AMENDED CLAIMS
[received by the International Bureau on 27 September 2000 (27 09 00), original claims 1-61 replaced by new claims 1-154 (1 1 pages)]
Claim 1 A structural system comprising
(a) a plurality of torsion/toroidal elements, and
(b) means for connecting the torsion/toroidal elements
Claim 2 The structural system of claim 1 m which the torsion/toroidal elements are held firmly in position with respect to each other in a connection
Claim 3 A structural system comprising a plurality of torsion/toroidal elements which are connected to form a structure
Claim 4 The structural system of claim 3 in which the torsion/toroidal elements are held firmly in position with respect to each other in one or more connections
Claim 5 A structural system compπsing a plurality of torsion/toroidal elements which are connected so that the torsion/toroidal elements are held firmly in position in one or more of the connections
Claim 6 A structural system of torsion elements comprising
(a) a plurality of torsion elements which function with torsion as the principal load bearing mode, and
(b) means for connecting 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 said one or more of the torsion elements is connected, and so that the torsional load on said one or more of the other of the torsion elements is in the opposite direction to that of said one of the torsion elements Claim 7 The structural system of claim 6 in which the torsion elements are held firmly in position with respect to each other in a connection
Claim 8 The structural system of claim 7 in which the means for connecting torsion elements is adjustable so that the position of one or more of the torsion elements connected by said means for connecting may be changed with respect to other torsion elements connected to said one or more of the torsion elements by said means for connecting
Claim 9 The structural system of claim 6 in which the means for connecting torsion elements is such that a torsion element in a connection will not have substantial movement in the connection
Claim 10 The structural system of claim 6 in which the means for connecting torsion elements is such that a torsion element having been positioned in a connection will not have substantial movement in the connection
Claim 1 1 The structural system of claim 6 in which the means for connecting torsion elements is such that a torsion element having been positioned in a connection by adjustment of the connection will not have substantial movement in the connection Claim 12 The structural system of claim 6 in which the means for connecting torsion elements is such that any motion of a torsion element in a connection will be regulated by the connection
Claim 13 The structural system of claim 6 in which the means for connecting torsion elements is such that a torsion element may be moved in a connection and that such movement will be regulated by the connection
Claim 14 The structural system of claim 6 in which the means for connecting torsion elements is such that a torsion element may be moved in a connection and that such movement will be regulated by the connection so that the torsion element will not thereafter have substantial movement in the connection except as regulated by the connection
Claim 15 The structural system of claim 6 in which the means for connecting torsion elements is such that after a torsion element is moved in a connection such movement will be regulated by the connection so that the torsion element will not have substantial movement in the connection except as regulated by the connection
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Claim 16 The structural system of claim 6 in which the means for connecting torsion elements is such that after a torsion element is moved by a connection in the connection such movement will be regulated by the connection so that the torsion element will not have substantial movement m the connection unless again moved by the connection
Claim 17 The structural system of claim 6 in which the means for connecting torsion elements is such that a torsion element may be moved by a connection and then held by the connection in the position resulting from such movement so that the torsion element will not have substantial movement in the connection unless again moved by the connection
Claim 18 The structural system of claim 6 which the means for connecting torsion elements is actuated, so that one or more torsion elements may be mo\ ed by a connection and then held by the connection in the position resulting from such movement so that the torsion element will not have substantial movement in the connection unless again moved by the connection
Claim 19 A structural system of torsion elements for constructing frameworks of all sizes, comprising a plurality of torsion elements which function with torsion as the principal load bearing mode connected so 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 said one or more of the torsion elements is connected
Claim 20 The structural system of claim 19 in which the torsion elements are held firmly in position with respect to each other in one or more connections
