This page now keeps the exact module-based rack-travel identities and removes the oversimplified universal 17-tooth margin. The connected animation uses one common normalized pitch for the rack and pinion while the numeric ledger reports the entered metric geometry.
Ideal Metric Rack-and-Pinion Pitch Ledger
Enter module, integer pinion tooth count and pinion revolutions. The worksheet calculates ideal pitch diameter, circular pitch and no-slip rack travel; it does not decide undercut, tooth strength, backlash or suitability.
Equation Used
- m is the declared standard metric module and z is an integer tooth count.
- D=mz is the operative pinion pitch diameter.
- Rack and pinion share circular pitch p=pi m and roll ideally without slip.
- Each full pinion revolution advances the rack by the pitch circumference pi D.
- The animation normalizes physical scale while preserving a common displayed rack/pinion pitch.
- Pressure angle, addendum, dedendum, profile shift, undercut, backlash, accuracy, friction, loads, strength, wear, lubrication, manufacture, selection and safety are excluded.
Retains exact module and rack-travel identities, replaces the oversimplified z-17 output with circular pitch, and removes unsupported undercut, design and field claims.
Rotation at the pitch circle becomes equal rack travel
KHK defines metric module and circular pitch for compatible rack and pinion geometry. MIT's machine-design notes identify rack-and-pinion as rotary-to-linear motion.
The animation shares one normalized displayed pitch between rack teeth and pinion teeth; it is not a manufactured tooth profile.
Use this only as an ideal pitch ledger
The worksheet converts declared module and tooth count to pitch diameter and converts pinion revolutions to ideal no-slip rack travel.
It cannot select, size, rate or validate a real rack drive.
Ideal metric pitch identities
No universal undercut threshold follows from z alone.
A transparent ideal example
For m=5.5 mm, z=12 and n=1, D=66.0 mm, circular pitch=17.28 mm, rack travel per revolution=207.3 mm and total travel=207.3 mm.
Pitch compatibility is not tooth adequacy
A real gearset needs a defined pressure angle, tooth form, profile shift, addendum, dedendum, backlash, materials, accuracy, lubrication and load analysis.
The former universal 17-tooth margin, design, performance, application, maintenance and troubleshooting claims are removed or bounded.
Rack pitch questions
Is travel per revolution pi D?
Yes for ideal pitch-line rolling.
Does z below 17 always mean undercut?
No.
Does this calculate backlash?
No.
Are the displayed teeth production geometry?
No.
Rack-and-pinion pitch references
- KHK Gear Technical Reference: module, pitch diameter, circular pitch and rack-and-pinion geometry.
- MIT Elements of Mechanical Design: rack-and-pinion rotary-to-linear motion and gear types.
- KHK Circular-Pitch Racks and Pinions: rack travel per rotation and circular-pitch/module comparison.
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