In bevel gearing the wheels act upon each other at an angle; the pitch surfaces are cones and the teeth engage along straight lines which pass through the common vertex of the two cones. When the angle of contact is equal to 4! degrees they are called 'mitre gears.' In skew gearing the axles arc neither parallel nor intersecting, the pitch surfaces are hyperbo bids of revolution, and the teeth engage in hoes approximating to the general direction of the common element of the hyperboloids. Owing to the difficulty of constructing the teeth, this class of Rearing is not much used, and where the conditions require their application, two pairs of cone wheels are generally employed.
In screw gearing the axles of the cylinders are neither parallel nor intersecting, and the pitch surfaces arc in contact only at one point.
In its practical form it is known as 'endless screw' or 'worm gear,' and is commonly em ployed, to convert raped into slow motion. The mounting of the screw prevents any other motion except that of rotation, so that at each complete turn of the screw a tooth of the en gaging wheel passes across the line of centres, and there being no limit to this action, the wheel continues to rotate so long as the screw is turned around its axis.
In lace gear .. ,t •,,th consist of pins arranged in a ci le and fastened to a fiat cir cular plate attadr to an axis. The wheels act at right angles t each other and the points of contact are situa only upon the surfaces of the pins. Prior .o the introduction of bevel
gears, it was thy method usually employed to transmit motion hetween axes that were not parallel, but at .he present time it is almost exclusively used in connection with modern mill machinery.
There are a great many other forms of gear ing which are adapted for various purposes. Of them the stepped, twisted, spiral and differ ential gearing are the most important. (For description of differential geanng see Atrro mama). The particular advantage of the last named over ordinary spur gearing is the slight friction and the consequent lack of wear of the teeth. Bevel gears of this type have been used with great advantage in mowing machines. By the substitution of epicycloidal and hypocy cloidal curves and involutes for the circular arcs in the forms of the teeth, the rolling con tact action of the circles, in its relation to the production of a constant velocity ratio, is re placed exactly by a sliding contact action. The teeth of all gear wheels are designed upon the principles of these curves, so that when run ning together their action is smooth and free from vibration and shock.
For specific information rel ative to the application and design of gearing consult Rankine, 'Machinery and Millwork' Grant, 'Teeth of Gears': Kent, 'Mechanical Engineer's Pocket Book' (1903); and Stahl and Woods, 'Elementary Mechanism' (1903).