal elements comprising the frame of the surface of the sphere to
more elliptical
torsion/toroidal elements. This transformation would result in an increase in
the volume bounded by
the framework. A similar but isovolumetric pair of transformations is also
possible, as is the reversal
of the transformations described.
This aspect of the present invention thus demonstrated for spheroids is a
general property of
the structural system. This can be demonstrated further, schematically, with
the transformation of a
plane array of connected torsion/toroidal elements to a connected array of
torsion/toroidal elements in
the surface of a paraboloid, which can be accomplished by a calculated and
controlled changing of the
shape of the constituent connected torsion/toroidal elements comprising the
framework of the plane to
more elliptical torsion/toroidal elements, variably to form the framework of
the paraboloid. Such shape
shifting may be used to alter the shape or size of any array of elements: not
only those that provide the
framework of surfaces, but also the framework of solids.
The present invention may also be embodied in wheel and tire structures: as a
torsion/toroidal
wheel body, which has a toroidal shape without a central hub, and is the
component that rotates in
direct contact with the underlying surface or other wheels or rollers against
and on which it may be
operated or driven, as shown in FIG. 102; and as a tire structure that
includes a circular array of a
plurality of toroidal torsion support elements connected to form a toroidal
shape, as shown in FIGS.
103 and 104.
The structure of the toroidal wheel body is the framework of toroidal torsion
elements, as
shown in FIGS. 19, 87 and 88, is self- supporting, and may be constructed to
be flexible in order to
conform to irregularities of surfaces. In advanced forms of this embodiment of
the invention the
toroidal wheel body need not be circular, and its shape may be continuously
controlled by internal
actuators, such as those shown in FIGS. 89-9 1, to conform to the surface and
to the drive mechanism.
The toroidal wheel body framework may be used directly as a toroidal wheel
body, or sheathed in a
casing, as shown in FIG. 102. Without a casing, the framework toroidal wheel
body can operate on
mud, sand, snow, or other loose material constituting the underlying surface.
The tire structure may be used as an insert in a tire, as shown in FIG. 105,
incorporated directly
in the structure of the tire body or carcass, as shown in FIG. 103, or
connected to a central band, as
shown in FIG. 103, or hub structure for receiving an axle to form a complete
wheel structure. An object
of this embodiment of the invention is to provide a non-pneumatic support for
a wheel, as part of a
non-pneumatic tire or as part of the wheel itself, which can be assisted with
other pneumatic, fluidic,
or mechanical means with inclusions of those means within the tube of the
toroidal structure of the
invention. Although the present invention provides a non-pneumatic tire
support structure, it may also
19
CA 02367090 2009-12-24
be used in conjunction with pneumatic, fluid fil led, or other cushion
elements. The open interior of the
toroidal tube of the tire support structure also permits the inclusion of
other types of toroidal structures
within the toroidal tube, as shown in FIG. 34, and to allow for other
applications of the wheel and tire
structure.
