BIZOMAT MAKEOS · Strength
Hand Lever Design Check (Effort, Fulcrum Reaction, Arm Bending, Fulcrum Pin)
For a hand or foot lever carrying one or more loads, what effort does it take, and are the lever arm and the fulcrum pin strong enough?
Check of a lever of any class: the effort at the effort arm or the arm needed for a given effort, the mechanical advantage and the fulcrum reaction (as the lever force tool), the largest bending moment along the lever and the bending stress in a rectangular arm, and the double shear stress and bearing pressure of the fulcrum pin from the reaction, against your allowable stresses.
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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 for a given arm, or the arm for a given effort. |
| Lever type | choice | Where the fulcrum sits relative to the effort and loads. |
| Effort arm (fulcrum to effort) | mm | Distance from the fulcrum to where the effort is applied. |
| Available effort (arm mode) | N | Effort available (arm mode). |
| Loads (distance from the fulcrum; 0 = unused) | ||
| Load 1 | N | Load 1. |
| Distance 1 | mm | Distance of load 1 from the fulcrum. |
| Load 2 | N | Load 2 (0 if unused). |
| Distance 2 | mm | Distance of load 2 from the fulcrum. |
| Load 3 | N | Load 3 (0 if unused). |
| Distance 3 | mm | Distance of load 3 from the fulcrum. |
| Arm and pin | ||
| Arm thickness | mm | Thickness of the rectangular lever arm. |
| Arm depth (in the plane of the loads) | mm | Depth of the arm in the plane of bending (at the most stressed section). |
| Allowable bending stress | MPa | Allowable bending stress for the arm material. |
| Fulcrum pin diameter | mm | Diameter of the fulcrum pin. |
| Allowable pin shear stress | MPa | Allowable shear stress of the pin (double shear). |
| Allowable bearing pressure | MPa | Allowable bearing pressure between pin and lever (lower for a bushed or greased pivot that moves). |
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 the tool works out the effort needed at a given effort arm, or the effort arm needed for the effort you have available.
- 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
- In effort mode the available effort is ignored; in arm mode the effort arm you type is ignored.
What this means: Lever type
- What it is
- The lever class: where the fulcrum sits relative to the effort and the loads. It changes the fulcrum reaction and the bending moment along the lever.
- 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.
- Get it right
- First class has the fulcrum between effort and loads (a crowbar); second has the loads in the middle (a wheelbarrow); third has the effort in the middle.
What this means: Effort arm (fulcrum to effort)
- What it is
- The distance along the lever from the fulcrum pin centre to the point where the effort is applied, such as the centre of the hand grip or pedal.
- 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
- A longer arm lowers the effort in proportion.
- Get it right
- Measure along the lever at right angles to the forces; used only when solving for effort.
What this means: Available effort (arm mode)
- What it is
- The force the operator or actuator can apply at the effort point, used only when the tool solves for the effort arm.
- 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
- A larger available effort shortens the effort arm needed.
- Get it right
- Ignored when solving for effort. Check what an operator can apply at that position with a competent ergonomics source.
Loads (distance from the fulcrum; 0 = unused)
What this means: Load 1
- What it is
- The first load the lever must move or hold, acting at right angles to the lever at distance 1 from the fulcrum.
- 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.
- Effect on the result
- Effort, fulcrum reaction and bending moment all rise with it.
- Get it right
- Enter each load in newtons; multiply a mass in kg by 9.81 to get its weight in N.
What this means: Distance 1
- What it is
- The distance along the lever from the fulcrum pin centre to the line of action of load 1.
- 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.
- Effect on the result
- The load’s moment, and so the effort needed, rises in proportion to it.
- Get it right
- Measure from the fulcrum, not from the end of the lever.
What this means: Load 2
- What it is
- A second load on the lever, acting at right angles to the lever at distance 2 from the fulcrum. Leave it at 0 if there is no second load.
- 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.
- Get it right
- Enter it in newtons; 0 means the load is not used.
What this means: Distance 2
- What it is
- The distance along the lever from the fulcrum pin centre to the line of action of load 2.
- 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.
- Get it right
- Ignored while load 2 is 0.
