Thursday, April 11, 2002

(Dr. Wayne Book, advisor)

"Investigation of Vibration Control of Hypotrochoidally Driven Machinery"

__Abstract__

Two methods of command generation were developed to control the vibration
of

a hypotrochoidally driven machine. A hypotrochoidal gear is a
small gear

traveling along the interior teeth of a larger, fixed ring gear.
By

anchoring a mass at a point offset from the center of the small gear,
the

mass can be made to travel along a closed path with straight sides
and

curved corners. In this manner, the rotational motion of the
gear is

transformed into linear motion of the mass along some portions of the
path.

The gear can be driven with a rotary servomotor. A servomotor
can very

accurately control the position and speed of the mass along the path
in a

periodic fashion. There are many industrial applications
that involve

repetitive tasks requiring linear motion. One major application
is

packaging snack food in bags in a continuous process. One command

generation method uses a real-time optimization routine to determine

appropriate polynomial coefficients for a function used to calculate
the

desired servomotor trajectory as a series of time-dependent angular
position

setpoints. The other method is an input shaping scheme that prevents
a

polynomial trajectory from exciting structural natural frequencies.