Claim 21 The structural system of claim 20 in which one or more connections are adjustable so that the position of one or more of the torsion elements in such a connection may be changed in such a connection with respect to other torsion elements in such a connection
Claim 22 The structural system of claim 19 in which the connections are such that a torsion element in a connection will not have substantial movement in the connection
Claim 23 The structural system of claim 19 in which the connections are such that a torsion element having been positioned in a connection will not have substantial movement in the connection
Claim 24 The structural system of claim 19 in which the connections are such that a torsion element having been positioned in a connection by adjustment of the connection will not have substantial movement in the connection
Claim 25 The structural system of claim 19 m which the connections are such that any motion of a torsion element in a connection will be regulated by the connection
Claim 26 The structural system of claim 19 in which the connections are such that a torsion element may be moved in a connection and that such movement will be regulated by the connection
Claim 27 The structural system of claim 19 in which the connections are such that a torsion element may be moved in a connection and that such movement will be regulated by the connection so that the torsion element will not thereafter have substantial movement in the connection except as regulated by the connection
Claim 28 The structural system of claim 19 in which the connections are such that after a torsion element is moved in a connection such movement will be regulated by the connection so that the torsion element will not have substantial movement in the connection except as regulated by the connection
Claim 29 The structural system of claim 19 in which the connections are such that after a torsion element is moved by a connection in the connection such movement will be regulated by the connection so that the torsion element will not have substantial movement m the connection unless again moved by the connection
Claim 30 The structural system of claim 19 in which the connections are such that a torsion element may be moved by a connection and then held by the connection in the position resulting from such movement so that the torsion element will not have substantial movement in the connection unless again moved by the connection
Claim 31 Structural system of claim 19 in which one or more connections are actuated so that one or more torsion elements may be moved by a connection and then held by the connection in the position resulting from such movement so that the torsion element will not have substantial movement in the connection unless again moved by the connection
Claim 32 The structural system of claim 19 in which the torsion elements are connected so that the torsional load on said one or more of the other of the torsion elements is in the opposite direction to that of said one of the torsion elements
Claim 33 A structural system for constructing frameworks of all sizes, comprising a plurality of torsion elements which function principally by torsional load bearing, which are connected so 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 said one or more of the torsion elements is connected
Claim 34 The structural system of claim 33, in which one or more connections are adjustable so that the position of one or more of the torsion elements in such a connection may be changed in such a connection with respect to other torsion elements in such a connection
Claim 35 The structural system of claim 33, in which the connections are such that a torsion element in a connection will not have substantial movement in the connection
Claim 36 The structural system of claim 33, in which the connections are such that a torsion element having been positioned in a connection will not have substantial movement in the connection
Claim 37 The structural system of claim 33, in which the connections are such that a torsion element having been positioned in a connection by adjustment of the connection will not have substantial movement in the connection
Claim 38 The structural system of claim 33, in which the connections are such that any motion of a torsion element m a connection will be regulated by the connection
Claim 39 The structural system of claim 33, in which the connections are such that a torsion element may be moved in a connection and that such movement will be regulated by the connection
Claim 40 The structural system of claim 33, in which the connections are such that a torsion element may be moved in a connection and that such movement will be regulated by the connection so that the torsion element will not thereafter have substantial movement in the connection except as regulated by the connection
Claim 41 The structural system of claim 33, in which the connections are such that after a torsion element is moved in a connection such movement will be regulated by the connection so that the torsion element will not have substantial movement in the connection except as regulated by the connection
Claim 42 The structural system of claim 33, in which the connections are such that after a torsion element is moved by a connection in the connection such movement will be regulated by the connection so that the torsion element will not have substantial movement in the connection unless again moved by the connection
