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Cycles Upon Cycles: An Anecdotal History of "Higher Curves" in Science and Engineering
Student-Run Research| Speaker: | Rida Farouki, UC Davis |
| Location: | 2112 MSB |
| Start time: | Wed, Mar 5 2008, 12:10PM |
Description
We present an eclectic history of the role of certain transcendental
curves known generically as "roulettes" (produced by the rolling motions
of lines and circles) in various scientific and engineering
applications. The examples encompass the use of epicycloids and circle
involutes in defining gear tooth profiles; cycloids as the geometrical
and mechanical basis of Huygens' isochronous pendulum clock, and as the
solution of the brachistochrone problem; and
the use of epitrochoids in describing planetary orbits and the
combustion chamber of the Wankel rotary engine. These case studies
provide sobering evidence that, compared to modern endeavors, whatever
``geometric design research'' of the pre-computer
era lacked in labor-saving computational gadgetry was compensated for by
mathematical/physical insight and ingenuity.