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US 9,316,102 B2Granted
Rotors formed using involute curves
AssigneeExponential Technologies, Inc.
InventorsCurtis Patterson, Alejandro Juan, Kristjan Gottfried
Life of this patent
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Abstract
The present disclosure describes the use of involute curves for use in energy conversion devices, as well as timing or indexing gears. Several different embodiments are shown using rotors of several examples of lobe numbers and shapes.
Claims17
A device comprising:
- a first rotor and a second rotor;
- the axes of the first rotor and the second rotor are offset from collinear and intersecting,
- each rotor comprising:
- a spherical outer surface of radius R
- at least one lobe having a first circumferential side and a second circumferential side;
- the first circumferential side of each lobe is a curved surface formed of at least one spherical involute curve;
- the spherical involute curve is defined in Cartesian coordinates by the parametric curve;
- Involute
- =
- [
- X
-
- (
- t
- )
- Y
-
- (
- t
- )
- Z
-
- (
- t
- )
- ]
- =
- [
- R
-
- (
- sin
-
- (
- t
-
-
- sin
-
- (
- g
- )
- )
-
- sin
-
- (
- t
- )
- +
- cos
-
- (
- t
-
-
- sin
-
- (
- g
- )
- )
-
- cos
-
- (
- t
- )
-
- sin
-
- (
- g
- )
- )
- R
-
- [
- cos
-
- (
- t
-
-
- sin
-
- (
- g
- )
- )
-
- sin
-
- (
- g
- )
-
- sin
-
- (
- t
- )
- -
- sin
-
- (
- t
-
-
- sin
-
- (
- g
- )
- )
-
- cos
-
- (
- t
- )
- ]
- R
-
- [
- cos
-
- (
- t
-
-
- sin
-
- (
- g
- )
- )
-
- cos
-
- (
- g
- )
- ]
- ]
- t is the parametric curve parameter;
- g=asin(r/R);
- r is the radius of the base circle of the spherical involute;
- B=t*sin(g);
- and
- each lobe of the first rotor intermeshes with the lobes of the second rotor, around the periphery of the rotors.
148 more elements
A device comprising:
- a first rotor and a second rotor;
- where the axes of the first rotor and the second rotor are offset from collinear and intersecting,
- each rotor comprising:
- a spherical outer surface of radius R
- at least one lobe having a first circumferential side and a second circumferential side;
- the first circumferential side of each lobe is a curved surface formed of at least one spherical involute curve;
- where the spherical involute curve in Cartesian coordinates is defined by the parametric curve represented by the following matrix multiplication;
- Involute
- =
- [
-
- cos
-
- (
- t
- )
- -
- sin
-
- (
- t
- )
- 0
- sin
-
- (
- t
- )
- cos
-
- (
- t
- )
- 0
- 0
- 0
- 1
- ]
- [
-
- cos
-
- (
- g
- )
- 0
- sin
-
- (
- g
- )
- 0
- 1
- 0
- -
- sin
-
- (
- g
- )
- 0
- cos
-
- (
- g
- )
- ]
- [
-
- 1
- 0
- 0
- 0
- cos
-
- (
- B
- )
- -
- sin
-
- (
- B
- )
- 0
- sin
-
- (
- B
- )
- cos
-
- (
- B
- )
- ]
-
- [
-
- 0
- 0
- R
-
- ]
- t is the parametric curve parameter;
- g=asin(r/R);
- r is the radius of the base circle of the spherical involute;
- B=t*sin(g);
- and
- each lobe of the first rotor intermesh with a corresponding lobe of the second rotor, around the periphery of the rotors.
107 more elements
Dependencies are inferred from the claim text.