This page now limits its numeric result to an ideal one-pitch-per-click indexing convention. The connected animation shows a spring-biased pawl riding asymmetric rack teeth, and the former undocumented fixed tolerance is replaced by a clearly declared backlash comparison.
Ideal Rack Index and Declared Backlash Comparison
Enter a declared rack pitch, integer click count and backlash comparison. The worksheet calculates ideal indexed travel; it does not predict real backlash, reverse load capacity, wear or safe holding.
Equation Used
- Rack pitch p is a positive declared distance between equivalent adjacent tooth positions.
- N is an integer declared click count and each ideal click advances exactly one pitch.
- b is a separately declared backlash comparison and is not predicted from tooth geometry.
- The animated rack and pawl show qualitative forward override and re-engagement only.
- The on-screen tooth spacing is normalized for visibility and is not scaled from p.
- Tooth profile, pawl geometry, spring force, friction, clearances, stiffness, contact stress, load capacity, actual backlash, wear, release, manufacture, selection, operation and safety are excluded.
Retains exact ideal pitch-times-count arithmetic, replaces the undocumented 0.05 mm constant with a declared backlash input, and removes unsupported capacity and field claims.
A biased pawl rides the ramp and catches the stop face
US Patent 4,512,217 describes saw-toothed rack teeth with an inclined surface and an abutment surface. US20050252335 describes biased latches that override teeth in the forward direction and engage in shear to arrest reverse travel.
The animation shows that qualitative sequence while deliberately avoiding a load or backlash prediction.
Use this only as an ideal index ledger
The worksheet multiplies a declared pitch by an integer click count and compares a separately declared backlash value with pitch.
It cannot size, rate, select, release or validate a real rack-and-pawl device.
Ideal one-pitch-per-click arithmetic
The percentage is a declared comparison only; it is not a manufactured tolerance or safety margin.
A transparent ideal example
For p=6.0 mm, N=1 click and declared b=0.05 mm, ideal advance and total travel are 6.0 mm and the declared backlash comparison is 0.83 percent of pitch.
Pitch alone does not determine holding or backlash
Actual reverse travel and capacity depend on tooth and pawl profiles, engagement phase, clearances, spring force, stiffness, friction, materials, contact stress and wear.
The former universal 0.05 mm tolerance, load, application, maintenance and troubleshooting claims are removed or bounded.
Rack-index questions
Does every mechanism advance exactly one pitch?
No; that is the declared ideal convention here.
Is b predicted?
No.
Does a smaller pitch guarantee more load capacity?
No.
Does the animation calculate release motion?
No.
Rack-and-pawl references
- US Patent 4,512,217: saw-tooth rack surfaces and spring-biased engagement.
- US Patent Application 2005/0252335: forward override, reverse arrest and the definition of linear-ratchet backlash.
- NPTEL, Indexing Mechanisms: ratchet-and-pawl one-direction indexing and spring return.
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