the term gearing, which was once applied to wheels, shafts, and the general mechanism of mills and factories, has now in common use become restricted to tooth wheels, and is in this sense employed here. gearing as a means of transmitting motion is employed when the movement of machines, or the parts of machines, must remain relatively the same, as in the case of the traversing screw of an engine lathe—when a heavy force is transmitted between shafts that are near to each other, or when shafts to be connected are arranged at angles with each other. this rule is of course not constant, except as to cases where positive relative motion has to be maintained. noise, and the liability to sudden obstruction, may be reasons for not employing tooth wheels in many cases when the distance between and the position of shafts would render such a connection the most durable and cheap. gearing under ordinary strain, within limited speed, and when other conditions admit of its use, is the cheapest and most durable mechanism for transmitting power; but the amount of gearing employed in machinery, especially in europe, is no doubt far greater than it will be in future, when belts are better understood.

no subject connected with mechanics has been more thoroughly investigated than that of gearing. text-books are replete with every kind of information pertaining to wheels, at least so far as the subject can be made a mathematical one; and to judge from the amount of matter, formul?, and diagrams, relating to the teeth of wheels that an apprentice will meet with, he will no doubt be led to believe that the main object of modern engineering is to generate wheels. it must be admitted that the teeth of wheels and the proportions of wheels is a very important matter to understand, and should be studied with the greatest care; but it is equally important to know how to produce the teeth in metal after their configuration has been defined on paper; to understand the endurance of teeth under abrasive wear when made of wrought or cast iron, brass or steel; how patterns can be constructed from which correct wheels may be cast, and how the teeth of wheels can be cut [52]by machinery, and so on.

a learner should, in fact, consider the application and operative conditions of gearing as one of the main parts of the subject, and the geometry or even the construction of wheels as subsidiary; in this way attention will be directed to that which is most difficult to learn, and a part for which facilities are frequently wanting. gearing may be classed into five modifications—spur wheels, bevel wheels, tangent wheels, spiral wheels, and chain wheels; the last i include among gearing because the nature of their operation is analogous to tooth wheels, although at first thought chains seem to correspond more to belts than gearing. the motion imparted by chains meshing over the teeth of wheels is positive, and not frictional as with belts; the speed at which such chains may run, with other conditions, correspond to gearing.

different kinds of gearing can be seen in almost every engineering establishment, and in view of the amount of scientific information available, it will only be necessary to point out some of the conditions that govern the use and operation of the different kinds of wheels. the durability of gearing, aside from breaking, is dependent upon pressure and the amount of rubbing action that takes place between the teeth when in contact. spur wheels, or bevel wheels, when the pitch is accurate and the teeth of the proper form, if kept clean and lubricated, wear but little, because the contact between the teeth is that of rolling instead of sliding. in many cases, one wheel of a pair is filled with wooden cogs; in this arrangement there are four objects, to avoid noise, to attain a degree of elasticity in the teeth, to retain lubricants by absorption in the wood, and to secure by wear a better configuration of the teeth than is usually attained in casting, or even in cutting teeth.

tangent wheels and spiral gearing have only what is termed line contact between the bearing surfaces, and as the action between these surfaces is a sliding one, such wheels are subject to rapid wear, and are incapable of sustaining much pressure, or transmitting a great amount of power, except the surfaces be hard and lubrication constant. in machinery the use of tangent wheels is mainly to secure a rapid change of speed, usually to diminish motion and increase force.

by placing the axes of tangent gearing so that the threads or teeth of the pinions are parallel to the face of the driven teeth, [53] as in the planing machines of messrs wm. sellers & co., the conditions of operation are changed, and an interesting problem arises. the progressive or forward movement of the pinion teeth may be equal to the sliding movement between the surfaces; and an equally novel result is, that the sliding action is distributed over the whole breadth of the driven teeth.

in spiral gearing the line of force is at an angle of forty-five degrees with the bearing faces of the teeth, and the sliding movement equal to the speed of the wheels at their periphery; the bearing on the teeth, as before said, is one of line contact only. such wheels cannot be employed except in cases where an inconsiderable force is to be transmitted. spiral wheels are employed to connect shafts that cross each other at right angles but in different planes, and when the wheels can be of the same size.

it may be mentioned in regard to rack gearing for communicating movement to the carriages of planing machines or other purposes of a similar nature: the rack can be drawn to the wheel, and a lifting action avoided, by shortening the pitch of the rack, so that it will vary a little from the driving wheel. the rising or entering teeth in this case do not come in contact with those on the rack until they have attained a position normal to the line of the carriage movement.

(1.) into what classes can gearing be divided?—(2.) what determines the wearing capacity of gearing?—(3.) what is the advantage gained by employing wooden cogs for gear wheels?—(4.) why are tangent or worm wheels not durable?