The method of constructing any given toroidal element framework from other
toroidal
elements, such as the toroids shown in FIGS. 19, 24 and 25, is commenced with
the determination of
the component curvatures of the required toroidal shape followed by the
planning of the toroidal
framework. For example, a circular toroidal shape in one plane will have only
one radius of curvature,
the radius of the circular toroidal shape. A more complex toroidal shape, such
as the eliptical toroid
shown in FIGS. 35 and 36, will have more than one radius of curvature, the
number depending on the
number of elements to be used in the construction and the closeness of the
approximation to the
curvatures of the ellipse required. For such complex curved toroids the number
of constituent elements
and the radii of curvature will be interrelated. FIG. 106 is a schematic plan
for construction ofa toroidal
framework with smaller toroidal elements 151 showing the dimensional
quantities involved. For the
construction ofa given circular toroidal framework with a tube of
approximately circular cross section,
where the torus radius is RT, the toroidal tube radius is Tr, the number of
elements is n, the angle of
arc occupied by one element is Phi = 360/n, and the radius of a toroidal
element is r, the relations
among the angles and lengths labeled in FIG. 106 are as follows: RO = RT + Tr;
RI = RT - Tr; Ro =
RO - r; Ri = RI + r; Sin(Theta) = r/Ri; Sin(Psi) = r/Ro; Li = r/Tan(Theta); Lo
= r/Tan(Psi); x =
Ro*Sin(Phi - Psi), (*indicating multiplication between adjacent quantities);
Ld = Ro * Cos(Phi - Psi)
- Li; Tan(Alpha) _ (x - r)/Ld; Ej(dia) = (x - r)/Sin(Alpha). These relations
may be solved for Li, Ej(dia)
and Alpha, for a given RT, Tr, n and r, and together will be sufficient for
the plan of the circular
toroidal framework. This set of relations may be solved numerically by
standard mathematical methods,
and shall hereafter be referred to as the toroidal element framework planning
algorithm. The
construction of a toroidal framework involving multiple radii ofcurvature,
even in more than one plane,
maybe similarly planned by solving the relations for each circular framework
with which each segment
of the toroidal framework is approximated. The construction of the toroidal
element framework may
then be carried out by preparing a jig/mold for positioning the elements that
constitute the toroidal
framework from the specifications provided by the use of the toroidal element
framework planning
algorithm, positioning the constituent toroidal elements in the jig/mold, and
connecting the constituent
toroidal elements so positioned. For example, a simple jig/mold for a toroidal
framework in one plane
may be prepared by inserting a series of pins 152 in a flat surface on which a
plan as shown in FIG. 106
has been laid, the position of the pins outlining the positions of the
constituent elements 15 1. The
constituent elements may then be placed between the pins in the positions so
outlined and then
connected. The positions of the constituent elements may also be outlined by
triangular or rectangular
blocks, or other type of stop or clamp, or other means for positioning which
hold or define the angles
between the constituent elements in accordance with the plan for construction
of the toroidal
framework. Such other means of positioning also include depressions formed in
the plan surface which
could accomodate the constituent elements. The means for positioning may also
be adjustable to
CA 02367090 2009-12-24
conform to plans for construction of variously dimensioned toroidal frameworks
with varying
constituent elements. The connections may then be applied manually or with the
use of robotics with
the jig/mold containing the toroidal components stationary or in motion,
rotational or otherwise.
A jig/mold is also possible for non-flat surfaces using the same principles of
construction
therefor as described above, except that curvature in the additional dimension
would have to be taken
into account in setting the pins at the proper angles to the planes of
tangency to the non-flat surface to
properly position the toroidal elements to be connected.
The progression of construction of a dome with toroidal elements is
demonstrated for a dome
with interleaved layers of toroidal elements in FIGS. 99- 101. The method of
constructing such a dome
commences with the determination of the shape of the base of the dome. The
base may be circular or
that of a more complex curve which may be approximated by segments of
components with various
curvatures. FIGS. 107 and 108 are schematic diagrams for construction of a
dome framework with
toroidal elements 163 showing the dimensional quantities involved. The
vertical planes 161 and 162
are in the diagram only for the purpose of demonstrating the relationship
among the dimensions of the
dome framework and the toroidal elements of which it is constructed 163. For
the construction of a
given spherical dome framework where the number of base toroidal elements is
n, the sphere radius is
S, the horizontal element angle is f = 360/n, the declination of the base is
t, the vertical element angle
is e, and the element join angle is p, the relations among the angles and
lengths labeled in FIGS. 107
and 108 is as follows: for the element radius, R = S*Sin(e/2); for the upper
base radius, Ur = Cos(t +
e); for the upper base height, Uh = S*Sin (t + e); for the lower base radius,
Lr = S*Cos(t); for the lower
base height, Lh = S*Sin(t); and the relation between e and p is given by the
following simultaneous
equations:
e = 2 = ArcSin[Tan(0. 5.)g = Tan(45 - 0.5-p)] p = ArcCos 2 = S = Sin(0.5 = e)
~ [S = Cos(t+e) = Sin(0.5.1) + Cos(t) = Tan(0.5 =n]
This set of relations may be solved numerically by standard mathematical
methods, and shall hereafter
be referred to as the toroidal dome framework planning algorithm. The toroidal
dome framework
algorithm may be modified to assist in the planning of toroidal dome
frameworks of interleaved and
stacked layers for spheroid structures of virtually any base shape or
elevation.
