Gears and cranks

Gears are used to change the rotating speed in an automobile engineA gear is a wheel with teeth that interlock with matching teeth on a mating gear to transmit rotating motion and torque. Gears can transmit much higher forces than smooth wheels. Gears are used to change rotational forces and speeds in many machines, including automobile transmissions. Related to the gear is the sprocket, which is found in the drive train of a bicycle. A sprocket is a toothed wheel that engages a chain instead of another gear. Read the text aloud
Gear ratio and the equivalent wheel and axle simple machineInterlocking gears with different numbers of teeth turn at different rotational speeds. The gear ratio is the ratio of turns of the output gear to turns of the input gear. The gear ratio in the example is 16 ÷ 8 = 2. Each turn of the input gear moves 16 teeth through the point of contact, forcing the output gear to turn twice. The gear ratio is the inverse of the ratio of teeth. Note that, like two touching wheels, interlocking gears always rotate in opposite directions. Read the text aloud
GR= output turns input turns = input teeth output teeth
GR  = gear ratio
Gear ratio
Mechanical advantage of two gearsThe input gear’s teeth apply a force to the output gear’s teeth at the point of contact. At this point of contact, the input force equals the output force (if 100% efficiency is assumed). If the radii of the input and output gears differ, then the input and output torques will differ, too, because torque is force times radius. The mechanical advantage of two gears is the ratio of the output to input torque, which is equal to MA = ro/ri or 1/GR. As you can see in the illustration at right, the MA is also the ratio of the number of output teeth to the number of input teeth. Read the text aloud
(12.6) M A g = τ o τ i = output teeth input teeth
MAg  = mechanical advantage
τo  = output torque (N m)
τi  = input torque (N m)
MA of
two gears
Four gears in an example of a motorSmall electric motors turn at high speeds but produce low torque. Many robotic applications require low speed and high torque. Multiple gear ratios are used to both reduce the speed and increase the torque. The four gears in the diagram make an overall mechanical advantage of 16. Read the text aloud Show How does a four-gear machine work?
What is the <i>MA</i> and gear ratio for these two gears?For the two gears at right, what is the
  1. gear ratio if A is the input gear?
  2. mechanical advantage if A is the input gear?
  3. gear ratio if B is the input gear?
  4. mechanical advantage if B is the input gear?

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