A mutilated gear retains a toothed sector that advances an output gear for part of each turn. A coordinated holding ring and cam restrain the output during the remaining dwell. Calculate the ideal step and dwell from whole-tooth counts and input speed.
Mutilated-Gear Index Calculator
Enter a declared full driver pitch count, retained whole teeth, output gear tooth count and input speed. The worksheet reports ideal sector arc, output step and dwell. It does not design transition teeth, locking profiles, strength or safe speed.
Equation Used
- The declared driver blank has Nd compatible pitch positions and one retained sector of k whole teeth.
- Each retained driver tooth advances the No-tooth output by one ideal tooth pitch.
- The holding ring/cam is schematic and restrains the output only during the ideal dwell interval.
- Module, pressure angle, tooth form, transition relief, holding-profile geometry, backlash, interference, force, torque, inertia, impact, wear, lubrication, bearings, speed rating and safety are excluded.
The toothed sector sets the ideal output step; the remaining input angle sets dwell. The holding pair is schematic. Input speed changes the calculated dwell time, while animation playback uses an illustrative fixed cycle.
A toothed sector indexes; a separate holding pair restrains
The driver retains a whole-tooth sector. While that sector meshes, the output advances by the matching number of output tooth pitches. During the remaining input rotation, the output must be restrained by a coordinated holding device.
The engineering reference shows a holding ring on the input and a holding cam on the output and states that such holding is essential to prevent tooth topping at re-entry.
Intermittent rotation with a holding pair
This arrangement divides each input turn into an indexing interval and a dwell interval. The toothed sector advances the output during indexing; the coordinated holding pair restrains it while the teeth are disengaged. A particular application needs tooth and holding profiles designed for its geometry and load.
Whole-tooth pitch-count geometry
The dwell is an ideal input-angle interval. It is not a prediction of transition timing, settling or dynamic performance.
Declared pitch-count example
For a 24-position driver blank retaining two whole teeth and a 20-tooth output, the sector spans 30°, the ideal output step is 36°, and the ideal dwell is 91.7% of an input turn. At a declared 12 rpm, that ideal dwell lasts 4.583 s.
Tooth engagement and holding geometry
The retained sector must contain a whole number of compatible tooth pitches. During dwell, removing teeth alone provides no positive restraint: a coordinated holding pair must maintain the output position and release it for the next engagement. These pitch-count results do not establish suitable profiles, load capacity or operating speed.
Mutilated-gear intermittent questions
Does removing teeth alone positively lock the output?
No. A coordinated holding provision is required.
Why is the retained sector a whole number of teeth?
The calculator advances the output by whole compatible tooth pitches.
Does the displayed dwell time establish a safe cycle rate?
No. It is only the ideal angular interval divided by declared speed.
Mutilated-gear intermittent references
- Mechanisms for Intermittent Motion, Chapter 10, Fig. 10-10: engineering reference showing the driving gear, output gear, transfer teeth, holding ring and holding cam and explaining why holding is essential.
- US4195768A, Internal pinion revolution counter: primary patent describing a two-tooth gear segment, cooperating locking cam, full-tooth gear and mutilated transfer-pinion portion.
- US1811624A, Intermittent drive: primary patent describing a mutilated pinion, locking portion and successive rest/rotation operation.
Building or designing a mechanism like this?
Explore the precision-engineered motion control hardware used by mechanical engineers, makers, and product designers.
