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.
Claims18
A thermally compensated pendulum having a point of rotation, comprising:
- a first point mass A that extends a first distance a above the point of rotation, wherein the first point mass A has a first coefficient of thermal expansion α;
- a second point mass B that extends a second distance below the point of rotation, wherein the second point 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 pendulum having a center of gravity h and a point of rotation, comprising:
- an upper spoke having an upper end and a lower end, wherein the lower end is located at the point of rotation, and wherein the spoke extends vertically upward a distance r to the upper end;
- a first point mass A located at the upper end of the spoke;
- a member connected to the upper spoke at a distance c above the lower end of the upper spoke, the member extending around the lower end of the upper spoke to a lower point that having a distance c vertically below the point of rotation;
- a lower spoke having an upper end and a lower end, wherein the upper end is located at the lower point of the member, and wherein the spoke extends vertically downward a distance (r−c) to the lower end;
- and
- a second point mass B located at the lower end of the lower spoke;
- wherein upper spoke comprises a first portion that that extends from the lower end of the upper spoke to the member, and a second portion that extends from the member to the upper end;
- wherein the upper point mass A, the lower point mass B, the member, the lower spoke and the second portion of the upper spoke comprise a first material having a first coefficient of thermal expansion β;
- wherein the first portion of the upper spoke comprises a second material having a second coefficient of thermal expansion α;
- wherein the second coefficient of thermal expansion α is given as:
- α
- =
- (
- r
- -
- h
- )
- r
-
- β
- .
A pendulum having a center of gravity h and a point of rotation, comprising:
- a lower spoke having an upper end and a lower end, wherein the upper end is located at the point of rotation, and wherein the spoke extends vertically downward a distance r to the lower end;
- a second point mass B located at the lower end of the lower spoke;
- a member connected to the lower spoke at a distance c below the upper end of the lower spoke, the member extending around the upper end of the lower spoke to an upper point that having a distance c vertically above the point of rotation;
- an upper spoke having an upper end and a lower end, wherein the lower end is located at the upper point of the member, and wherein the spoke extends vertically upward a distance (r−c) to the upper end;
- and
- a first point mass A located at the upper end of the upper spoke;
- wherein lower spoke comprises a first portion that that extends from the upper end of the lower spoke to the member, and a second portion that extends from the member to the lower end;
- wherein the upper point mass A, the lower point mass B, the member, the upper spoke and the second portion of the lower spoke comprise a first material having a first coefficient of thermal expansion β;
- wherein the first portion of the lower spoke comprises a material having a second coefficient of thermal expansion α;
- and
- wherein the second coefficient of thermal expansion α is given as:
- α
- =
- (
- r
- +
- h
- )
- r
-
- β
- .
A pendulum having a point of rotation, comprising:
- a first mass suspended below a pivot at the point of rotation having a first volume;
- and
- a member located above the pivot having a second volume;
- wherein the second volume is chosen to equalize the first moment and the second moment.
Dependencies are inferred from the claim text.