This page now treats the mutilated pinion as a one-revolution advance/dwell schedule. It calculates the exact ideal pitch-line travel during the declared toothed arc and explicitly excludes the separate return, reset and locking hardware required for a complete cyclic machine.
Ideal One-Revolution Advance/Dwell Schedule
Enter a declared pinion pitch diameter, toothed fraction and constant input speed. The worksheet calculates ideal engaged travel, angular schedule and pitch-line speed only.
Equation Used
- D is the declared pitch diameter and f is the declared fraction of a revolution carrying effective teeth.
- The pinion rotates at constant declared speed n and rolls ideally at the rack pitch line during the toothed interval.
- The rack advances by pi D f during engagement and is shown stationary through the toothless interval.
- The animation uses normalized illustrative teeth rather than a production involute profile.
- Rack return, reset, dwell locking and the mechanism that reconnects successive cycles are excluded.
- Tooth entry impact, acceleration, backlash, friction, loads, strength, wear, manufacture, selection, operation and safety are excluded.
Retains the exact ideal sector identities, removes the implied automatic reciprocating cycle, and makes return, reset and locking exclusions explicit.
A toothed sector advances the rack, then the toothless arc dwells
The Mechanical Devices Sourcebook documents mutilated gears among intermittent-motion devices. During the toothed portion, ideal pitch-line rolling advances the rack; during the toothless portion, this limited model assigns zero additional travel.
Practical cyclic mechanisms require added return, reset or locking elements. US Patent 3,408,877 illustrates such additional pin, slot and locking relationships rather than relying on a lone mutilated gear.
Use this only as a one-revolution schedule
The worksheet reports ideal engaged travel, advance angle, dwell angle and pitch-line speed from three declarations.
It does not define a complete reciprocating cycle or validate a real indexing machine.
Ideal sector schedule
The repeated animation wraps position for display; that wrap is not a physical reset.
A transparent ideal example
For D=50 mm, f=40 percent and n=60 rpm, engaged travel is 62.8 mm, the advance arc is 144 degrees, the dwell arc is 216 degrees and engaged pitch-line speed is 157.1 mm/s.
An advance/dwell ledger is not a complete drive
Real machinery must define how the rack is held during dwell, returned or reset, and re-engaged without impact or interference.
Backlash, tooth form, loads, acceleration, strength, wear and guarding remain outside this worksheet.
Mutilated-pinion questions
Does the rack automatically return?
No.
Is dwell positively locked?
Not by this model.
Is the displayed tooth profile manufacturable?
No; it is illustrative.
Does the calculator size a real drive?
No.
Intermittent-motion and rack references
- Mechanical Devices Sourcebook, intermittent-motion chapter: mutilated gears and related intermittent mechanisms.
- US Patent 3,408,877: practical intermittent rack drive with additional pin, slot and locking elements.
- KHK Gear Technical Reference: pitch diameter and rack pitch-line relationships.
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