An eccentric mangle wheel uses a guided pinion and alternating tooth paths to reverse its rotation. Explore the arrangement and calculate the driving pinion pitch diameter, travel and speed from module, tooth count and rpm.
Eccentric Mangle-Wheel Pinion Calculator
Enter metric module, pinion teeth and constant input speed. Eccentricity changes the qualitative guide drawing only; reversal timing and output speed are not inferred without the actual pitch curves and groove.
Equation Used
- Module and tooth count define a compatible ideal metric spur-pinion pitch circle.
- The entered rpm is the constant driving-pinion speed used for pitch-line unit conversion.
- Illustrated guide eccentricity is dimensionless and qualitative; it is not used to predict output motion.
The calculation describes the driving pinion. The eccentric guide and crossover are illustrated qualitatively; output motion requires the actual wheel pitch curves and guide geometry.
Eccentric tooth path and guided pinion shaft
Brown's movement 192 describes a mangle wheel whose tooth series and pinion-shaft guide groove are eccentric to the wheel axis. The driven pinion continues in one direction while the guide keeps it engaged around the outer and inner tooth paths, reversing the wheel at the crossovers.
The animation marks outer, crossover and inner states. It is a topology diagram, not a generated tooth or guide profile.
Historical topology and pinion unit conversion
Use the calculator only to convert a specified metric pinion module, tooth count and speed into pitch diameter, pitch travel and pitch-line speed. It cannot select or rate a mangle mechanism or predict output motion.
Standard driving-pinion pitch quantities
These identities do not supply the eccentric wheel's instantaneous transmission ratio. That requires the actual pitch curves, guide groove and crossover geometry.
Arithmetic example
For m=4 mm, z=12 and n=56.25 rpm, pinion pitch diameter is 48 mm, pitch travel is 0.151 m/rev, ideal pitch-line speed is 0.141 m/s and angular speed is 5.89 rad/s. No output reversal period is claimed.
Model boundary
The eccentric tooth path has a varying radius, so a single tooth-count ratio does not determine the complete output motion. Guide-groove and crossover geometry are also needed to calculate displacement, instantaneous ratio and reversal timing.
Eccentric mangle-wheel questions
Why is output speed not calculated?
Brown explicitly states that it varies through the revolution. A constant tooth-count ratio cannot represent that geometry.
Are the two directions equally fast?
Not generally. Brown notes that forms using different outer and inner radii run more slowly on the larger-radius branch.
Does the eccentricity slider define a real wheel?
No. It changes only the qualitative guide drawing.
Historical and primary references
- Henry T. Brown, Five Hundred and Seven Mechanical Movements, movements 192-194: describes the eccentric guide and tooth series, continuous speed variation, guided pinion shaft and unequal-speed inner/outer forms.
- Brown, movement 36: states that the pinion converts continuous rotation into reciprocating wheel rotation and that the groove guides its shaft to keep engagement.
- US3490306A, Device for the actuation of a mangle wheel: documents a guided pinion housing following tracks associated with a mangle or ring gear.
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