M.S. Thesis Presentation by Nathan Cook
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.