Chapter GEAR TRAINS Cycle and epicycle, orb in orb JOHN MILTON.PARADISE LOST 9 9.0 INTRODUCTION The earliest known reference to gear trains is in a treatise by Hero of Alexandria(c.100 B.C.).Gear trains are widely used in all kinds of mechanisms and machines,from can openers to aircraft carriers.Whenever a change in the speed or torque of a rotating de- vice is needed,a gear train or one of its cousins.the belt or chain drive mechanism,will usually be used.This chapter will explore the theory of gear tooth action and the design of these ubiquitous devices for motion control.The calculations involved are trivial compared to those for cams or linkages.The shape of gear teeth has become quite stan- dardized for good kinematic reasons which we will explore. Gears of various sizes and styles are readily available from many manufacturers. Assembled gearboxes for particular ratios are also stock items.The kinematic design of gear trains is principally involved with the selection of appropriate ratios and gear diam- eters.A complete gear train design will necessarily involve considerations of strength of materials and the complicated stress states to which gear teeth are subjected.This text will not deal with the stress analysis aspects of gear design.There are many texts which do.Some are listed in the bibliography at the end of this chapter.This chapter will dis- cuss the kinematics of gear tooth theory,gear types,and the kinematic design of gearsets and gear trains of simple,compound,reverted,and epicyclic types.Chain and belt drives will also be discussed.Examples of the use of these devices will be presented as well. 432