Machinery's Handbook, 31st Edition
2290
Elliptic Gears OTHER GEAR TYPES Elliptic Gears
Gears of this type provide simple means of obtaining a quick-return motion but they present a rather cumbersome manufacturing problem and, as a general rule, it is preferable to obtain quick-return motions by some other type of mechanism. When elliptic gears are used, the two gears that mesh with each other must be equal in size, and each gear must revolve about one of the foci of the ellipse forming the pitch line, as indicated by the dia gram, in Fig. 1. By the use of elliptic gears so mounted, it is possible to obtain a variable motion of the driven shaft, because the gear on the driving shaft, while revolving one half of a revolution, will engage with only a small portion of the circumference of the driven gear, while during the other half of its revolution, the driving gear will engage with a great deal more than one-half of the total number of teeth in the driven gear; hence, the cutting stroke of a machine tool, for example, may be made to have a slow motion, while the return stroke is at a rapid rate. The ellipse has two points, each of which is called a focus, located as indicated at A and B . The sum of the distance between the foci and the elliptic curve is constant at all points and is equal to the longer or major axis of the ellipse. On account of this peculiarity of the ellipse, two equal ellipses can be made to mesh with each other during a complete revolution about their axes, if one is mounted on a shaft at its focus A and the other at its focus B . Pitch Lines
A
B
Focus – Center of Rotation
Fig. 1. General Arrangement of Elliptic Gears. Planetary Gearing
Planetary or epicyclic gearing provides means of obtaining a compact design of trans mission, with driving and driven shafts in line, and a large speed reduction when required. Typical arrangements of planetary gearing are shown by the following diagrams which are accompanied by speed ratio formulas. When planetary gears are arranged as shown by Fig. 5, Fig. 6, Fig. 9 and Fig. 12, the speed of the follower relative to the driver is in- creased, whereas Fig. 7, Fig. 8, Fig. 10, and Fig. 11 illustrate speed-reducing mechanisms. Direction of Rotation.— In using the following formulas, if the final result is preceded by a minus sign (negative), this indicates that the driver and follower will rotate in opposite directions; otherwise, both will rotate in the same direction. Compound Drive.— The formulas accompanying Fig. 19 through Fig. 22 are for obtain- ing the speed ratios when there are two driving members rotating at different speeds. For example, in Fig. 19, the central shaft with its attached link is one driver. The internal gear z , instead of being fixed, is also rotated. In Fig. 22, if z = 24, B = 60 and S = 3 1 ∕ 2 , with both drivers rotating in the same direction, then F = 0, thus indicating, in this case, the point where a larger value of S will reverse follower rotation. Planetary Bevel Gears.— Two forms of planetary gears of the bevel type are shown in Fig. 23 and Fig. 24. The planet gear in Fig. 23 rotates about a fixed bevel gear at the center of which is the driven shaft. Fig. 24 illustrates the Humpage reduction gear. This is some- times referred to as cone-pulley back-gearing because of its use within the cone pulleys of certain types of machine tools.
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