A mangle rack converts continuous pinion rotation into back-and-forth rack motion. The fixed-axis pinion alternately engages the upper and lower racks; calculate ideal speed and travel while either straight rack is engaged.
Mangle-Rack Straight-Engagement Calculator
Enter pitch diameter, constant pinion speed and a stated straight rack travel. Results apply only while one straight rack is engaged; the end-transfer and reversal interval is not solved.
Equation Used
- The pinion rotates at the entered constant speed and rolls without slip on one straight rack at a time.
- D is pitch diameter and S is an independently entered straight-engagement rack travel.
- The animated end transfer is schematic and does not define a manufacturable reversing mechanism.
The pinion stays on a fixed shaft while the double-rack frame moves. The calculation covers straight engagement; the illustrated end transfer is schematic and reversal time is additional.
Fixed pinion, alternating upper and lower racks
Historical descriptions place a continuously rotating pinion between upper and lower racks on a reciprocating frame. The pinion engages the two racks alternately. End shoes, a wrist pin or related transfer parts arrest, shift and reverse the rack at each end.
The animation shows the fixed pinion, translating double rack and a schematic end-transfer state. It does not reproduce one specific patented transfer mechanism.
Historical motion-conversion topology
Use the calculator only for ideal pitch-line travel during a straight rack engagement. It cannot select, size, rate, diagnose or prescribe a real mangle-rack drive. Reversal dynamics require the actual rack, pinion, shoes, guides, clearances, load and speed.
Ideal straight-engagement pitch kinematics
These are ordinary no-slip rack-and-pinion pitch relationships. They intentionally stop before the historical end-transfer and reversal geometry.
Arithmetic example
For D=50 mm, n=80 rpm and S=300 mm, ideal pitch travel is 0.1571 m/rev, straight rack speed is 0.209 m/s, the straight travel uses 1.91 pinion revolutions and takes 1.43 s. Reversal time is additional and not calculated.
Model boundary
The straight-engagement relationships do not describe how the rack changes engagement at its ends. End shoes, guides and transfer parts must be considered separately, together with acceleration, clearance and load.
Mangle-rack model questions
Does the pinion travel around the rack?
Not in the historical fixed-axis form represented here. The pinion stays on its shaft while the double rack frame reciprocates and shifts engagement.
Does straight-travel time include reversal?
No. It excludes the end-transfer interval.
Can rpm be chosen from this calculator?
No. Safe speed depends on complete geometry, inertia, load, contact stress, guides, clearances and testing.
Primary and historical references
- US471369A, Reciprocating mechanism for printing presses: describes the mangle or Napier movement with upper and lower racks, a driving pinion between them, and end shoes/wrist pin used during reversal.
- USPTO Class 74 definition, Mangle Connections: defines a mangle as a toothed member engaged on opposite sides alternately to convert continuous pinion rotation into reciprocating motion.
- Elementary Mechanism, Cornell University scan, section 72: shows the pinion and double rack and states that continuous rotation produces reciprocating motion.
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