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Theoretical analysis for the design of the French watt balance experiment force comparator
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Image of FIG. 1.
FIG. 1.

Schematic diagram of the force comparison in the watt balance experiment.

Image of FIG. 2.
FIG. 2.

Schematic diagram of the two static equilibriums: (a) with the mass on the pan and (b) without the mass on the pan.

Image of FIG. 3.
FIG. 3.

Schematic diagram of ideal cramped flexure strip for the central pivot of the beam. is the radius of curvature of the flexure strip deformed by a torque when under a load .

Image of FIG. 4.
FIG. 4.

Schematic diagram of the flexure-strip force balance.

Image of FIG. 5.
FIG. 5.

Schematic diagram of all the rotation axes of a balance prototype (pivots of the beam and gimbals of the pan and coil suspensions).

Image of FIG. 6.
FIG. 6.

Example of tilting of a two-section suspension due to an eccentric load with gimbals having nonzero stiffnesses and .

Image of FIG. 7.
FIG. 7.

Plot of the surface presenting the angle with respect to the length of the first section and the relative length for , , and .

Image of FIG. 8.
FIG. 8.

Schematic diagram of the beam with two articulated suspension (the main rotation axes are represented).

Image of FIG. 9.
FIG. 9.

Schematic diagram of a model of the two-section suspension similar to a double pendulum.

Image of FIG. 10.
FIG. 10.

Example of graphical representation of the variation of angles (a) and (b) with the initial conditions , , , and .


Generic image for table
Table I.

Main characteristics of the future French watt balance.

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Table II.

Free oscillation frequencies about the main rotation axes of the balance depending on the initial conditions and suspended mass values for fixed dimensional configuration.

Generic image for table
Table III.

Mechanical characteristics of the force balance.


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Scitation: Theoretical analysis for the design of the French watt balance experiment force comparator