Method and apparatus for measuring thrust

A method of calibrating an apparatus, comprising:

• providing an apparatus;
• wherein the apparatus comprises:
• a frame;
• a cross beam;
• two flexure pivots,
• wherein the cross beam is interconnected to the frame via the two flexure pivots, and
• wherein when the cross beam is rotated about an axis of rotation from a steady state angular rotation position, the two flexure pivots apply a corresponding two restoring forces that tend to rotate the cross beam back to the steady state angular rotation position;
• and
• an angular rotation deflection detector,
• wherein when the cross beam is rotated about the axis of rotation from the steady state angular rotation position, the angular rotation deflection detector detects an angular rotation deflection of the cross beam about the axis of rotation;
• measuring n cycles of damped oscillations of the cross beam about the axis of rotation, where n is an integer, and where n>1;
• determining a first amplitude, x0, of a first peak and an nth amplitude, xn, of an nth peak of the n cycles of damped oscillations of the cross beam about the axis of rotation;
• and
• determining a logarithmic decrement δ, where
• δ
• =
• 1
• n
• ⁢
• ln
• ⁢
• ⁢
• x
• 0
• x
• n
• ;
• determining a damping ratio ζ, where
• ς
• =
• 1
• 1
• +
• (
• 2
• ⁢
• ⁢
• π
• δ
• )
• 2
• ;
• determining a damped frequency of the n cycles of damped oscillations of the cross beam about the axis of rotation, ωd;
• estimating a natural frequency, ωn, where
• ω
• n
• =
• ω
• d
• 1
• -
• ς
• 2
• ;
• and
• determining a spring constant, kθ, where kθ=ωn2·Iθ, and where Iθ is a moment of inertia of the cross beam about the axis of rotation.

A method of measuring thrust exerted by a device, comprising:

• providing an apparatus,
• wherein the apparatus comprises:
• a frame;
• a cross beam;
• two flexure pivots,
• wherein the cross beam is interconnected to the frame via the two flexure pivots, and
• wherein when the cross beam is rotated about an axis of rotation from a steady state angular rotation position, the two flexure pivots apply a corresponding two restoring forces that tend to rotate the cross beam back to the steady state angular rotation position;
• an angular rotation deflection detector,
• wherein when the cross beam is rotated about the axis of rotation from the steady state angular rotation position, the angular rotation deflection detector detects an angular rotation deflection of the cross beam about the axis of rotation;
• and
• a magnetic damper,
• wherein as the cross beam oscillates about the axis of rotation, eddy currents are induced in the magnetic damper that produce induced magnetic fields that dampen oscillations of the cross beam, and
• wherein the method comprises:
• mounting a device on the cross beam;
• activating the device to exert a thrust;
• measuring an angular rotation deflection of the cross beam about the axis of rotation caused by the thrust;
• and
• determining the thrust from the angular rotation deflection of the cross beam about the axis of rotation caused by the thrust.

A method of detecting a mechanical vibration, comprising:

• providing an apparatus,
• wherein the apparatus comprises:
• a frame;
• a cross beam;
• two flexure pivots,
• wherein the cross beam is interconnected to the frame via the two flexure pivots, and
• wherein when the cross beam is rotated about an axis of rotation from a steady state angular rotation position, the two flexure pivots apply a corresponding two restoring forces that tend to rotate the cross beam back to the steady state angular rotation position;
• an angular rotation deflection detector,
• wherein when the cross beam is rotated about the axis of rotation from the steady state angular rotation position, the angular rotation deflection detector detects an angular rotation deflection of the cross beam about the axis of rotation;
• and
• a magnetic damper,
• wherein as the cross beam oscillates about the axis of rotation, eddy currents are induced in the magnetic damper that produce induced magnetic fields that dampen oscillations of the cross beam about the axis of rotation, and
• wherein the method comprises:
• coupling a mechanical vibration to the apparatus;
• measuring an angular rotation deflection of the cross beam about the axis of rotation caused by the thrust;
• and
• detecting the mechanical vibration from the angular rotation deflection of the cross beam about the axis of rotation caused by the mechanical vibration coupled to the apparatus.