. Theory of structures and strength of materials. Let P be the effort and Q the weight lifted, the directions;of P Rud Q being parallel. Let W be the weight of the wheel and axle. Let R^ and R^ be the vertical reactions at the bearings. Let/ be the radius of the wheel. Let ^ axle. Let r bearings. Take moments about the axis. Then Pp â Q? ~ Ri sin 0 â R^r sin 0 = o. . (4) TOOTHED GEARING. 331 But Hence, R,-\-K= W+P+Q- (5> Pp- Qg=( W-\- P + Q)r sin 0 = ( W-\- P+ 0/r, or Efficiency.âIn turning through an angle d,motive work = PpQ,useful work = Qq^, (6) .*. efficiency = Q . Qgl_QgPpB - Pp and t
. Theory of structures and strength of materials. Let P be the effort and Q the weight lifted, the directions;of P Rud Q being parallel. Let W be the weight of the wheel and axle. Let R^ and R^ be the vertical reactions at the bearings. Let/ be the radius of the wheel. Let ^ axle. Let r bearings. Take moments about the axis. Then Pp â Q? ~ Ri sin 0 â R^r sin 0 = o. . (4) TOOTHED GEARING. 331 But Hence, R,-\-K= W+P+Q- (5> Pp- Qg=( W-\- P + Q)r sin 0 = ( W-\- P+ 0/r, or Efficiency.âIn turning through an angle d,motive work = PpQ,useful work = Qq^, (6) .*. efficiency = Q . Qgl_QgPpB - Pp and the ratio tt is given by eq. (6). i6. Toothed Gearing.âIn toothed gearing the friction ispartly rolling and partly sliding, but the former will be disre-garded, as it is small as compared with the Fig. 2S5. Let the pitch-circles of a pair of teeth in contact at thepoint B touch at the point A ; and consider the action beforereaching the line of centres 0,0^, , along the arc ofapproach. 332 THEORY OF STRUCTURES. The line AB is normal to the surfaces in contact at thepoint B. Let R be the resultant reaction at B. Its direction, themotion being steady, makes an angle 0, equal to the angle offriction, with AB. Let ^ be the angle between 0^0^ and AB. Let the motive force and force of resistance be respectivelyequivalent to a force P tangential to the pitch-circle (9,, andto a force Q tangential to the pitch-circle 0â. Let i\ , 7\ be the radii of the two wheels. The work absorbed by friction in turning through the smallarc (is = {P-Q)ds (I) Consider the wheel O^, and take moments about the centre. Pr^ = R\r^ sin {d â (p)-\-X sin (pl, ... (2) where AB = x. Similarly, from the wheel O^ Qr.^ = R\r^ sin {0 â <p) â X sin ^\. ... (3)Hence, X Q sin {B - 0) â - sin 0 T ~ X â
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Keywords: ., bookcentury1800, bookdecade1890, bookpublishernewyo, bookyear1896
