BIZOMAT MAKEOS · Mechanics
Toggle Joint Force
What output force does this toggle joint produce for the applied force?
Output (resisting) force and mechanical advantage of an equal-arm toggle joint from the applied force and the link angle, for clamps, presses and crushers.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Force applied at the joint (perpendicular to the output line) | N | Force applied to the central joint, at right angles to the line along which the output moves. |
| Angle of each link from the output line | ° | Angle between each link and the output line; it falls towards zero as the links straighten. |
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: Force applied at the joint (perpendicular to th…
- What it is
- The force pushing on the central pin of the toggle, acting at right angles to the line along which the output moves.
- 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 500 N as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Output force and link forces rise in direct proportion.
- Get it right
- It must act at right angles to the output line; an angled force needs resolving first.
What this means: Angle of each link from the output line
- What it is
- The angle between each link and the output line. It gets smaller as the links straighten towards a straight line.
- Units and format
- Enter a number in °: degrees of angle. The form accepts 0.1° to 89.9°. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 10° as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- As the angle approaches zero the output force rises very steeply.
- Get it right
- Measure from the output line, not from the direction of the applied force.
Method and formulas
- From the handbook relation 2R sin α = P cos α: output R = P ÷ (2 tan α).
- Each link carries P ÷ (2 sin α).
- Example: 500 N at 10° gives 1,417.8 N output, a mechanical advantage of 2.8356.
Limitations
- Frictionless pins and rigid links; near the straight position, elasticity and clearances limit the real force.
- The output force grows without limit as the angle approaches zero in theory only.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Size toggle clamps and press linkages
- Show how force rises near the straight position
- Check actuator force for a toggle
Who it is for
- Design engineers
- Maintenance engineers
- Machine builders
What you get
- Output force
- Mechanical advantage
- Force on each link
Interpreting the result
- Design the frame and pins for the force at the smallest working angle.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 172–174. Topic reference; no source tables or recommended settings are reproduced.
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