Claim 43 The structural system of claim 33, in which the connections are such that a torsion element may be moved by a connection and then held by the connection in the position resulting from such movement so that the torsion element will not have substantial movement in the connection unless again moved by the connection
Claim 44 The structural system of claim 33, in which one ormore connections are actuated so that one ormore torsion elements may be moved by a connection and then held by the connection in the position resulting from such movement so that the torsion element will not have substantial movement in the connection unless again moved by the connection
Claim 45 The structural system of claim 33 in which the torsion elements are connected so that the torsional load on said one or more of the other of the torsion elements opposes the torsional load on said one of the torsion elements
Claim 46 A method for constructing frameworks of all sizes with torsion elements comprising connecting a plurality of torsion elements to form a structure so that the torsional load on one or more of the torsion elements is transmitted to the other torsion elements to which said one of the torsion elements is connected
Claim 47 The method for constructing frameworks of claim 46 wherein the torsion elements are connected so that the torsional load on said other torsion elements is in the opposite direction to that of said one or more of the torsion elements
Claim 48 The method for constructing frameworks of claim 46 wherein said structure is formed according to a plan for said structure
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Claim 49 The method for constructing frameworks of claim 46 further comprising a first step of fabricating a plurality of torsion elements
Claim 50 A system for constructing frameworks of all sizes, comprising
(a) a plurality of torsion elements, and
(b) means for connecting 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 said one or more of the torsion elements is connected Claim 51 A structural system of toroidal elements for structural frameworks comprising
(a) a plurality of toroidal elements, and
(b) means for connecting the toroidal elements, so that a structural framework is formed
Claim 52 The structural system of claim 51 in which the toroidal elements are held firmly in position with respect to each other
Claim 53 The structural system of claim 52 in which the means for connecting toroidal elements is adjustable so that the position of one or more of the toroidal elements connected by said means for connecting may be changed with respect to other toroidal elements connected to said one or more of the toroidal elements by said means for connecting
Claim 54 The structural system of claim 51 in which the means for connecting toroidal elements is such that a toroidal element in a connection will not have substantial movement in the connection
Claim 55 The structural system of claim 51 in which the means for connecting toroidal elements is such that a toroidal element having been positioned in a connection will not have substantial movement in the connection
Claim 56 The structural system of claim 51 in which the means for connecting toroidal elements is such that a toroidal element having been positioned in a connection by adjustment of the connection will not have substantial movement in the connection
Claim 57 The structural system of claim 51 in which the means for connecting toroidal elements is such that any motion of a toroidal element in a connection will be regulated by the connection
Claim 58 The structural system of claim 51 in which the means for connecting toroidal elements is such that a toroidal element may be moved in a connection and that such movement will be regulated by the connection
Claim 59 The structural system of claim 51 in which the means for connecting toroidal elements is such that a toroidal element may be moved in a connection and that such movement will be regulated by the connection so that the toroidal element will not thereafter have substantial movement in the connection except as regulated by the connection
Claim 60 The structural system of claim 51 in which the means for connecting toroidal elements is such that after a toroidal element is moved in a connection such movement will be regulated by the connection so that the toroidal element will not have substantial movement in the connection except as regulated by the connection
Claim 61 The structural system of claim 51 in which the means for connecting toroidal elements is such that after a toroidal element is moved by a connection in the connection such movement will be regulated by the connection so that the toroidal element will not have substantial movement in the connection unless again moved by the connection
Claim 62 The structural system of claim 51 in which the means for connecting toroidal elements is such that a toroidal element may be moved by a connection and then held by the connection in the position resulting from such movement so that the toroidal element will not have substantial movement in the connection unless again moved by the connection
