A Text-Book On Applied Mechanics: Specially Arranged for the Use of Science ... 2
A Text-Book On Applied Mechanics: Specially Arranged for the Use of Science ... 2
Andrew Jamieson
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At that instant, the wheel A is rotating about this line as an instantaneous axis. Clearly, this instantaneous axis passes through the pitch point, p, and is parallel to the axis of A or B. Hence, at a given instant any point, P, on wheel A is rotating about the axis through p, with an angular velocity (w^ + u^). By similar reasoning, if each of the wheels in internal contact receive an angular - w^, then wheel B will be brought to rest,, and any point on wheel A will be rotating about the inst...antaneous axis through p, with an angular velocity (w^ - w^). If, then, P be a point of contact between a pair of teeth, P /? is the direction of the common normal to the two teeth at that point, and the velocity of P perpendicular to Fp is the velocity of sliding between the teeth. Let V s= Velocity of pitch circles. „ V = Velocity of P perpendicular to "Pp. „ r = Distance of P from pitch point, p. Then, from what has been demonstrated above, we get :^ Or, V = («i + w^) r, for external gearing, „ = (wjL - W2) ^y » internal „ But, V = Wj Rj, = W2 Rg- Let arc p P be denoted by a?, and suppose the wheels to receive a small* citcular* displacement, dx, as measured along the pitch 298 LECTURE XVI.
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