This revision models one rigid pivoted step arm and a declared vertical point load at its endpoint. It reports exact deployed-position geometry and ideal pivot moment without turning that arithmetic into a capacity or safety claim.
Pivoted Step Point-Load Moment Explorer
Enter a declared vertical point load, pivot-to-load distance and deployed arm angle. The worksheet resolves the horizontal moment arm and ideal moment about the pivot.
Equation Used
- The arm is rigid and rotates in one plane about one fixed ideal pivot.
- The declared force acts vertically at the endpoint in the entered deployed position.
- Angle theta is measured from horizontal, positive upward.
- The animation prescribes stow-to-deploy rotation and does not solve motion or impact.
- Arm self-weight, distributed tread load, multiple supports, latch and stop reactions, friction, compliance, stress, fatigue and dynamics are excluded.
- No safe-load, accessibility, vehicle fitment or service conclusion is made.
Replaces an implied human-load rating worksheet and unsupported design and maintenance advice with exact declared point-load moment geometry only.
A rigid step rotates between stowed and deployed positions
Retractable-step patents describe a step pivotally supported between a raised or retracted position and a lowered or extended position. This animation keeps that topology deliberately simple: one rigid arm, one fixed pivot and one endpoint.
The motion is prescribed for visualization. The declared force construction applies only at the entered deployed position.
Real step assemblies require their complete rated structure
Practical assemblies can include multiple arms, brackets, pivots, stops, latches, drives and a separate tread. Their ratings depend on the actual load path, materials, joints and installation; this worksheet does not select or approve any of them.
Use the perpendicular distance to the vertical force line
OpenStax defines torque magnitude as force times perpendicular lever arm. With theta measured from horizontal and force vertical, the perpendicular distance is the endpoint's horizontal coordinate x=L cos(theta). The signed vertical endpoint offset is y=L sin(theta).
A declared geometry example
A declared 1000 N vertical point load applied 220 mm from the pivot at 0 degrees gives a 220.0 mm horizontal arm, 0.0 mm vertical offset and 220.0 N·m (162.3 lb-ft) ideal pivot moment.
Ideal pivot moment is not step capacity
The calculation omits arm and tread self-weight, distributed or off-centre loading, multiple supports, latch and stop reactions, stress concentrations, fasteners, welds, bearing pressure, deflection, fatigue, corrosion, slip, impact and misuse. It therefore cannot establish a safe human load, factor of safety or service interval.
Unsupported universal load factors, pin fits, material properties, wear limits, failure timelines, maintenance procedures, branded examples and cost claims are removed.
Pivoted-step geometry questions
Why use L cos(theta)?
For a vertical force, the perpendicular distance to its line of action is horizontal.
Is the entered force a recommended user weight?
No. It is only a declared point load.
Does the animation calculate deployment dynamics?
No. Its motion is prescribed.
Can this result rate a step?
No.
Pivoted-step and torque references
- US 2022/0134956, Retractable step for vehicle wheel well: a pivotally supported member moving between raised and substantially horizontal lowered positions.
- US 7,219,911, Retractable vehicle step assembly: a step pivotally connected to a mounting bracket and movable between extended and retracted positions.
- OpenStax University Physics, Torque: torque magnitude and perpendicular lever-arm definition.
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