Claim 63 The structural system of claim 51 in which the means for connecting toroidal elements is actuated, so that one or more toroidal elements may be moved by a connection and then held by the connection in the position resulting from such movement, so that the toroidal element will not have substantial movement in the connection unless again moved by the connection
Claim 64 A structural system of toroidal elements for constructing non-domical and non-spherical frameworks, compπsing a plurality of toroidal elements which are connected to form a structural framework
Claim 65 The structural system of claim 64 in which the toroidal elements are held firmly in position with respect to each other
Claim 66 The structural system of claim 65 in which one or more connections are adjustable so that the position of one or more
of the toroidal elements in such a connection may be changed in such a connection with respect to other toroidal elements in such a connection
Claim 67 The structural system of claim 64 in which the connections are such that a toroidal element in a connection will not have substantial movement in the connection
Claim 68 The structural system of claim 64 in which the connections are such that a toroidal element having been positioned in a connection will not have substantial movement in the connection
Claim 69 The structural system of claim 64 in which the connections are such that a toroidal element having been positioned in a connection by adjustment of the connection will not have substantial movement in the connection
Claim 70 The structural system of claim 64 in which the connections are such that any motion of a toroidal element in a connection will be regulated by and in the connection
Claim 71 The structural system of claim 64 in which the connections are such that a toroidal element may be moved in a connection and that such movement will be regulated by the connection
Claim 72 The structural system of claim 64 in which the connections are such that a toroidal element may be moved in a connection and that such movement will be regulated by the connection so that the toroidal element will not thereafter have substantial movement in the connection except as regulated by the connection
Claim 73 The structural system of claim 64 in which the connections are such that after a toroidal element is moved in a connection such movement will be regulated by the connection so that the toroidal element will not have substantial movement in the connection except as regulated by the connection
Claim 74 The structural system of claim 64 which the connections are such that after a toroidal element is moved by a connection m the connection such movement will be regulated by the connection so that the toroidal element will not have substantial movement in the connection unless again moved by the connection
Claim 75 The structural system of claim 64 in which the connections are such that a toroidal element may be moved by a connection and then held by the connection in the position resulting from such movement so that the toroidal element will not have substantial movement in the connection unless again moved by the connection
Claim 76 The structural system of claim 64 in which one or more connections are actuated so that one or more toroidal elements may be moved by a connection and then held by the connection in the position resulting from such movement so that the toroidal element will not have substantial movement m the connection unless again moved by the connection
Claim 77 The structural system of claim 64 m which the non-domical and non-spherical framework structures may range in size from nanostructures to an extremely large scale
Claim 78 A structural system of toroidal elements for tower, domical and spherical structures comprising
(a) a plurality of toroidal elements which are connected to form a plurality of level layers of toroidal elements in closed courses, wherein the connections between said plurality of toroidal elements are not the result of interlinking or intersection of toroidal elements,and
(b) means of connecting said level layers of connected toroidal elements in a stack, so that the framework of a tower, domical or spheπcal structure is formed
Claim 79 The structural system of claim 78 wherein the oπentation of said level layers is horizontal
Claim 80 The structural system of claim 78 wherein each of said level layers has the same number of toroidal elements
Claim 81 The structural system of claim 78 wherein the toroidal elements comprising said level layers have the same size within each layer
Claim 82 The structural system of claim 78 wherein each of said level layers has the same size and shape
Claim 83 The structural system of claim 78 wherein the toroidal elements comprising said level layers have the same size from layer to layer
Claim 84 The structural system of claim 78 wherein said means of connecting said level layers is such that each toroidal
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element comprising one of said level layers in the stack can be connected to one toroidal element comprising each of the other of said level layers in the stack which are adjacent to said one of said level layers
Claim 85 The structural system in claim 78 wherein one or more of said level layers have a conical shape
