Toggle Mechanism Clamping Force

The mechanical advantage of a toggle linkage - a hold-down clamp, a knee (toggle) press, a rivet or crimp squeezer.

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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

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