BIZOMAT MAKEOS · Mechanics
Lever Force with Several Loads
What effort balances these loads on a lever, or how long must the effort arm be?
Balance of a lever about its fulcrum: the effort needed at a given arm to hold up to three loads at their distances, or the arm length needed for a given effort, with the mechanical advantage and the fulcrum reaction.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Solve for | choice | Find the effort or the effort-arm length. |
| Lever type | choice | Arrangement of fulcrum, loads and effort (sets the fulcrum reaction). |
| Effort arm (fulcrum to effort) | mm | Distance from the fulcrum to where the effort is applied. |
| Available effort (arm mode) | N | Effort available, when solving for the arm. |
| Loads (distance from the fulcrum; 0 = unused) | ||
| Load 1 | N | First load. |
| Distance 1 | mm | Its distance from the fulcrum. |
| Load 2 | N | Second load. |
| Distance 2 | mm | Its distance. |
| Load 3 | N | Third load. |
| Distance 3 | mm | Its distance. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Solve for
- What it is
- Whether to find the effort needed at a known effort arm, or the effort arm needed when the available effort is known.
- Units and format
- Choose one of 2 options from the list: Effort at a given arm; Arm for a given effort.
- Example
- The form opens with “Effort at a given arm” selected as a worked example. Choose the option that matches your case.
- Get it right
- Only the effort arm is used when solving for the effort, and only the available effort when solving for the arm.
What this means: Lever type
- What it is
- Where the fulcrum sits relative to the effort and the loads. It does not change the effort or arm found; it sets the fulcrum reaction and the arrangement check.
- Units and format
- Choose one of 3 options from the list: Fulcrum between effort and loads; Loads between fulcrum and effort; Effort between fulcrum and loads.
- Example
- The form opens with “Fulcrum between effort and loads” selected as a worked example. Choose the option that matches your case.
What this means: Effort arm (fulcrum to effort)
- What it is
- The distance along the lever from the fulcrum to the point where the effort is applied, measured at right angles to the line of the effort; used when solving for the effort.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 1000000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 600 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The effort needed is inversely proportional to this arm.
What this means: Available effort (arm mode)
- What it is
- The force you can apply at the effort point, such as a hand, cylinder or actuator force; used when solving for the arm length.
- Units and format
- Enter a number in N: newtons. The form accepts 0.000001 N or more. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 100 N as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The arm needed is inversely proportional to the available effort.
Loads (distance from the fulcrum; 0 = unused)
What this means: Load 1
- What it is
- A load acting on the lever at the matching distance from the fulcrum. Zero leaves the row out.
- Units and format
- Enter a number in N: newtons. The form accepts 0 N or more. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 800 N as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Enter a force in newtons: multiply a mass in kg by gravity.
What this means: Distance 1
- What it is
- The distance from the fulcrum to the line of action of the matching load, measured along the lever at right angles to the load.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 1000000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 100 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Measure every distance from the fulcrum, not from the end of the lever.
What this means: Load 2
- What it is
- A load acting on the lever at the matching distance from the fulcrum. Zero leaves the row out.
- Units and format
- Enter a number in N: newtons. The form accepts 0 N or more. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0 N as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Distance 2
- What it is
- The distance from the fulcrum to the line of action of the matching load, measured along the lever at right angles to the load.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 1000000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Load 3
- What it is
- A load acting on the lever at the matching distance from the fulcrum. Zero leaves the row out.
- Units and format
- Enter a number in N: newtons. The form accepts 0 N or more. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0 N as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Distance 3
- What it is
- The distance from the fulcrum to the line of action of the matching load, measured along the lever at right angles to the load.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 1000000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
Method and formulas
- Moments about the fulcrum: F x = W₁a₁ + W₂a₂ + W₃a₃.
- F = Σ W a ÷ x, or x = Σ W a ÷ F.
- Fulcrum reaction: F + ΣW when the fulcrum is between effort and loads, otherwise the difference of the two.
- Example: 800 N at 100 mm with a 600 mm effort arm needs 133.33 N.
Limitations
- Rigid, weightless lever in static balance; add the lever’s own weight as a load at its centre of gravity.
- Pivot friction is neglected.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Size a hand lever or foot pedal
- Check a clamping or brake lever
- Find the counterweight arm for a balance lever
Who it is for
- Design engineers
- Mechanical engineers
- Maintenance fitters
What you get
- Effort or effort-arm length
- Mechanical advantage
- Fulcrum reaction
Interpreting the result
- A third-class lever always needs more effort than load; it trades force for movement.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 167–168. Topic reference; no source tables or recommended settings are reproduced.
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