Claim 86 The structural system in claim 78 wherein the size of one or more of said level layers is smaller than another of said level layers which are adjacent to said one or more of said layers
Claim 87 The structural system in claim 78 wherein the size of all the toroidal elements comprising one of said level layers is smaller than the size of the toroidal elements comprising another of said level layers which are adjacent to said one of said level layers
Claim 88 The structural system in claim 78 wherein each of said level layers have a conical shape, and the solid angle of such conical shapes is the same from layer to layer in the stack
Claim 89 The structural system in claim 78 wherein each of said level layers have a conical shape, and the solid angle of such conical shapes increases from the first of said level layers in the stack to the last of said level layers in the stack
Claim 90 The structural system of Claim 78 wherein a spherical structure is formed by connection of the level layers of the bases of two domical structures which are in opposite polar orientation
Claim 91 The structural system of Claim 78 further compπsing one or more intermediate latitudinal toroidal elements, wherein a spherical structure is formed by connection of the level layers of the bases of two domical structures which are in opposite polar orientation to said one or more intermediate latitudinal toroidal elements
Claim 92 The structural system of Claim 78 further comprising one or more intermediate latitudinal toroidal elements, wherein any two of said level layers which are adjacent in the stack are connected to each other by being connected to said one or more intermediate latitudinal toroidal elements
Claim 93 The structural system of Claim 78 further comprising one or more intermediate longitudinal toroidal elements, wherein the toroidal elements comprising the structure formed by the stacking of said level layers are connected to said one or more intermediate longitudinal toroidal elements
Claim 94 The structural system of Claim 78 wherein the level layers which are adjacent in the stack are arranged so that each toroidal element comprising any one of said adjacent level layers can be connected to one of the toroidal elements compπsing each of the other of said adjacent level layers
Claim 95 The structural system of Claim 78 wherein said means of connecting said level layers is such that each toroidal element compπsing one of said level layers in the stack can be connected to two toroidal element compπsing each of the other of said level layers in the stack which are adjacent to said one of said level layers
Claim 96 The structural system of Claim 78 wherein the level layers which are adjacent in the stack are interleaved so that each toroidal element comprising any one of said adjacent level layers can be connected to two of the toroidal elements comprising each of the other of said adjacent level layers with which it is interleaved
Claim 97 The structural system of Claim 78 wherein a spherical structure is formed by connection of the level layers of the bases of two dome structures which are in opposite polar orientation, wherein the level layers of said bases are interleaved
Claim 98 A spheπcal structure of toroidal elements compπsing a plurality of toroidal elements of substantially the same size arranged in the planes of the surfaces of an imaginary regular poyhedron, with most of said toroidal elements being connected to others of said toroidal elements where said toroidal elements are nearly tangent to one another near the midpoints of the edges of the imaginary regular polyhedron
Claim 99 The spherical structure of Claim 98 wherein said plurality of toroidal elements lie in the surface of the spheπcal structure
Claim 100 The spherical structure of Claim 98 further compπsing one or more additional toroidal elements connected to said plurality of toroidal elements, wherein said one or more additional toroidal elements lie m the surface of the spherical structure, so that said one or more additional toroidal elements bπdge one or more spaces between said plurality of toroidal elements in
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the surface of the spherical structure
Claim 101 The spherical structure of Claim 98 further compπsing one or more additional toroidal elements connected to said plurality of toroidal elements, wherein said one or more additional toroidal elements are within the spherical structure, so that said one or more additional toroidal elements reinforce the spherical structure from within
Claim 102 A toroidal element framework planning algorithm, which comprises the diagram shown in FIG 106 showing the geometric relations among the angles and lengths, and the following relations to be solved by standard mathematical procedures for the quantities Li, Ej(dιa) and Alpha, for a given RT, Tr, n and r, wherein 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 RO = RT + Tr, RI = RT - Tr, Ro = RO - r, Ri = RI + r, Sιn(Theta) = r/Ri, Sιn(Psι) = r/Ro, Li = r/Tan(Theta), Lo = r/Tan(Psι), x = Ro * Sιn(Phι - Psi), (* indicating multiplication between adjacent quantities), Ld = Ro * Cos(Phι - Psi) - Li,
Tan(Alpha) = (x - r)/Ld, Ej(dιa) = (x - r)/Sιn(Alpha)
