The screw is a modification of the inclined plane combined with a lever. The threads of a screw or a bolt are an inclined plane that has been rolled into the shape of a cylinder. A lever is used to turn the threads, which causes the load to move along the cylinder. An example of this principle is the screw type jack.
Figure 4.16 illustrates this principle as it is used in a jack, where the jack handle is the force arm. The same principle applies to a bolt and nut. In the case of a
FIGURE 4.16. Lever equation applied to a screw jack.
bolt and nut the lever arm is the wrench, and the resultant force is the clamping pressure.
The distance between any two threads, called pitch, determines the amount of movement per revolution. The mechanical advantage is determined by the ratio of the radius of the lever and the pitch distance. The lever equation can be used to express this relationship mathematically:
Fa x Aa = Fr x Ar where Fa = Forced applied at the end of the lever arm; Fr = Amount of weight the jack will lift; Aa = Length of the lever arm; Ar = Pitch of the threads.
Problem: If the lever arm in Figure 4.16 is 18 in long and the pitch of the threads is 0.125 in, how much weight will the jack lift when 50.0 lb of force is applied (ignoring friction)?
Solution: Rearranging the equation to solve for Fr gives:
Fr = —-a =-= 7,200 lb or 7.20 E3 lb r Ar 0.125 in
This problem illustrates that when using a screw jack a small amount of force will lift a large load. The disadvantage is that the load will only be lifted 0.125 inches (1/8 of an inch) for every revolution of the handle.
Friction will affect the performance of this machine more than the others. With the proper lubrication it can be kept to a manageable level.
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