Duct fabricated with additive manufacturing
Ducts manufactured by depositing one or more runs of material in a helix, a plurality of conjoined planar spirals, and a conjoined plurality of conical spirals.
1. An article of manufacture comprising:
a first spiral of a run of material that comprises a medial terminus and a lateral terminus;
a second spiral of the run of material that comprises a medial terminus and a lateral terminus;
a third spiral of the run of material that comprises a medial terminus and a lateral terminus;
a first inter-spiral yoke of the run of material connected at a first position to the medial terminus of the first spiral and at a second position to the medial terminus of the second spiral; and
a second inter-spiral yoke of the run of material connected at a third position to the lateral terminus of the second spiral and at a fourth position to the lateral terminus of the third spiral.
2. The article of claim 1 wherein the run of material comprises a continuous fiber from the medial terminus of the first spiral to the lateral terminus of the third spiral.
3. The article of claim 1 wherein the first spiral is a planar spiral.
4. The article of claim 1 wherein the first spiral is a conjoined planar spiral.
5. The article of claim 1 wherein the first spiral is a conical spiral.
6. The article of claim 1 wherein the first spiral is a conjoined conical spiral.
7. The article of claim 1 wherein the first spiral and the second spiral are conjoined.
8. The article of claim 1 wherein the run of material is deposited from the medial terminus of the first spiral to the lateral terminus of the first spiral, and wherein the run of material is deposited from the lateral terminus of the second spiral to the medial terminus of the second spiral.
9. The article of claim 1 is a cylindrical conjoined spiral duct.
10. The article of claim 1 is a rectangular-with rounded-corners conjoined spiral duct.
11. An article of manufacture comprising:
a first spiral of a run of material having a longitudinal axis described by a vector function:
{right arrow over (r)} ( s, k )=< f ( s, k ), g ( s, k ), h ( s, k )>;
a second spiral of the run of material having a longitudinal axis described by the vector function:
{right arrow over (r)} ( s, k+ 1)=< f ( s, k+ 1), g ( s, k+ 1), h ( s, k+ 1)>;
a third spiral of the run of material having a longitudinal axis described by the vector function:
{right arrow over (r)} ( s, k+ 2)=< f ( s, k+ 2), g ( s, k+ 2), h ( s, k+ 2)>;
a first inter-spiral yoke of the run of material connected at a first position to a first point along the run of material, wherein the first point is described by
{right arrow over (r)} ( S M , k )=< f ( S M , k ), g ( S M , k ), h ( S M , k )>;
and at a second position to a second point along the run of material, wherein the second point is described by
{right arrow over (r)} ( S M , k+ 1)=< f ( S M , k+ 1), g ( S M , k+ 1), h ( S M , k+ 1)>; and
a second inter-spiral yoke of the run of material connected at a third position to a third point along the run of material, wherein the third point is described by
{right arrow over (r)} ( S L , k+ 1)=< f ( S L , k+ 1), g ( S L , k+ 1), h ( S L , k+ 1)>
and at a fourth position to a fourth point along the run of material, wherein the fourth point is described by
{right arrow over (r)} ( S L , k+ 2)=< f ( S L , k+ 2), g ( S L , k+ 2), h ( S L , k+ 2)>;
wherein s is a real number with the domain s: [S L , S M ], wherein S L is the lateral terminus, S M is the medial terminus; and
wherein k is an integer with the domain k: [k, k+2].
12. The article of claim 11 wherein the run of material comprises a continuous fiber from {right arrow over (r)}(S M , k)=<f(S M , k), g(S M , k), h(S M , k)> to {right arrow over (r)}(S L , k+2)=<f(S L , k+2), g(S L , k+2), h(S L , k+2)>.
13. The article of claim 11 wherein the first spiral is a planar spiral.
14. The article of claim 11 wherein the first spiral is a conjoined planar spiral.
15. The article of claim 11 wherein the first spiral is a conical spiral.
16. The article of claim 11 wherein the first spiral and the second spiral are conjoined; and
wherein the second spiral and the third spiral are conjoined.
17. The article of claim 11 wherein the run of material has an isolating axis i(t); and wherein i(t)={right arrow over (r)}(s, k)−{right arrow over (r)}(s−2π, k) the domain s: [S L +2π, S M ].
18. The article of claim 11 wherein the run of material is deposited from {right arrow over (r)}(S L , k) clockwise to {right arrow over (r)}(S M , k) and counter-clockwise from {right arrow over (r)}(S M , k+1) to {right arrow over (r)}(S L , k+1).
19. The article of claim 11 wherein the run of material is deposited from {right arrow over (r)}(S L , k) counter-clockwise to {right arrow over (r)}(S M , k) and clockwise from {right arrow over (r)}(S M , k+1) to {right arrow over (r)}(S L , k+1).
20. The article of claim 11 wherein the run of material has an conjoining axis j(t), and wherein j(t)={right arrow over (r)}(S M , k+1)−{right arrow over (r)}(S M , k).