Claim 103 A method of constructing any given toroidal element framework from other toroidal elements which compπses determining the component curvatures of the required toroidal shape, planning the toroidal framework using the toroidal element framework planning algorithm, positioning the constituent toroidal elements as prescribed by said planning algorithm, and connecting the constituent toroidal elements so positioned
Claim 104 The methods of claims 103 in which a third step is added following the first two steps, which comprises constructing ajig/mold for positioning the toroidal elements from the specifications provided by the use of said planning algoπthm
Claim 105 The methods of claims 103 in which a third step is added following the first two steps, which comprises constructing the toroidal elements of the sizes prescribed by the use of said planning algoπthm
Claim 106 Ajig/mold for positioning torsion/toroidal elements for construction of a toroidal element framework compπsing
(a) a surface plate, and
(b) means for positioning torsion toroidal elements on the surface plate, so that the torsion/toroidal elements are held in the positions so outlined for m order to be connected to form a toroidal element
Claim 107 Ajig/mold for positioning torsion/toroidal elements for construction of a toroidal element framework compπsing
(a) a surface plate, and
(b) stops attached to the surface plate outlining the positions of the torsion/elements on the surface plate, so that the torsion/toroidal elements are held in the positions so outlined for in order to be connected to form a toroidal element Claim 108 The jig/mold of claim 106 or 107 m which the specifications for positioning of the torsion/toroidal elements is provided by the use of the toroidal element framework planning algoπthm
Claim 109 A toroidal dome framework planning algoπthm which compπses the diagrams shown in FIGS 107 and 108 showing the geometric relations among the angles and lengths, and the following relations to be solved by standard mathematical procedures for the quantities e and p, and thus all dependent quantities, wherein the number of base toroidal elements is n, the sphere radius is S, the hoπzontal 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 * Sm(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 * Sιn(t), and the relation between e and p is given by the following simultaneous equations
e = 2 • ArcSin[Tan(θ.5 • /) t Tan(45 - 0.5 * p)]
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t) - Cos(t) ♦ Tan(θ.5 • /)]J
Claim 1 10 A method of construction of a dome with toroidal elements which comprises determining the shape of the dome and the shape of the base of the dome, planning the toroidal dome framework using a toroidal dome framework planning algorithm, positioning the constituent toroidal elements as prescribed by said planning algoπthm, and connecting the toroidal elements so positioned at the locations on said toroidal elements indicated by the use of said planning algoπthm Claim 111 A method for providing structures utilizing torsion/toroidal elements, which comprises fabricating a plurality of torsion/toroidal elements, and connecting the torsion/toroidal elements so that a structure is formed
Claim 112 A horizontal arch comprising a plurality of toroidal compression members which are connected side-to-side, in an unbroken series, in an arc of a curve in a horizontal plane, and in a level layer, all of the compression members being either laterally connected to an adjacent compression member or to a fixed structure at the termini of the series, wherein the positions of the bottoms of all such compression members are fixed along the arc, wherein adjacent compression members lean together toward the center of curvature of the arc, so that the sides of adjacent compression members are in contact above and within the perimeter of the arc, wherein horizontal cohesiveness of the compression members is augmented by the application of vertically downward loading on each compression member, and w herein vertical load bearing of the compressive members is augmented by the hoπzontal cohesiveness of the compression members against each other
Claim 113 (Amended) A horizontal arch comprising a plurality of planar toroidal compression members which are connected side-to-side, in an unbroken seπes, in an arc of a curve in a hoπzontal plane, and in a level layer, all of the compression members being either laterally connected to an adjacent compression member or to a fixed structure at the termini of the series, wherein the positions of the bottoms of all such compression members are fixed along the arc, wherein adjacent compression members lean together toward the center of curvature of the arc, so that the sides of adjacent compression members are in contact above and within the perimeter of the arc, wherein horizontal cohesiveness of the compression members is augmented by the application of vertically downward loading on each compression member, and wherein vertical load beaπng of the compressive members is augmented by the horizontal cohesiveness of the compression members against each other Claim 114 A hoπzontal arch comprising a plurality of torsion toroidal compression members which are