US2006135288A1PendingUtilityA1
Great-circle geodesic dome
Est. expiryDec 22, 2024(expired)· nominal 20-yr term from priority
Inventors:Randell L. Mills
E04B 1/3211E04B 7/105
53
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Claims
Abstract
The present invention is a structural system and a method of fabricating the system comprised of finite elements called basis elements such as great circles or partial great circles to form a great-circle geodesic sphere, dome, or arch called a great sphere, dome, and arch, respectively. The structure is generated by forming a pattern of the basis element rotated at incremental angles about a rotational axis from an initial position to define a so-called primary component orbitsphere-cvf. The primary component orbitsphere defines a stationary pattern as well as a structural element called a secondary component orbitsphere-cvf that is constructed according to the pattern of the primary orbitsphere-cvf. The secondary component orbitsphere-cvf is initially oriented at the initial position and is incrementally rotated about the rotational axis to form the great-sphere-type structure.
Claims
exact text as granted — not AI-modified1 . A geodesic structure comprising:
a plurality of circle elements defining a geodesic structure, the circle elements having substantially the same diameter bound to one another such that the forces are equalized on the geodesic structure.
2 . A geodesic structure according to claim 1 , wherein the circle elements are half circles and the geodesic structure comprises a dome.
3 . A geodesic structure according to claim 1 , wherein the circle elements are full circles and the geodesic structure comprises a sphere.
4 . A geodesic structure according to claim 1 , wherein the geodesic structure comprises an arch.
5 . A geodesic structure according to claim 1 , wherein no more than two circle elements are aligned on an axis.
6 . A geodesic structure according to claim 1 , wherein the circle elements are aligned according to Eqs. (1-71).
7 . A geodesic structure according to claim 1 , wherein the circle elements all have the same diameter.
8 . A geodesic structure according to claim 1 , wherein the circle elements overlap one another.
9 . A geodesic structure according to claim 1 , wherein the circle elements are intertwined with one another.
10 . A geodesic structure according to claim 1 , wherein the circle elements are arranged according to the structure of a primary component orbitsphere-cvf wherein each circle element of the primary component orbitsphere-cvf is replaced by a secondary orbitsphere-cvf.
11 . A geodesic structure according to claim 10 , wherein each circle element of each orbitsphere-cvf element comprises a structural element.
12 . A geodesic structure according to claim 11 , wherein the structural element comprises at least one a tube, bar, rod, or beam.
13 . A geodesic structure according to claim 12 , wherein the structural elements are welded, bolted, riveted, clamped, glued, or otherwise fastened at their crossings with other such elements to form the architectural structure.
14 . A geodesic structure according to claim 1 , wherein the architectural structure has the form or a portion of the form provided by at least one of Eqs. (67-69).
15 . A geodesic structure according to claim 1 , wherein the geodesic structure comprises a container, dish, or vessel formed from the circle elements.
16 . A geodesic structure according to claim 1 , wherein the circular elements comprise framing to provide structural strength.
17 . A geodesic structure according to claim 16 , wherein the framing is covered with a continuous membrane or a tiling that forms a continuous or partially continuous covering of the framing.
18 . A geodesic structure according to claim 10 , wherein a number of secondary component orbitsphere-cvf elements is equal to the number of great-circle elements of the primary component orbitsphere-cvf.
19 . A uniform current-density structure comprising a plurality of great-circle element loops wherein the circle elements are arranged according to the structure of a primary component orbitsphere-cvf wherein each circle element of the primary component orbitsphere-cvf is replaced by a secondary orbitsphere-cvf to form Y 0 0 (φ,θ).
20 . The uniform current-density function having a magnetic moment along the z-axis that is twice the magnitude of the magnetic moment in the xy-plane.
