APPLIED HKCIIAN 



[RECIPBOCATIXO MOTION. 



th noocmrj itrnngth But wh<>n it it in'. M 1 tint tho 

 roUtiou of the wheel shall cause the screw to rotate, tho 

 iliHiiiotvr of the screw xliouUl be in.vle M small and its 

 i M great M possible, so that the thread and the 

 teeth may have small obliquity to the axis of the sore*. 

 In either case the screw-thread may be considered as a 

 continuous inclined plane presented to the teeth of the 

 wheel, and tho effect of greater or less obliquity becomes 

 very evident. In the fintcaae, where the screw drives the 

 wheel, A B (Fig. 2.>1) being tho axis of tho screw, K L, 

 part of iU incline.! surface, travelling in tho diroctiou of 



Pi(. Ml. 



o 



the arrow C, has to move the tooth of the wheel in the 

 direction of the arrow D ; tho greater the inclination of 

 K L to the axis, or the more nearly it approaches to a 

 perpendicular to it, the better its effect to move the tooth, 

 or the less is the lateral strain it produces on the tooth. 

 In the second case, where a tooth moving in the direction 

 of the arrow G, and pressing against the inclined side of 

 the screw-thread M N, causes it to travel in the direction 

 of the arrow H, the less the inclination of M X to the 

 axis E F, or the more nearly it approaches to coincidence 

 with it, the better is the action of the tooth to give it 

 lateral motion, or tho loss is the longitudinal strain in 

 the direction of the axis. 



Before leaving the subject of toothed gearing', it is 

 proper to remark, that tho form of tooth which we have 

 described the involute of the circle presents one dis- 

 advantage in use. The surfaces of the tooth do not roll 

 over one another when in motion, but rub or slide along 

 each other, ami consequently absorb a portion of the 

 power in mere useless friction, and in time wear each 

 other out. There is a form for teeth which secures 

 rolling contact of their surfaces, called tho epicycloidal 

 t<>th, from tho name of tho mathematical curve, the 

 epicycloid, adopted in its formation. If ono circle bo 

 caused to roll round the circumference of another circle 

 at rest, every point in tho circumference of tho rolling 

 circle describes a curve, called the epicycloid, which is 

 the resultant of it* two motions, the rotation round its 

 own centre and the revolution round the centre 

 of the other circle. If now the circle which 

 was fixed be caused to roll round the other, 

 every point in its circumference would similarly /* 

 describe the epicycloidal curve proper to its mo- 

 tion. Ami if bow circles were caused to roll on 

 each other at their du relative speeds, the relative 

 motion of every point in their circumferences 

 would be traced along their respective epicycloidal 

 curves. If these curves were cut out in thecircum- * x 



ferenoes of the two wheels, like teeth, projecting 

 between and interlacing with each other, their 

 surfaces would bear against each other without any slid- 

 ing or rubbing motion, but simply rolling along one 

 r like wheels upon rails. The loss of power from 

 friction, and tho amount of wear would Ixj therefore 

 very small 80 far epicycloidal teeth are of great 

 advantage. But there is one great difficulty attend- 

 ing tli-iii which practically forbids their general adoption. 

 As the form of the epicycloidal depends not only on the 

 size of the rolling circle, but also on that of the circle 

 round whirh it rollx, a wli-ol made to gear with one of 

 a given nizo cannot properly gear with one of any other 

 sise. With tin; involute teeth, on the contrary, it was 

 shown that the same form applies to gearing with any 

 size whatever. Ina great many applications of gearing, 

 it is DeCBMary to change tho wheels and pinions in order 

 to change the rates of motion ; and if opicycloidal teeth 



were employed, tho number of wheels and pinion* neces- 

 sary to give the required changes would Ue enormous; 

 whereas with involute teeth, a large number of changes 

 can be effected by different combinations of a few wheels 

 and pinions. Moreover, for large work, wheels 

 pinions are generally cast from patterns which are COM ly, 

 and it therefore becomes important to make the t 

 such as will suit all cases, instead of being limited to one 

 particular case. When teeth are cut out of the solid 

 metal, tho form of tho cutter .can as readily be mbde to 

 suit tho epicycloid as tho involute ; and in such cases, 

 especially for clock-work, and all work of 

 an exact and li_;lit character, the epicycloid 

 is certainly [.referable to the involute. 



KKCIPROCATINQ MI > m >\. Al- 

 though continuous rotary movements are 

 p tho most convenient for coiinnin 



power from one point to another, \> i 

 there are many operations to which machi- 

 nery is adapted demanding motions of an- 

 other character. These arc chiefly of a reci- 

 procating kind ; and, whether the recipro- 

 cating movements take place in a straight 

 line or about a centre or axis, it becomes important t 

 quire into the modes by which continuous rotary m 

 may be converted into them, or the converse. Some- 

 it is desirable that these reciprocating movements should 

 be continuous ; at others that there should be intervals 

 of rest between them ; occasionally that the.)- should be 

 equal in velocity ; and, a_;ain, that the time occupi. 

 them should vary, according to tho special character of 

 the work to bo done, and tho intensity of the force trans- 

 mitted. To describe all the known modes of effe 

 these objects would be to compile a list of almost all tho 

 mechanical inventions ever made, and, were it possible, 

 would demand space far beyond the limits of a tr. 

 like this. Wo will, therefore, merely draw attention to 

 some of the modes of converting motion most generally 

 applied in machinery. Tho arrangement best ad.i 

 to any particular case, or the special modification of 

 action that may be most suitable, are matters that must 

 be loft to tho ingenuity of tho designer. 



The most simple arrangement for converting conti- 

 nuous rotary motion into reciprocating motion, is tho 

 crank or eccentric, which we have already described in 

 connection with the steam-engine. It is generally con- 

 venient to obtain tho reciprocating movement in the arc 

 of a circle instead of in a straight line. For instance, 

 the revolving crank A (Fig. 252), connected by a ro I I! 

 with the arm of a lover mounted on an axis or spindle 

 D, causes it to vibrate in the arc of a circle round the 

 fig. 252. 



centre D ; another lever E, fixed 

 at any part of tho spindle D, can 

 thus be put in reciprocating mo- 

 tion through equal angles, and 

 communicate through a connect- 

 ing-rod F, reciprocating motion 

 to some other body at G. When 

 the arms C and E are in one 

 plane, they form a Mi-crank lever, 

 and are generally connected by 

 the rib H for the sake of strength. 

 The dotted lines on the figure 

 mark tho centre lines of tho levers 

 at the extreme points of their ex- 

 cursions. The first lever C, in its 

 central position, it at right angles 



to a line drawn 



