SUN AND PLANET MOTION FRICTION. ] APPLIED MECHANICS. 



899 



cities of the wheels at these points vary inversely as the 

 lengths of these radii. If, for instance, C A be J-th of 

 A B, and therefore C B = ths of C A, K M being equal 

 to C A, and K L to C B, when the points B and M are 

 engaged, the wheel 2 is revolving with 3 times the angu- 

 lar velocity of 1, because the radius C B is three times 

 the length of K M ; but when the points A and L are 

 engaged, the wheel 2 is revolving with Jrd of the angu- 

 lar velocity of 1, because A C is Jrd of 'K L. So at all 

 points intermediate to these, except at N, O, P, and Q, 

 where the radii are equal, the relative angular velocities 

 of the wheels vary between the limits we have named. 



For some purposes in the manufacture of textile fabrics, 

 gearing like that in Fig. 263 is employed. These vary the 

 Fig. 263. 



'ilar velocities 4 times in every revolution ; and the 

 principal condition of their construction is, that the dis- 

 tance between their centres must be a constant quantity. 

 SUN AND PLANET. The sun and planet-wheel is a 

 contrivance for converting a reciprocating into a rotary 

 motion. It was employed by Watt instead of the crank 

 in a steam-engine, not because he preferred it to the 

 latter, but because, through the bad faith of a workman 

 who patented the crank as his own invention, he was 

 precluded from employing it. The sun or central wheel 

 A (Fig. 264) gears with the planet-wheel B, which is 



caused to revolve round 

 A without rotating round 

 its own centre, being 

 fixed to the end of the 

 connecting-rod, and re- 

 tained in gear with A by 

 means of a link which 

 \ connects their centres, 

 \ and revolves freely with 

 >U^4PS 1 _ '1 B. When the sun and 



*5 



rj-. 



\ <-. 



planet-wheels have equal 

 numbers of teeth, every 

 revolution of the latter 

 causes 2 revolutions of 

 the former, as may be 

 understood by watching 

 the relative positions of 

 a tooth in each at different parts of a revolution. When 

 the planet is vertically above the sun-wheel, the tooth B of 

 the one is engaged with the space A of the other ; and when 

 the planet has made half a revolution, so as to be verti- 

 cally below the sun, the sun has made a complete revolu- 

 tion, so as to bring the space A quite round to the point 

 where it was at the commencement. One half-revolution 

 of A is owing to the half-revolution of B propelling it 

 round, while the other half-revolution of A is effected by 

 the roll of the toothed half circumference of B presenting 

 fresh teeth and spaces to A at the successive points of 

 its revolution. When the numbers of teeth in the two 

 wheels are different, the velocity of the sun-wheel varies 

 accordingly, as may be best understood by an example. 

 Let us suppose that the sun-wheel has 40 teeth, and that 

 the planet has 60 ; then, during one revolution of the 

 planet, it has presented the whole of its 50 teeth to the 

 sun-wheel, and therefore turned it through 60 teeth, as 

 well as its own complete revolution of 40 teeth. The 

 gun-wheel, therefore, during 1 revolution of the planet- 

 wheel, turns round a distance equivalent to 00 of its 

 teeth, or Jfjths = 2^ revolutions. 

 FRICTION-BREAKS. It is often necessary to pro- 



vide the means of stopping the motion of machinery 

 when the mere cessation of power in the prime mover is 

 not sufficient for the purpose. In a crane, when lower- 

 ing a heavy weight, it may be desirable to lower it to a 

 certain point and no farther, and therefore to stop the 

 machinery of the crane wheu the weight has descended 

 sufficiently far. Or, again, in any apparatus provided 

 with a fly-wheel, or parts moving with considerable 

 momentum, such as might continue the movement after 

 the power has been withdrawn, it may be essential to 

 provide the means of stopping the movement more sud- 

 denly. The most simple arrangement for this purpose 

 is the break or friction-strap (Fig. 2C5). a is a wheel 



Fig. 269. 



revolving with the rest of the machinery, and 6 6 a 

 flexible strap of iron passing round part of its circum- 

 ference. One end of this strap, being fixed by a pin to 

 some motionless part of the machine, and the other 

 attached to a lever c pivoted on a fulcrum d, on applying 

 force to the long arm of the lever, the strap is drawn 

 tightly round the circumference of the wheel, and the 

 friction caused by the close contact soon brings the 

 wheel to rest. The great advantage of employing fric- 

 tion as a means of arresting motion, consists in the 

 circumstance that it acts, not suddenly, but gradually. 

 Were some solid obstacle presented to the motion of any 

 part of a train of heavy or rapidly moving machinery, 

 the momentum of all the moving parts would have to 

 besuddenly destroyed ; and as no time would be afforded 

 for this operation, the strain would be incalculably great, 

 and inevitable damage would ensue. But when the 

 friction-break is employed, the wheel to which it is 

 applied makes perhaps two or three revolutions before it 

 comes finally to rest, and the time so occupied allows 

 the momentum of a)l the parts connected with it to 

 expend itself, in overcoming the great additional resis- 

 tance caused by the friction. 



In putting an extensive train of machinery in motion, 

 the inertia of all the parts at rest has to be overcome in 

 like manner ; and were this done suddenly, the strain 

 would be as great as in the opposite case of suddenly 

 arresting their motion. This contingency is generally 

 met by the use of pulleys and straps in communicating 

 the power. A strap, communicating motion from one 

 pulley to another, acts only by its friction on their circum- 

 ferences ; and when the strain which it has to overcome 

 exceeds the force due to its friction, the strap slips at first 

 to a considerable extent, but gradually less and less, un- 

 til the proper velocity is attained, and the strap and 

 circumference of the pulley move in unison. In cases 

 where straps cannot be conveniently applied for driving 

 a train, a friction coupling is employed. Fig. 20G is a 

 diagram of one very generally used. A is the driving 

 shaft, and B the driven shaft, the ends of which are free 

 to revolve in the boss of a wheel C, true and smooth on 

 its circumference, to which is applied a friction -strap D, 

 worked by a suitable lever. Within the wheel C a bevel- 

 pinion F is mounted in bearings, its axis being at right 

 angles to that of the wheel and shafts ; and bevel-wheels 

 G and H, one on each shaft, are fitted to gear with the 

 pinion F. If the friction -strap D be loose, so as to leave 

 the wheel C free to revolve, the rotation of the shaft A, 

 and its wheel G, gives motion to the pinion F, and causes 



