Classification of Levers

A lever is a rigid member that turns about a fixed pivot called the fulcrum. The effort is the input force applied to it; the load is the output force or resistance it acts against. Both forces are measured in newtons (N).

Think of using a crowbar to lift an object. Your hand supplies the effort, the point where the bar rests supplies the fulcrum, and the object provides the load. Changing their positions changes how much force and movement the lever produces. A lever can make a large load easier to move, change the direction of movement, or produce a larger output movement from a small input movement.

The three classes of lever are distinguished by which of these three elements lies in the middle. The arrangement can be drawn either way round without changing its class.

Class 1: the fulcrum is in the middle

A class 1 lever has the fulcrum between the effort and the load. The effort and load points move in opposite directions: pushing one end down raises the other.

Scissors contain two class 1 levers. The central screw is the fulcrum, your fingers apply effort at the handles, and the material being cut provides resistance at the blades. Placing tougher material nearer the screw makes it easier to cut because the load is closer to the fulcrum while the effort remains farther away.

A crowbar used for lifting is another example. A long effort arm and a short load arm give force multiplication. Moving the fulcrum closer to the load increases this effect. However, class 1 does not automatically mean force multiplication: a shorter effort arm than load arm gives a smaller output force but a larger output movement.

Class 2: the load is in the middle

A class 2 lever has the load between the fulcrum and the effort. The effort point is farther from the fulcrum than the load point, so the ideal lever multiplies force. The effort must move farther than the load, and the two points move in the same direction.

In a bottle opener, the fulcrum is where the opener bears against the cap, the load is where it hooks under the cap, and your hand applies effort farther along the handle. The longer handle makes the cap easier to lift.

A foot pump can also use a class 2 lever. The pedal pivots at one end, your foot supplies effort at the other, and the connection to the pump is between them. The pedal’s larger movement produces a smaller movement with greater force at the pump connection.

Class 3: the effort is in the middle

A class 3 lever has the effort between the fulcrum and the load. Its effort arm is shorter than its load arm. It therefore has a mechanical disadvantage: the effort must be greater than the output load. In return, the load moves farther and faster than the effort point. Both move in the same direction.

Tweezers show why this arrangement is useful. The joined end is the fulcrum, your fingers apply effort along the arms, and the load is at the tips. A small finger movement produces a larger movement at the tips.

The lifting arm of a hydraulic engine hoist is also a class 3 lever. It pivots at the top of the upright frame, the hydraulic piston pushes upward partway along the arm, and the engine hangs at its outer end. The long arm can reach over the car body, but the piston must provide a force greater than the engine’s load. Classification describes the lifting arm, not the hydraulic system supplying its effort.

Mechanical advantage compares forces

Mechanical advantage (MA) tells you how many times the output load compares with the input effort:

An MA greater than 1 means force multiplication. An MA of 1 means equal input and output forces. An MA below 1 means a mechanical disadvantage. MA has no unit because it divides one force by another.

For example, suppose a lever moves a load of 240 N with an effort of 60 N. Its mechanical advantage is $240 \div 60 = 4$: the output load is four times the input effort.

You can rearrange the equation to find either force:

Suppose a lever has an MA of 3 and must move a load of 150 N. The required effort is $150 \div 3 = 50\text{ N}$. Alternatively, an effort of 40 N acting through a mechanism with an MA of 3 produces a load force of $3 \times 40 = 120\text{ N}$.

Velocity ratio compares movements

Force multiplication does not provide something for nothing. A smaller effort has to act through a greater distance to move the load through a smaller distance. Velocity ratio (VR) measures this trade-off:

Use corresponding distances from the same movement, expressed in the same units. For example, suppose the effort moves 200 mm while the load moves 40 mm. Then $VR = 200 \div 40 = 5$. The effort moves five times as far as the load. VR has no unit.

For a straight lever with parallel effort and load forces acting perpendicular to it, VR can also be found from its arm lengths:

Both arms are measured from the fulcrum. For example, an effort arm of 300 mm and a load arm of 100 mm give $VR = 3$. In a class 2 lever, the effort arm extends past the load; in a class 3 lever, the load arm extends past the effort.

Efficiency connects force and movement

An ideal lever has no energy losses, so $MA = VR$ and its efficiency is 100%. Real mechanisms lose some input energy through friction and deformation. Their actual MA is lower than their VR.

Efficiency is the proportion of input work transferred into useful output work. It can be calculated from the two ratios:

Suppose a lever lifts a load of 240 N using an effort of 60 N. During the same movement, the effort travels 200 mm and the load travels 40 mm. Its MA is 4 and its VR is 5, so its efficiency is $(4 \div 5) \times 100 = 80\%$. This means 80% of the input work becomes useful output work.

These relationships help designers choose a suitable arrangement. A force-multiplying lever reduces the effort needed but requires more input travel. A class 3 lever sacrifices force to increase output movement or reach. Reducing friction improves efficiency, allowing more of the input work to perform the intended task.