. A text book of physics, for the use of students of science and engineering . have Fig. 59.—Use of an idle wheel. Taking the wheels in pairs, we w„ n< nr w,. 1h n Also,Hence A = W^ wB X wD X tuF JD n0 MF and w_ = a). nt (oF nA x nc x nE It will be noticed that this result is similar to that obtained for the train of belts shown in Fig. 57. Cham drives are sometimes usedinstead of belts in order to avoidslipping. An ordinary bicycle pro-vides an example. The circumferencesof the toothed chain wheels, taken atthe centres of the links of the chain,have the same linear velocity as thefinTHiiii
. A text book of physics, for the use of students of science and engineering . have Fig. 59.—Use of an idle wheel. Taking the wheels in pairs, we w„ n< nr w,. 1h n Also,Hence A = W^ wB X wD X tuF JD n0 MF and w_ = a). nt (oF nA x nc x nE It will be noticed that this result is similar to that obtained for the train of belts shown in Fig. 57. Cham drives are sometimes usedinstead of belts in order to avoidslipping. An ordinary bicycle pro-vides an example. The circumferencesof the toothed chain wheels, taken atthe centres of the links of the chain,have the same linear velocity as thefinTHiiiiiiiimii i hi™ chain, hence we have the same rule as in the case of two belt pulleys, viz. w. FL. R, PLAN Fig. CO.—Train of wheels. Further, the numbers of teeth onthe wheels are proportional to thecircumferences, and therefore to the radii of the wheels ; hence wA t»_ a. In early bicycles the driving was accomplished by means of cranksfixed to the axle of the front wheel ; thus one revolution of the / 60 DYNAMICS CHAP. crank gave one revolution to the wheel, and moved the bicyclethrough a distance equal to the circumference of the wheel. Whenthe statement is made that the gear of a modern bicycle is so much,say 70, it is meant that for one revolution of the cranks the bicyclewill travel a distance equal to that which would be covered by anold-fashioned machine having a driving wheel 70 inches in d be the diameter of the back wheel of the safety bicycle, andlet »A and nB be the numbers of teeth on the crank chain wheel andthe small chain wheel respectively, then Gear=D = ^<Z. bExample.—Varying angular velocity.—In Fig. 61 a point travels withuniform velocit
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