. The railroad and engineering journal . nt is attached to thegenerating circle at P, and that as the wheel, pinion and circlerevolve, that this point describes an internal or hypocycloidalcurve/ q on the surface of the wheel and an epicloidal curve,p r, on the surface of the pinion.* Then as ^hese curves are * The method of drawing these curves was describedIroblems 93 and 93. I Chapter XI, i^ec 472 THE RAILROAD AND [October, 1891. traced simultaneously by the same point on both the wheel andpinion, the two curves will touch or be tangent to each otherat every position in the path of the poin
. The railroad and engineering journal . nt is attached to thegenerating circle at P, and that as the wheel, pinion and circlerevolve, that this point describes an internal or hypocycloidalcurve/ q on the surface of the wheel and an epicloidal curve,p r, on the surface of the pinion.* Then as ^hese curves are * The method of drawing these curves was describedIroblems 93 and 93. I Chapter XI, i^ec 472 THE RAILROAD AND [October, 1891. traced simultaneously by the same point on both the wheel andpinion, the two curves will touch or be tangent to each otherat every position in the path of the point. Next, take a center. A, on the line b P D, and with a radiusequal to Y2 ^ P describe another generating circle, 0 b Q P, drawn, their form mutt be produced by the angular movementof the tracing point, which is equal to that of the two pitch cir-cles. Consequently, the motion which is transmitted from thepinion to the wheel, or vice versci, will have the same velocity asthat of the tracing point and pitch circles. Therefore the linear. D tangent to the pitch circles at P. Suppose, as before, that atracing point is attached to this generating circle at P and thatthe two pitch circles and O h Q P are in contact at P, and allturn in the reverse direction to that indicated by the darts with-out slipping, and that the tracing point marks a curve, P f, onthe surface of the wheel and a line, P e, on the pinion. Then,as P f and P e have also been drawn simultaneously by thesame point, they must touch or be tangent to each other at every ..li iB E Fig 339- F - ~L 0 \ / / 1 /^ 7 ._,..-A 1 A~^ V j \ \ y^ - s / \ K G J/ H D C position in the path of the point. It follows, then, that if thecurve / P </ forms the outline of a tooth on the wheel, and r P ethat of a tooth of the pinion, that they will be tangent to eachother in every position in which these outlines are in contactwhile the wheel and pinion revolve. This is shown in fig. 33S,in which I, 2, 3-14 and 1, 2, 3-14 represent suc
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Keywords: ., bookcentury1800, bookdecade1880, booksubjectrailroa, bookyear1887
