A treadle and pitman turn a rocking foot motion into crank rotation. The calculator relates the treadle, pitman and crank dimensions to the crank torque supplied by a downward force at the treadle-end pin.
Related actuator design tools
This model applies foot force to a treadle. If a separate actuator drives the linkage instead, calculate its pin geometry, required stroke and force across the entire cycle; foot-force torque does not by itself size that actuator.
For crank motion, review the throw radius and the changing angle between the actuator and driven link. Those two details decide whether the actuator is pushing efficiently or fighting the geometry.
If the application needs synchronized motion, feedback should be treated as a requirement rather than an accessory. Two open-loop actuators wired together can drift apart when friction, load, or mounting geometry differs between sides.
- Map actuator stroke to the actual output travel before choosing a model.
- Check for binding, changing leverage, and peak load near the ends of travel.
- Decide whether timed motion is acceptable or position feedback is required.
For a FIRGELLI design review, calculate the load case with the FIRGELLI actuator force calculator and plan the switching or controller arrangement with the linear actuator wiring diagram generator. If an actuator or cylinder is already installed, the linear actuator replacement finder helps keep the comparison tied to real dimensions.
Crank with Treadle Interactive Calculator
Adjust a rigid treadle–pitman–crank linkage. Pitman length changes leverage, foot force changes drive torque, and incompatible geometry remains visible.
Equation Used
- Foot force and pitman act at the same treadle-end pin.
- Lower working assembly of the two circle intersections.
- Downward force applied only on descent.
- Flywheel carry-through assumed, not dynamically solved.
Defined mounting, planar rigid links, downstroke force only. Flywheel dynamics are not calculated.
A fixed hinge, rigid pitman and crank
The animation shows a foot board pivoting on its hinge, a pitman joining its end to a crank pin, and a flywheel on the fixed crankshaft. This is the linkage principle illustrated by Brown movement 158, mirrored here for readability.
The foot and pitman share the modeled treadle-end pin. The crankshaft location is calculated explicitly from the chosen dimensions; it is not an independently adjustable mounting point.
The operator applies the entered downward force on the descending stroke and unloads the foot on the return. Flywheel carry-through is assumed for illustration. The model does not integrate inertia or predict steady running speed.
Adjust treadle and pitman dimensions
Use the four controls to compare geometry and applied force. Treadle length and total rocking angle set a target stroke and crank radius. Pitman length changes the shaft position, intermediate geometry and leverage. Foot force scales calculated drive torque.
At incompatible settings, the diagram remains visible. A dashed separation shows a rod end that cannot meet the treadle pin at that crank angle. No full-cycle torque is reported for that combination.
Defined mounting geometry and exact closure
Let a be hinge-to-foot-pin length, α the total rocking angle, Lp the pitman length and F the downward foot force. Set r=a sin(α/2). The target vertical foot stroke is 2r and the rod ratio is Lp/r.
Take the hinge as (0,0), with positive y upward. The crank center is C=(a cos(α/2),Lp). For crank angle θ, P=C+r(cosθ,sinθ). The foot point B is found by intersecting the radius a circle about the hinge and the radius Lp circle about P, using the lower working assembly.
This mounting gives the intended endpoint positions (a cos(α/2),±r) when Lp>r. It provides a full nonsingular crank revolution only for Lp>r; equality is a limiting change-point arrangement.
Downstroke torque follows virtual work: T=max(0,−F dBy/dθ)/1000 in N·m when dimensions are in millimetres. The derivative follows both rigid-link constraints. Peak torque is the largest downstroke value over a complete crank revolution.
Default dimensional comparison
At a=400 mm and α=12°, the target vertical stroke is 83.62 mm and crank radius 41.81 mm. With Lp=180 mm, the rod ratio is about 4.31. The crank center is about 397.81 mm horizontally and 180 mm vertically from the hinge.
At 120 N downward force, the live torque changes over the downstroke and is zero at its endpoints. Its peak is calculated from the actual linkage, rather than assuming the foot force acts tangentially on the crank.
Doubling foot force doubles drive torque without changing the path. Changing pitman length changes intermediate leverage while retaining the target rocker endpoints for valid combinations.
Kinematics are not a complete machine design
The flywheel rim is schematic. No mass, rotational inertia, speed, energy loss, operator cadence, bearing load, structural strength or collision clearance is sized. A physical frame, board and rod require appropriate spatial separation even when the planar pin centers close.
The torque result applies to the stated mounting, with foot force and pitman connected at the same treadle-end pin. A different force position or crankshaft mounting requires a separate calculation.
Treadle questions
Why is pitman length important?
It changes the four-bar geometry and the rate of vertical foot movement per crank angle, which changes torque.
Why is torque zero on the return stroke?
The modeled operator unloads the foot while the mechanism raises it. The flywheel is assumed to carry the return motion.
Why is the full-cycle torque unavailable with a short rod?
In this defined mounting, Lp must exceed crank radius for a nonsingular full crank rotation. Some poses can still close when the complete cycle cannot.
Does the loop prove the flywheel can keep turning?
No. Its inertia and losses are not inputs; the loop shows geometry only.
Mechanism reference
Henry T. Brown, Five Hundred and Seven Mechanical Movements, movement 158: a pivoted treadle connected to a rotating disc by a rod. The calculator uses the stated mounting geometry and downward foot force to relate treadle motion to crank torque.
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