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Kinematics of Gears

# Kinematics of Gears - Kinematics of Gears Chapter 8...

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1 Kinematics of Gears Chapter 8 Material in this lecture was taken from chapter 8 of Mott, Machine Elements in Mechanical Design, 2003 Kinematics of Gears Gears are toothed, cylindrical wheels used for transmitting motion and power from one rotating shaft to another. The teeth of a driving gear mesh accurately in the spaces between teeth on the driven gear. Mott, Machine Elements in Mechanical Design, 2003 Speed Reduction Ratio Often gears are employed to produce a change in the speed of rotation of the driven gear relative to the driving gear. If the smaller top gear (pinion) is driving the larger, lower gear (gear), the larger gear will rotate more slowly. The amount of speed reduction is dependent on the ratio of the number of teeth in the pinion to the number of teeth in the gear according to: – n p / n g = N G / N P

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2 Kinds of Gears The major types of gears are: – Spur gears – Helical gears – Bevel gears – Worm/wormgear sets Kinds of Gears con’t Spur gears have teeth that are straight and arranged parallel to the axis of the shaft that carries the gear. The curved shape of the faces of the spur gear teeth have a special geometry called an involute curve. This shape makes it possible for two gears to operate together with smooth, positive transmission of power. Kinds of Gears con’t The teeth of helical gears are arranged so that they lie at an angle with respect to the axis of the shaft. The angle, called the helix angle, can be virtually any angle. Typical helix angles range from approximately 10 o to 30 o , but angles up to 45 o are practical. The helical teeth operate more smoothly than equivalent spur gear teeth, and stresses are lower.
3 Kinds of Gears con’t Bevel gears have teeth that are arranged as elements on the surface of a cone. The teeth of straight bevel gears appear to be similar to spur gear teeth, but they are tapered, becoming wider at the outside and narrower at the top of the cone. Bevel gears typically operate on shafts that are 90 o to each other. Specially designed bevel gears can operate on shafts that are at some angle other than 90 o . Kinds of Gears con’t When both bevel gears in a pair have the same number of teeth, they are called miter gears and are used only to change the axes of the shafts to 90 degrees. No speed change occurs. A rack is a straight gear that moves linearly instead of rotating. When a circular gear is mated with a rack, the combination is called a rack and pinion drive. Kinds of Gears con’t A worm and its mating wormgear operate on shafts that are at 90 o to each other. They typically accomplish a rather large speed reduction ratio compared to other types of gears.

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Kinematics of Gears - Kinematics of Gears Chapter 8...

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