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# Gears - Gears Gears are machine elements that transmit...

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Gears Gears are machine elements that transmit motion by means of successively engaging teeth. The gear teeth act like small levers . 7.1 Gear Classification Gears may be classified according to the relative position of the axes of revolution. The axes may be 1. parallel, 2. intersecting, 3. neither parallel nor intersecting. Here is a brief list of the common forms. We will discuss each in more detail later. Gears for connecting parallel shafts Gears for connecting intersecting shafts Neither parallel nor intersecting shafts Gears for connecting parallel shafts 1. Spur gears

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The left pair of gears makes external contact , and the right pair of gears makes internal contact 2. Parallel helical gears 3. Herringbone gears (or double-helical gears) 4. Rack and pinion (The rack is like a gear whose axis is at infinity.) Gears for connecting intersecting shafts
1. Straight bevel gears 2. Spiral bevel gears Neither parallel nor intersecting shafts 1. Crossed-helical gears 2. Hypoid gears 3. Worm and wormgear 7.2 Gear-Tooth Action 7.2.1 Fundamental Law of Gear-Tooth Action

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Figure 7-2 shows two mating gear teeth, in which Tooth profile 1 drives tooth profile 2 by acting at the instantaneous contact point K . N 1 N 2 is the common normal of the two profiles. N 1 is the foot of the perpendicular from O 1 to N 1 N 2 N 2 is the foot of the perpendicular from O 2 to N 1 N 2 . Figure 7-2 Two gearing tooth profiles Although the two profiles have different velocities V 1 and V 2 at point K , their velocities along N 1 N 2 are equal in both magnitude and direction. Otherwise the two tooth profiles would separate from each other. Therefore, we have (7-1) or (7-2) We notice that the intersection of the tangency N 1 N 2 and the line of center O 1 O 2 is point P , and
(7-3) Thus, the relationship between the angular velocities of the driving gear to the driven gear, or velocity ratio , of a pair of mating teeth is (7-4) Point P is very important to the velocity ratio, and it is called the pitch point . Pitch point divides the line between the line of centers and its position decides the velocity ratio of the two teeth. The above expression is the fundamental law of gear-tooth action . 7.2.2 Constant Velocity Ratio For a constant velocity ratio, the position of P should remain unchanged. In this case, the motion transmission between two gears is equivalent to the motion transmission between two imagined slipless cylinders with radius R 1 and R 2 or diameter D 1 and D 2 . We can get two circles whose centers are at O 1 and O 2 , and through pitch point P . These two circle are termed pitch circles . The velocity ratio is equal to the inverse ratio of the diameters of pitch circles. This is the fundamental law of gear-tooth action.

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Gears - Gears Gears are machine elements that transmit...

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