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James J. Ling.
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Linear Mechanical Systems
GEAR TRAINS
Gears are used to transmit torque and motion of constant ratio from one shaft to another (there are noncircular gears which are used to transmit nonuniform motion, such as elliptical gears. Noncircular gears are beyond the topic of this chapter). Gears can transmit large torque and they can be made compact.
Kinematically, gear is a form closed kinematic pair with two degrees-of-freedom that is used to join two links. In everyday usage gear refers to a rigid body which has toothed kinematic elements to form a gear pair. One can utilise both meanings as long as there is no confusion.
Since a gear pair is form closed, there is a constant speed ratio between the links. Due to these characteristics they are also called "positive drive" mechanisms in contrast to friction drives such as rollers and belt drives.
Gear trains are called "linear mechanical systems" since the angular relationship between the links can be expressed in terms of a linear function. Other linear mechanical systems are belts (flat, V-belt, timing belt), rollers and chain drives. These mechanical systems can also be kinematically analysed using the methods that will be discussed in this section. However, in case of friction drives, one must assume that there is no slippage and one must neglect the velocity pulsation in case of chain drives.
Direction of rotation of the links (gears) may be clockwise or counter-clockwise. In spatial gear trains, however, this convention may also be misleading. In such cases arrows may be used on the figure to indicate the direction of rotation of each link. In gear trains sometimes it is necessary to employ positive and negative signs for speed to indicate that the speed is in the same or opposite sense from some preselected direction (e.g. input speed direction). Usually the direction will not be indicated by the equations and must be obtained by the inspection of the mechanism.
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