connected side-to-side, m an unbroken series, in an arc of a curve in a horizontal plane, and in a level layer, all of the compression members being either laterally connected to an adjacent compression member or to a fixed structure at the termini of the series, wherein the positions of the bottoms of all such compression members are fixed along the arc, wherein adjacent compression members lean together toward the center of curvature of the arc, so that the sides of adjacent compression members are in contact above and within the peπmeter of the arc, wherein horizontal cohesiveness of the compression members is augmented by the application of vertically downward loading on each compression member, and wherein vertical load beaπng of the compressive members is augmented by the hoπzontal cohesiveness of the compression members against each other
Claim 115 A hoπzontal arch comprising a plurality of planar compression members which are connected side-to-side, in an unbroken series, in an arc of a curve in a horizontal plane, and in a level layer, all of the compression members being either laterally connected to an adjacent compression member or to a fixed structure at the termini of the series, wherein the positions of the bottoms of all such compression members are fixed along the arc, wherein adjacent compression members lean together toward the center of curvature of the arc, so that the sides of adjacent compression members are in contact above and within the perimeter of the arc, wherein horizontal cohesiveness of the compression members is augmented by the application of vertically downward loading on each compression member, and wherein vertical load beaπng of the compressive members is augmented by the hoπzontal cohesiveness of the compression members against each other
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Claim 116 The horizontal arch as in any one of claims 1 12-1 15 wherein the magnitude of vertical downward loading on each compression member is approximately the same for all of the compression members
Claim 117 The horizontal arch as in any one of claims 1 12-115 wherein the tops of the compression members comprising the horizontal arch he in a single hoπzontal plane
Claim 118 The horizontal arch as in any one of claims 112-115 wherein the size of the compression members comprising the horizontal arch is the same
Claim 119 The horizontal arch as in any one of claims 1 12-115 wherein the shape of the compression members comprising the horizontal arch is the same
Claim 120 The horizontal arch as in any one of claims 112-1 15 wherein the internal structure of the compression members comprising the horizontal arch is the same
Claim 121 The horizontal arch as in any one of claims 112-115 wherein the arc is a closed completely outwardly convex curve with no straight segments
Claim 122 A toroidal wheel comprising a toroidal framework of torsion elements, further compnsing
(a) a plurality of torsion elements which function with torsion as the principal load beaπng mode, and
(b) means for connecting the torsion elements so that the torsional load on one of the torsion elements is transmitted to one or more of the other of the torsion elements to which said one of the torsion elements is connected, so that the toroidal framework is self-supporting Claim 123 (Amended) The toroidal wheel of claim 122 wherein the toroidal framework of torsion elements is not supported by any spokes, hub, or wheel disk
Claim 124 The toroidal wheel of claim 122 wherein the toroidal wheel is operated in a mount/dπve
Claim 125 The toroidal wheel of claim 122 further compπsing support elements integrated with the toroidal framework of torsion elements
Claim 126 The toroidal wheel of claim 122 further compπsing a means for operating the toroidal wheel so that it can rotate m contact with a surface against which it is operated
Claim 127 The toroidal wheel of claim 122 further compnsing a means for driving the toroidal wheel in rotation in contact with a surface against which it is operated Claim 128 A toroidal wheel comprising a toroidal framework of torsion elements, further compπsing
(a) a plurality of torsion elements which function with torsion as the principal load beaπng mode, and
(b) means for connecting the torsion elements so that the torsional load on one of the torsion elements is transmitted to one or more of the other of the torsion elements to which said one of the torsion elements is connected, wherein the toroidal framework is not supported by any spokes, hub, or wheel disk
Claim 129 The toroidal wheel of claim 128 wherein the toroidal framework of torsion elements is self-supporting
Claim 130 (Amended) The toroidal wheel as in any one of claims 122 and 128 wherein the toroidal framework of torsion elements is sheathed in a casing with a surface which has gear teeth
Claim 131 A toroidal wheel compπsing a toroidal framework of torsion elements, further compπsing
(a) a plurality of torsion elements which function with torsion as the pnncipal load bearing mode, and
