The historical self-adjusting step-ladder for wharfs uses pivoted steps: one edge is hinged to inclined string-pieces and the other is supported by rods suspended from handrail bars, so the treads remain horizontal as the ladder inclination changes.
Where actuator force enters the Self-adjusting Ladder Mechanism design
When self-adjusting ladder mechanism is driven by a linear actuator, the actuator force changes through the travel as the geometry changes. A comfortable static force number at one position can still leave the actuator overloaded near the start or end of stroke.
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.
A senior review would normally separate the required output force from the actuator force. Output force belongs to the mechanism; actuator force belongs to the installed geometry. Confusing those two numbers is one of the most common causes of undersized linear actuators.
- 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.
Self-adjusting Wharf Step-ladder Geometry
Explore exact rise/run projections for the historical horizontal-tread wharf ladder mechanism.
Equation Used
- Inclination is measured above horizontal.
- Tread hinges are equally spaced along a straight rigid string-piece.
- The linkage constrains every tread horizontal.
- Construction details, loads, strength, environment and code compliance are excluded.
Tread count N creates N−1 equal intervals between the first and last hinge locations.
Horizontal treads on an inclined ladder
Movement 387 in Five Hundred and Seven Mechanical Movements identifies a wharf ladder intended to accommodate rise and fall of tide. The step hinges follow the inclined string-piece while the supporting rod linkage preserves a horizontal tread.
This differs from a modern telescoping leg leveler; the former rack-and-pawl calculator described the wrong mechanism and has been replaced.
What the calculator determines
Select ladder inclination α, number of treads N and hinge spacing p measured along the string-piece. The calculator resolves vertical rise and horizontal run per spacing, total rise and stringer span between the first and last tread hinges.
Inclined-stringer projections
Rise per step is p sin α and horizontal run per step is p cos α. With N tread hinges, there are N−1 intervals, so total rise is (N−1)p sin α and stringer span is (N−1)p.
Selected-input arithmetic
At 55°, with 8 treads spaced 300 mm along the string-piece, rise per interval is about 245.7 mm, run is about 172.1 mm, total rise is about 1,720 mm and hinge-to-hinge stringer span is 2,100 mm.
Model boundary
The projection arithmetic is exact for the selected ideal geometry, but the historical source does not provide construction dimensions. Tread depth, handrail offset, hanger joints, end constraints, tide range, landing interface, materials, loads, deflection, corrosion, slip resistance, guards and code compliance are not designed here.
Questions
Why N−1 intervals?
N tread hinge locations have N−1 spaces between the first and last.
Are the treads really horizontal in the diagram?
Yes; each rendered tread endpoint has the same vertical coordinate as its hinge.
Can this specify a usable ladder?
No. It is an educational kinematic reference, not structural or safety guidance.
References & Further Reading
- Wikipedia contributors. Ladder. Wikipedia
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