The construction of the dome framework may then be carried out by connecting
the toroidal
elements of the sizes prescribed by the use of the toroidal dome framework
planning algorithm at the
locations on said toroidal elements indicated by the use of the toroidal dome
framework planning
algorithm, positioning the constituent toroidal elements according thereto,
which may be facilitated by
the use of a jig/mold from the specifications provided by the use of the
toroidal dome framework
planning algorithm, and connecting the constituent toroidal elements so
positioned. The connections
may then be applied manually or with the use of robotics. Such domes may also
be joined in opposition
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at their bases to form complete or partial spheroid constructions. In the case
of construction of towers,
such as those shown in FIGS. 87 and 88, the method of construction would
proceed similarly.
While the invention has been disclosed in connection with a preferred
embodiment, it will be
understood that there is no intention to Iimit the invention to the particular
embodiment shown, but it
is intended to cover the various alternative and equivalent constructions
included within the spirit and
scope of the appended claims.
Best Mode for Carrying Out Invention
The best mode is the preferred embodiment of the present invention and employs
toroidal
elements that are constructed with the use of torsion elements which are
toroidal in shape. The
preferred embodiment using toroidal torsion elements converts most
compression, tension and flexion
loading of constructions using the system to torsional loading of the torsion
elements of which the
constructions are comprised. The use of toroidal torsion elements makes
possible the construction of
toroids which are self-supporting.
Industrial Applicability
The use of the invention includes every conceivable structure: bridges,
towers, furniture,
aircraft, land and sea vehicles, appliances, instruments, buildings, domes,
airships, space structures and
vehicles, and planetary and space habitats. The magnitude I of such structures
contemplated and made
structurally and economically feasible by the system range from the minute to
the gigantic. The
structures that are possible with the use of the present invention are not
limited to any particular design,
and may even be freeform.
Some of the structural forms can be applied to construct buildings for
unstable foundation
conditions and which can survive foundation movement and failure.
The principal objects of the present invention are:
1. To provide a universal structural system for all types of immobile and
mobile structures
comprised of connected torsion/toroidal elements and having a high degree of
structural integrity,
strength, efficiency, and flexibility.
2. To provide a structural system in which structural loading in the form of
compression,
tension and flexion is converted to torsional loading of the torsion elements
of which it is constructed
so that such torsion elements bear the greatest part of the structural
loading.
3. To provide a structural system in which a structure constructed of
torsion/toroidal elements
is uniformly loaded so that the material of which such torsion elements are
composed is uniformly
stressed, thereby achieving a high strength-to-weight ratio.
4. To provide a structural system in which loads are well distributed over all
of the
torsion/toroidal elements.
5. To provide a structural system which is integrated and attractive in
appearance, allowing for
aesthetic design with self- supporting toroidal torsion elements in which
curved structures are
architecturally natural.
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CA 02367090 2009-12-24
6. To provide a structural system with dynamic shape shifting and dynamic
redistribution of
loading by adjustable and/or actuated structural connections while maintaining
structural strength and
integrity.
7. To provide a structural system which is economical, adaptable to automated
design,
automated fabrication, and efficient structurally and in ultimate assembly, in
its smallest elements and
its largest structural forms.
8. To provide a structural system in which all structural characteristics of
all elements can be
precisely predicted, designed, and known.
9. To provide a structural system in which conventional structural elements
such as beams,
joists, decks, trusses, etc. can be constructed of torsion/toroidal elements
and incorporated in
conventional structures as conventional structural elements.
10. To provide a structural system in which various torsion/toroidal elements
may be
standardized and databased with all dimensional, material and loading
characteristics so as to provide
for automated selection of components for structural design therewith.
11. To provide a structural system that is compatible with conventional
structural systems.
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