Under the selected ideal indexing assumption, each completed handle stroke advances the rack by one selected tooth pitch, so lift is np. Load force is mg. If β is explicitly defined as the contact-normal angle from the vertical lift axis, the frictionless normal required for vertical equilibrium is W/cosβ.
Rack-and-Pawl Skip Jack · Ideal Indexing Ledger
Explore an ideal one-tooth-per-stroke ledger on a recognizable illustrative rack-and-pawl jack.
Equation Used
- Each completed ideal stroke advances exactly one selected tooth pitch.
- Mass-to-force conversion uses standard gravity 9.80665 m/s².
- The selected contact normal is β from the vertical lift axis and friction is omitted.
- Lever geometry, transitions, friction, strength, stability, lowering and ratings are excluded.
β is explicitly defined as the selected contact-normal angle from the vertical lift axis, replacing the ambiguous generic flank-angle label.
Ideal rack indexing with alternating pawls
The visual shows a recognizable rack jack: a drive pawl presents one upward index while a body-mounted holding pawl represents retention during reset. The cycle is schematic; exact pivot locations, engagement transitions and lever geometry are not synthesized.
What the calculator determines
Select tooth pitch, completed ideal strokes, supported mass and a declared contact-normal angle from the lift axis. The calculator reports ideal indexed lift, gravitational load force, the frictionless contact-normal projection and strokes per 100 mm.
Selected ideal ledger
lift = np; W = 9.80665m; N = W/cosβ; strokes per 100 mm = 100/p.
Selected-input arithmetic
At 10 mm pitch, one completed ideal stroke indexes 10 mm. A selected 5 tonne mass corresponds to 49.03 kN gravitational force. With contact normal 60° from the lift axis, the ideal frictionless normal is 98.07 kN.
Kinematic and force projection only
Real jacks require complete lever ratios, pawl-pivot geometry, full tooth engagement, friction, spring control, structural stress, stability, controlled lowering, overload protection and rated testing. This calculator does not determine hand effort, capacity, safe working load or suitability for lifting.
Questions
Is β a generic tooth flank angle?
No. Here β is specifically the selected angle between the contact normal and vertical lift axis.
Does the reported normal prove a pawl or tooth is safe?
No. It is only a frictionless force-component projection.
References & Further Reading
- Wikipedia contributors. Jack (device). Wikipedia
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