Simple Machine - Mechanical Advantage

Mechanical Advantage

A simple machine has an applied force that works against a load force. If there are no friction losses, the work done on the load is equal to the work done by the applied force. This allows an increase in the output force at the cost of a proportional decrease in the distance moved by the load. The ratio of the output force to the input force is the mechanical advantage of the machine.

If the simple machine does not dissipate or absorb energy, then its mechanical advantage can be calculated from the machine's geometry. For example, the mechanical advantage of a lever is equal to the ratio of its lever arms. A simple machine with no friction or elasticity is often called an ideal machine.

For an ideal simple machine the rate of energy in, or power in, equals the rate of energy out, or power out, that is

Because power is the product of a force and the velocity of its point of application, the applied force times the velocity the input point moves, v_in, must be equal to the load force times the velocity the load moves, v_out, given by

So the ratio of output to input force, the mechanical advantage, of a frictionless machine is equal to the "velocity ratio"; the ratio of input velocity to output velocity:

(Ideal Mechanical Advantage)

In the screw, which uses rotational motion, the input force should be replaced by the torque, and the velocity by the angular velocity the shaft is turned.