21 . The geodesic structure according to claim 10 , wherein the circle elements are arranged according to the structure of a primary component orbitsphere-cvf represented by
[
x
′
y
′
z
′
]
=
[
1
2
+
cos
θ
2
1
2
-
cos
θ
2
-
sin
θ
2
1
2
-
cos
θ
2
1
2
+
cos
θ
2
sin
θ
2
sin
θ
2
-
sin
θ
2
cos
θ
]
[
0
r
n
cos
ϕ
r
n
sin
ϕ
]
[
x
′
y
′
z
′
]
=
[
(
1
2
-
cos
θ
2
)
r
n
cos
ϕ
-
sin
θ
2
r
n
sin
ϕ
(
1
2
+
cos
θ
2
)
r
n
cos
ϕ
+
sin
θ
2
r
n
sin
ϕ
-
sin
θ
2
r
n
cos
ϕ
+
cos
θ
r
n
sin
ϕ
]
22 . The geodesic structure according to claim 21 , wherein the circle elements are arranged according to the structure of a primary component orbitsphere-cvf wherein each circle element of the primary component orbitsphere-cvf is replaced by a secondary orbitsphere-cvf represented by
[
x
′
y
′
z
′
]
=
∑
m
=
1
m
=
M
[
1
2
+
cos
(
m
2
π
M
)
2
1
2
-
cos
(
m
2
π
M
)
2
-
sin
(
m
2
π
M
)
2
1
2
-
cos
(
m
2
π
M
)
2
1
2
+
cos
(
m
2
π
M
)
2
sin
(
m
2
π
M
)
2
sin
(
m
2
π
M
)
2
-
sin
(
m
2
π
M
)
2
cos
(
m
2
π
M
)
]
·
∑
n
=
1
n
=
N
[
cos
(
π
4
)
-
sin
(
π
4
)
0
sin
(
π
4
)
cos
(
n
2
π
N
)
cos
(
π
4
)
cos
(
n
2
π
N
)
sin
(
n
2
π
N
)
-
sin
(
π
4
)
sin
(
n
2
π
N
)
-
cos
(
π
4
)
sin
(
n
2
π
N
)
cos
(
n
2
π
N
)
]
[
0
r
n
cos
ϕ
r
n
sin
ϕ
]
23 . The uniform current-density structure of claim 20 wherein the circle elements are arranged according to the structure of a primary component orbitsphere-cvf represented by
[
x
′
y
′
z
′
]
=
[
sin
2
θ
2
-
cos
2
θ
2
-
sin
θ
2
-
cos
2
θ
2
sin
2
θ
2
-
sin
θ
2
sin
θ
2
sin
θ
2
-
cos
θ
]
[
0
r
n
cos
ϕ
r
n
sin
ϕ
]
(
36
)
[
x
′
y
′
z
′
]
=
[
-
cos
2
θ
2
r
n
cos
ϕ
-
sin
θ
2
r
n
sin
ϕ
sin
2
θ
2
r
n
cos
ϕ
-
sin
θ
2
r
n
sin
ϕ
sin
θ
2
r
n
cos
ϕ
-
cos
θ
r
n
sin
ϕ
]
(
37
)
24 . The uniform current-density structure of claim 23 wherein the circle elements are arranged according to the structure of a primary component orbitsphere-cvf wherein each circle element of the primary component orbitsphere-cvf is replaced by a secondary orbitsphere-cvf represented by
[
x
′
y
′
z
′
]
=
∑
m
=
1
m
=
M
[
1
2
+
cos
(
m
2
π
M
)
2
1
2
-
cos
(
m
2
π
M
)
2
-
sin
(
m
2
π
M
)
2
1
2
-
cos
(
m
2
π
M
)
2
1
2
+
cos
(
m
2
π
M
)
2
sin
(
m
2
π
M
)
2
sin
(
m
2
π
M
)
2
-
sin
(
m
2
π
M
)
2
cos
(
m
2
π
M
)
]
·
∑
n
=
1
n
=
N
[
cos
(
π
4
)
-
sin
(
π
4
)
0
sin
(
π
4
)
cos
(
n
2
π
N
)
cos
(
π
4
)
cos
(
n
2
π
N
)
sin
(
n
2
π
N
)
-
sin
(
π
4
)
sin
(
n
2
π
N
)
-
cos
(
π
4
)
sin
(
n
2
π
N
)
cos
(
n
2
π
N
)
]
[
0
r
n
cos
ϕ
r
n
sin
ϕ
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