Hiscox catalogued a toggle stump puller among historical construction devices. This page uses that subject only to illustrate an ideal symmetric two-link toggle; it does not predict the force or capability of a stump-pulling machine.
The abstract toggle results below cannot size an actuator for a stump puller. For a separate actuator-driven linkage, a complete geometry and load model is needed to check force throughout the motion before selecting a product.
With leverage, force is traded against travel. A bracket change that improves force can also increase required stroke, slow the output motion, or move the actuator into a poor mounting angle.
If extra force is added as a margin, confirm that the frame, hinge, pins, and brackets can take the load. A stronger actuator can protect the motor from stalling while quietly moving the failure point into the structure.
- Calculate actuator force at the worst bracket angle, not just at mid-stroke.
- Check stroke, retracted length, and extended length against the mechanism envelope.
- Confirm the structure can accept the higher loads created by a stronger actuator.
For a FIRGELLI actuator application, run the FIRGELLI actuator force calculator, then compare available stroke, force, and mounting envelope in the FIRGELLI linear actuator range. If the goal is to replace an existing unit, use the linear actuator replacement finder before assuming the new actuator is a direct fit.
Toggle Stump Puller Interactive Calculator
Enter an ideal transverse knee force and link angle from the straight axis. Results are abstract equilibrium and geometric ratios, not chain tension, operator effort, stump force, machine capacity or safe load.
Equation Used
- Two equal links are symmetric about the knee and each makes angle theta with the straight axis.
- Links are rigid two-force members with frictionless pins.
- The entered force is transverse at the knee; the ideal output is an axial end reaction.
- The displacement quotient is instantaneous and follows from x=2L cos theta and y=L sin theta.
- The historical puller's lever, gearing, ratchet, chain path, frame, stump interaction, friction, deformation, stress, capacity and safety are omitted.
Historical Subject, Idealized Toggle
Gardner D. Hiscox includes a device titled Toggle Stump Puller in the construction-and-devices section of Mechanical Movements, Powers, Devices and Appliances. Period stump-puller advertising also documents cable, ratchet and multiple-power machines, but advertising claims are not engineering ratings.
The schematic uses a frame, chain-to-stump context and a highlighted two-link knee only to identify the subject. The calculated model is the abstract toggle, not the complete historical machine.
What This Calculator Does
The tool resolves an entered transverse knee force into an ideal axial end reaction for two symmetric pin-jointed links. It also reports the reciprocal instantaneous displacement quotient.
The entered force is not an operator's handle pull, and the axial reaction is not a chain load or stump-extraction prediction.
Ideal Toggle Ratios
R = FkM
q = 1/M = 2 tan theta
For x=2L cos theta and y=L sin theta, the instantaneous travel-magnitude quotient |dx/dy| is 2 tan theta. Ideal virtual work gives the reciprocal force quotient. Theta must remain greater than zero.
Worked Ideal Example
At theta=2 degrees and Fk=150 lbf, the ideal force quotient is about 14.3, the axial end reaction is about 2,147 lbf, and the instantaneous axial/knee travel quotient is about 0.070 in/in.
These are abstract toggle values; no real chain tension, handle force, stump resistance or machine rating follows from them.
Model Boundary
- Historical context: historical toggle-stump-puller subject and general stump-puller context.
- Calculated: ideal symmetric-toggle equilibrium and instantaneous differential geometry.
- Not calculated: historical machine dimensions, lever or gearing ratio, ratchet behavior, chain routing, frame reactions, ground support, stump/root resistance, eccentric load, friction, clearance, deformation, stress, buckling, fatigue, rated capacity, operation or safety.
Frequently Asked Questions
Is the axial reaction the chain tension?
No. The chain path and complete machine are not modeled.
Is the input an operator's handle pull?
No. It is an ideal transverse force applied directly at the toggle knee.
Does the travel quotient predict chain travel?
No. It is only the instantaneous end/knee quotient of the ideal two-link geometry.
Why does force quotient grow near zero degrees?
The rigid, frictionless model becomes singular at straight alignment.
Does this determine whether a stump can be removed?
No.
Can it select chain, pins, frame, anchorage or operating procedure?
No. Use authenticated machine data and qualified safety and engineering guidance.
References
- Gardner D. Hiscox, Mechanical Movements, Powers, Devices and Appliances, construction-and-devices section: Toggle Stump Puller.
- University of Maryland, Engineering Mechanics: Statics lecture notes: free-body equilibrium and toggle-mechanism mechanical advantage.
- U.S. Department of Agriculture, Clearing Land of Brush and Stumps: historical land-clearing and stump-puller context.
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