(b) means for connecting the torsion elements so that the torsional load on one of the torsion elements is transmitted to one or more of the other the torsion elements to which said one of the torsion elements is connected, wherein the toroidal framework is self- supporting and is not supported by any spokes, hub, or wheel disk Claim 132 The toroidal wheel as in any one of claims 122, 128, and 131 wherein the shape of the toroidal framework of torsion elements is controlled by internal actuators
Claim 133 The toroidal wheel as in any one of claims 122, 128, and 131 wherein the shape of the toroidal framework of torsion elements is controlled by one or more actuators in the connections between the torsion elements of the toroidal wheel
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framework, said actuators being able to change the angular relationship between connected torsion elements
Claim 134 The toroidal wheel as in any one of claims 122, 128, and 131 wherein the toroidal framework of torsion elements is sheathed in a casing with a friction surface
Claim 135 A wheel and tire structure comprising a plurality of torsion framework components comprising
(a) a plurality of torsion elements which function with torsion as the principal load bearing mode, and
(b) means for connecting the torsion elements so that the torsional load on one of the torsion elements is transmitted to one or more of the other of the torsion elements to which said one of the torsion elements is connected, said torsion framework components being connected in an array to form a toroidal shape, and a means for connecting said torsion framework components so that loading of the wheel and tire structure loads the torsion framework components Claim 136 The wheel and tire structure of Claim 135 wherein the torsion framework components are embedded in a common matrix of resilient elastomeπc material
Claim 137 The wheel and tire structure of Claim 135 wherein the torsion framework components are attached to a common band within the hole of such toroidal array
Claim 138 The wheel and tire structure of Claim 135 wherein the torsion framework components are attached to a central hub structure within the hole of such toroidal array
Claim 139 The wheel and tire structure of Claim 135, further compπsing one or more toroidal support components which are not torsion framework components, said one or more toroidal support components being connected in said array with said torsion framework components
Claim 140 The wheel and tire structure of Claim 139, further compπsing a means for connecting said one or more toroidal support components with said torsion framework components so that loading of the wheel and tire structure loads said one or more toroidal support components
Claim 141 The wheel and tire structure of Claim 139 wherein said one or more toroidal support components are embedded in a common matrix of resilient elastomeπc material together with said torsion framework components Claim 142 The wheel and tire structure of Claim 139 wherein said one or more toroidal support components are attached to a common band together with said torsion framework components
Claim 143 The wheel and tire structure of Claim 139 wherein said one or more toroidal support components are attached to a central hub structure together with said torsion framework components Claim 144 A wheel and tire structure, compπsing a plurality of toroidal support components one or more which is a resilient self-supporting toroidal framework of connected torsion elements, and a means for connecting said toroidal support components in an array to form a toroidal shape Claim 145 The wheel and tire structure of Claim 144 wherein the means for connecting said toroidal support components is such that loading of the wheel and tire stucture loads the toroidal support components
Claim 146 The wheel and tire structure of Claim 144 wherein each toroidal support component is embedded in a common matrix of resilient elastomeπc mateπal
Claim 147 The wheel and tire structure of Claim 144 wherein each toroidal support component is embedded in a common matrix of resilient elastomeπc material so that loading of the wheel and tire stucture loads the toroidal support components Claim 148 The wheel and tire structure of Claim 144 wherein each toroidal support component is attached to a common band Claim 149 wheel and tire structure of Claim 148 wherein the common band is within the hole of such toroidal array Claim 150 The wheel and tire structure of Claim 144 wherein each toroidal support component is attached to a common band
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so that loading of the wheel and tire stucture loads the toroidal support components
Claim 151 The wheel and tire structure of Claim 144 wherein each toroidal support component is attached to a central hub structure
Claim 152 The wheel and tire structure of Claim 151 wherein the central hub structure is within the hole of such toroidal array
Claim 153 The wheel and tire structure of Claim 144 wherein each toroidal support component is attached to a central hub so that loading of the wheel and tire stucture loads the toroidal support components
Claim 154 In a wheel and tire structure comprised of a toroid- forming array of connected radial toroidal support components, a toroidal support component comprising a resilient self-supporting toroidal framework of connected torsion elements
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