What this means: Load 3
- What it is
- A third load on the lever, acting at right angles to the lever at distance 3 from the fulcrum. Leave it at 0 if there is no third load.
- 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.
- Get it right
- Enter it in newtons; 0 means the load is not used.
What this means: Distance 3
- What it is
- The distance along the lever from the fulcrum pin centre to the line of action of load 3.
- 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.
- Get it right
- Ignored while load 3 is 0.
Arm and pin
What this means: Arm thickness
- What it is
- The thickness of the rectangular lever arm at right angles to the plane of the loads. It is also used as the length of the fulcrum pin bearing in the lever.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 10000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 10 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Arm bending stress and pin bearing pressure both fall in proportion to it.
- Get it right
- If the lever has a boss or bush at the fulcrum wider than the arm, the bearing check is conservative because it uses this thickness.
What this means: Arm depth (in the plane of the loads)
- What it is
- The depth of the lever arm in the plane of the loads, measured at the most heavily stressed section, usually at the fulcrum or the effort point.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 10000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 30 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Bending stress falls with the square of the depth, so it is the most effective dimension to increase.
- Get it right
- For a tapered arm use the depth at the section with the largest bending moment, not the average depth.
What this means: Allowable bending stress
- What it is
- The highest bending stress you allow in the arm material, from the material’s yield strength divided by your chosen safety factor or from a design standard.
- Units and format
- Enter a number in MPa: megapascals (1 MPa = 1 N/mm²). The form accepts 0.000001 MPa to 10000 MPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 120 MPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Take the strength from the material supplier’s data sheet; the tool does not apply a safety factor for you.
What this means: Fulcrum pin diameter
- What it is
- The diameter of the pin at the fulcrum about which the lever pivots. The pin is checked in double shear and in bearing against the lever.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 10000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 10 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Pin shear stress falls with the square of the diameter; bearing pressure falls in proportion to it.
- Get it right
- Use the pin diameter at the shear planes, not a reduced diameter at a groove for a clip.
What this means: Allowable pin shear stress
- What it is
- The highest shear stress you allow in the fulcrum pin material, which the tool compares with the double shear stress from the fulcrum reaction.
- Units and format
- Enter a number in MPa: megapascals (1 MPa = 1 N/mm²). The form accepts 0.000001 MPa to 10000 MPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 60 MPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Take it from the pin material data or your design standard, with your own safety factor included.
What this means: Allowable bearing pressure
- What it is
- The highest contact pressure you allow between the pin and the lever bore, worked out over the projected area pin diameter times arm thickness.
- Units and format
- Enter a number in MPa: megapascals (1 MPa = 1 N/mm²). The form accepts 0.000001 MPa to 10000 MPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 50 MPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- A pivot that moves under load usually needs a lower allowable pressure than a fixed joint; use the bush or bearing maker’s figure.
Method and formulas
- Effort = Σ W a ÷ x (or arm = Σ W a ÷ F); reaction = F + W for the first class, |W − F| otherwise (as the lever force tool).
- Bending moment found at the fulcrum, each load and the effort; arm stress = 6M ÷ (b h²).
- Pin shear = 2R ÷ (π d²) in double shear; bearing = R ÷ (d b).
- Example: 133.33 N effort; 80 N·m bending gives 53.333 MPa in the arm; the pin carries 933.33 N.
Limitations
- Uniform rectangular arm at the most stressed section; tapered arms need the depth at that section.
- Static load; add a factor for jerks and people standing on pedals.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Size a hand lever or foot pedal
- Check a clamping lever on a fixture
- Check the fulcrum pin of a toggle or brake lever
Who it is for
- Design engineers
- Toolmakers
- Fixture designers
What you get
- Effort, arm, advantage and fulcrum reaction
- Largest bending moment and arm stress
- Fulcrum pin shear and bearing
Interpreting the result
- The largest moment is at the fulcrum for a first-class lever and under a load for second- and third-class levers.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 167–168, 257–270. Topic reference; no source tables or recommended settings are reproduced.
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Open the Hand Lever Design Check (Effort, Fulcrum Reaction, Arm Bending, Fulcrum Pin) calculator