Enhanced compound pendulums and systems
AssigneeThe Long Now Foundation
InventorW. Daniel Hillis
Life of this patent
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Abstract
Enhanced compound pendulums provide thermal compensation and/or barometric compensation, such as for a mechanical clock system. The enhanced compound pendulums are simple to construct, and can be more easily compensated than conventional, single-bob pendulums. The enhanced compound pendulums typically comprise material that is added above the point of rotation. Thermal expansion factors for components of the enhanced compound pendulums may preferably be chosen to provide thermal compensation to the first order. In some embodiments of enhanced compound pendulums, volume is added above the pivot to provide barometric compensation, such as by equalizing the moments above and below the pivot, or by providing geometric symmetry above and below the pivot, with a lower density above the pivot.
Claims10
A thermally compensated pendulum having a point of rotation, comprising:
- a first mass A having a corresponding center of mass that extends a first distance a above the point of rotation, wherein the first mass A has a first coefficient of thermal expansion α;
- a second mass B having a corresponding center of mass that extends a second distance b below the point of rotation, wherein the second mass B has a second coefficient of thermal expansion β;
- wherein the first coefficient of thermal expansion α is given as:
- α
- =
- bB
- aA
-
- (
- -
- a
- 2
-
- A
- -
- 2
-
-
- aAb
- +
- b
- 2
-
- B
- )
- (
- a
- 2
-
- A
- -
- 2
-
-
- aBb
- -
- b
- 2
-
- B
- )
-
- β
- .
A compound pendulum having a point of rotation and a center of gravity, comprising:
- an upper mass A above the point of rotation;
- a lower mass B below the point of rotation;
- a connecting member connected between the upper mass A and the lower mass B, wherein the connecting member has a first coefficient of thermal expansion α;
- and
- a spoke connected below the point of rotation to the connecting member and extending to the point of rotation, wherein the spoke has a second coefficient of thermal expansion β;
- wherein h is the distance from the point of rotation to the center of gravity, wherein r is the radius about the point of rotation, and wherein the ratio of the first coefficient of thermal expansion α to the second coefficient of thermal expansion β is approximately given as:
- α
- β
- =
- (
- h
- +
- r
- )
- (
- r
- )
- .
A compound pendulum having a point of rotation and a center of gravity, comprising:
- an upper mass A above the point of rotation;
- a lower mass B below the point of rotation;
- a connecting member connected between the upper mass A and the lower mass B, wherein the connecting member has a first coefficient of thermal expansion α;
- and
- a spoke connected above the point of rotation to the connecting member and extending to the point of rotation, wherein the spoke has a second coefficient of thermal expansion β;
- wherein h is the distance from the point of rotation to the center gravity, wherein r is the radius about the point of rotation, and wherein the ratio of the first coefficient of thermal expansion α to the second coefficient of thermal expansion 62 is approximately given as:
- α
- β
- =
- (
- r
- -
- h
- )
- (
- r
- )
- .
Dependencies are inferred from the claim text.