By Damir Jelaska(auth.)
Chapter 1 advent (pages 1–16):
Chapter 2 Geometry of Cylindrical Gears (pages 17–156):
Chapter three Integrity of Gears (pages 157–240):
Chapter four parts of Cylindrical apparatus force layout (pages 241–278):
Chapter five Bevel Gears (pages 279–330):
Chapter 6 Planetary apparatus Trains (pages 331–386):
Chapter 7 computer virus apparatus Drives (pages 387–431):
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Extra resources for Gears and Gear Drives
3 Involute Teeth and Involute Gears So far, the two-dimensional meshing process of involute teeth proﬁles has been observed. 14). Thus, any gear cylinder is deﬁned by the corresponding diameter and width b. In rolling a straight line over a base circle, any point of the straight line traces out an involute – the involute tooth proﬁle. The real tooth ﬂank is generated by rolling a plane over a base cylinder whose transverse (cross-) section is the base circle. It is important to note that any point of the plane traces out its own involute curve.
In this, point A of the stick forms curve a, point B traces out curve b and successive positions of the stick kinematic poles trace out the curve pp. If now the triangles A1B1P1, A2B2P2 and A3B3P3 are displaced in the last position of the stick in the way A1B1, A2B2 and A3B3 are covered with AB, new positions P01 ; P02 and P03 will be obtained for the instantaneous pole of speeds. By joining these points, the curves of relative positions are obtained, relative to the last position of stick AB of instantaneous pole of speeds.
As the pitch circles roll one upon the other, it becomes clear that the teeth of both gears are distributed over their own pitch circles with same pitch pw, that is: pw1 ¼ pw2 ¼ pw : ð2:14Þ This pitch has to ﬁnd a place over the perimeter of the pitch diameters as many times as the number of teeth in the gears: ð2:15Þ z1;2 Á pw ¼ pd w1;2 where z1,2 are the numbers of teeth of gears 1 and 2. It follows that: d w2 z2 ¼ : d w1 z1 ð2:16Þ Gears and Gear Drives 24 The analytical expression of the main rule of toothing now gets a ﬁnal form: i¼ n1 v1 d w2 z2 ¼ ¼ ¼ ¼ const: n2 v2 d w1 z1 ð2:17Þ In the case of an external gear pair, the two cylindrical gears rotate in opposite directions, that is their angular speeds or rotational speeds have opposite signs; the transmission ratio is negative.