Toggle Mechanism Clamping Force
The mechanical advantage of a toggle linkage - a hold-down clamp, a knee (toggle) press, a rivet or crimp squeezer.
Example
You enter
- Input force at the knee (lb) 50
- Toggle angle from lockup (deg) 10
You get
- Mechanical advantage 2.8356
- Output (clamping) force 141.8 lb
Details, formula, and sources
The mechanical advantage of a toggle linkage - a hold-down clamp, a knee (toggle) press, a rivet or crimp squeezer, an injection-mold clamp. Two equal links meet at a knee driven perpendicular to the output line, so F_out = F_in/(2 tan theta), theta the angle of each link from the straight (lockup) line. Near lockup the advantage runs toward infinity - a light hand force becomes a big clamp force, which is why a toggle clamp snaps hard and holds at over-center. The catch is the reciprocal: the output moves only 2 tan theta per unit of input travel (huge force, almost no stroke), and pushing PAST lockup releases it. 50 lb at 10 degrees gives 142 lb (MA 2.84); at 5 degrees, 286 lb (MA 5.72). Ideal frictionless linkage; joint friction, link buckling, and pin shear are separate. A design aid; Machinery's Handbook and the clamp maker govern.
F_out = F_in / (2 tan theta), theta the angle of each link from the straight (lockup) line; output travel per unit input travel = 2 tan theta; MA = 1/(2 tan theta).
The symmetric toggle-linkage mechanical advantage F_out = F_in/(2 tan theta) (Machinery's Handbook; standard statics of the toggle joint), by name.
The toggle-joint force relation is a standard published statics result; the input force and toggle angle are the user's inputs.
Estimate. AHJ and licensed professional govern.
Field names used by the API: input_force_lb, toggle_angle_deg, mechanical_advantage, output_force_lb
- Advantage F_out = F_in/(2 tan theta) for a symmetric toggle; diverges at lockup (theta -> 0)Machinery's Handbook
- Travel trade-off output travel per unit input travel = 2 tan theta = 1/MA; over-travel past lockup releaseskinematics
- Scope ideal frictionless linkage; friction, link buckling, pin shear are separatescope of this tile