. A text book of elementary mechanics, for the use of colleges and schools. number of teeth in the Weight-wheel. The final equation above may be written: W ~ B X T This is another application of the principle explainedin Art. 200, since, in the case supposed, the machine isreally compounded of the wheel and axle and the toothedwheels. 212.] TOOTHED WHEELS. 223 211. Toothed Wheels on the Principle of Work. Sup-pose (Fig. 153) that the power continues to act throughone circumference of its lever-arm, 2ttR (= s); if. notoothed wheels intervened, the weight would rise througha distance equal to th
. A text book of elementary mechanics, for the use of colleges and schools. number of teeth in the Weight-wheel. The final equation above may be written: W ~ B X T This is another application of the principle explainedin Art. 200, since, in the case supposed, the machine isreally compounded of the wheel and axle and the toothedwheels. 212.] TOOTHED WHEELS. 223 211. Toothed Wheels on the Principle of Work. Sup-pose (Fig. 153) that the power continues to act throughone circumference of its lever-arm, 2ttR (= s); if. notoothed wheels intervened, the weight would rise througha distance equal to the circumference of the axle,%7zr (= 1i). But the ratio of the distances throughwhich the toothed wheels will turn is the inverse ratio oftheir number of teeth; that is, if the smaller wheel has20 and the larger 40 teeth, the former will revolve twice /40\ T (—), while the other turns once; or, in general, —. There-fore P %nr t r X 7F = TT X w 2ttB R r as above. 212. Application of Toothed Wheels. An illustrationof the use of this machine is seen in Fig. 154, to which. Fig. 164. the final equation of Art. 210 applies. Severa* series ortrains of toothed wTheels are employed in derricks 224 STATICS. [213. and cranes for raising very large weights. One of these,with three pairs of toothed wheels, is represented inFig. 155. The relation of the power to the weight here,by the preceding principles, is: t t V (r) tyr Jt T 2J/ Tn For example, if P = 10 lbs., the radius of the axleinches, that of the crank-arm (R) = %\ feet; s %p if, also, the number of ^ [j? teeth in each of the smaller wheels (t, V, t)is 20, and of the largerwheels (T, T, T)120,then the weight which. could be raised, all hurt-ful resistances being leftout of account, would be21,600 lbs., or about 10tons. 213. An excellent illustra-tion of the use of toothedwheels, where a gain inpower is required, is af-forded by the back gearsof a large turning-lathe. Thearrangement is such that the
Size: 1728px × 1446px
Photo credit: © The Reading Room / Alamy / Afripics
License: Licensed
Model Released: No
Keywords: ., bookcentury1800, bookdecade1880, booksubjectmechanics, bookyear18
