Page 71 - The Mechatronics Handbook

FIGURE 5.8 Illustration of Coriolis acceleration, which
results from translation within a reference frame that is
rotating with respect to an inertial reference frame.

FIGURE 5.9 Schematic of a vibratory gyroscope.

the angular momentum-based gyroscopic mechanics of conventional-scale devices. A Coriolis accelera-
tion results from linear translation within a coordinate frame that is rotating with respect to an inertial
reference frame. In particular, if the particle in Fig. 5.8 is moving with a velocity v within the frame xyz,
and if the frame xyz is rotating with an angular velocity of ω with respect to the inertial reference frame
XYZ, then a Coriolis acceleration will result equal to a c = 2ω x v. If the object has a mass m, a Coriolis
inertial force will result equal to F c = -2mω x v (minus sign because direction is opposite a c ). A vibratory
gyroscope utilizes this effect as illustrated in Fig. 5.9. A flexure-suspended inertial mass is vibrated in the
x-direction, typically with an electrostatic comb drive. An angular velocity about the z-axis will generate
a Coriolis acceleration, and thus force, in the y-direction. If the “external” angular velocity is constant
and the velocity in the x-direction is sinusoidal, then the resulting Coriolis force will be sinusiodal, and
the suspended inertial mass will vibrate in the y-direction with an amplitude proportional to the angular
velocity. The motion in the y-direction, which is typically measured capacitively, is thus a measure of the
angular rate. Examples of these types of devices are those by Bernstein et al. [49] and Oh et al. [50]. Note
that though vibration is an essential component of these devices, they are not technically resonant sensors,
since they measure amplitude of vibration rather than frequency.

5.4 Nanomachines

Nanomachines are devices that range in size from the smallest of MEMS devices down to devices
assembled from individual molecules [51]. This section briefly introduces energy sources, structural
hierarchy, and the projected future of the assembly of nanomachines. Built from molecular components
performing individual mechanical functions, the candidates for energy sources to actuate nanomachines
are limited to those that act on a molecular scale. Regarding manufacture, the assembly of nanoma-
chines is by nature a one-molecule-at-a-time operation. Although microscopy techniques are currently
used for the assembly of nanostructures, self-assembly is seen as a viable means of mass production.

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