A mangle rack reverses its output by changing which rack face engages the rotating pinion. Explore the guided transfer, then use module and tooth count to calculate pitch diameter and ideal straight-run motion.
Form-3 Module and Straight-Run Calculator
Enter straight pitch-path length, module, pinion teeth and constant speed. The results cover pitch diameter and one ideal straight engagement; end-loop geometry and full-cycle rate are not inferred.
Equation Used
- The module and tooth count describe a compatible ideal spur-pinion pitch circle.
- The pinion rolls without slip on one straight rack at the entered constant speed.
- The guided end-loop animation is schematic and does not define a complete form-3 construction.
Metric module and tooth count define the ideal pinion pitch diameter. The straight-run calculation uses that diameter and the entered speed; the end-loop shape and full-cycle timing require additional geometry.
Guided transfer between opposite rack faces
Historical mangle-rack mechanisms use a continuously rotating pinion and opposite rack faces so the output can reverse without reversing the input. A guide, shoe, wrist pin or carrier controls the change from one rack face to the other at the ends.
The animation shows an entered straight run and a schematic end loop. It does not assert the exact geometry of a particular surviving form-3 machine.
Module sizing and straight-run arithmetic only
Use the calculator to connect metric module and tooth count to ideal pitch diameter, travel per revolution and straight-run speed. It cannot derive total stroke, loop radius, cycle rate, safe speed or machine capacity.
Standard pitch circle plus no-slip straight run
Module m and pitch diameter d use consistent millimetre units before conversion to metres. L is explicitly the straight pitch-path length, not the rack's overall outside length.
Arithmetic example
For L=1.50 m, m=6 mm, z=20 and n=50 rpm, pitch diameter is 120 mm, pitch travel is 0.377 m/rev, ideal straight speed is 0.314 m/s and the run takes 4.77 s. End transfer adds time that is not calculated.
Model boundary
Pinion pitch diameter does not determine the entire end loop or the available rack stroke. Those depend on the guide, carrier and transfer geometry. The entered straight pitch-path length covers only the portion represented by the no-slip rack-and-pinion equations.
Form-3 model questions
Does d=mz define the complete mechanism?
No. It defines only the ideal metric pinion pitch diameter.
Is entered L the outside rack length?
No. It is the independently known straight pitch-path length.
Why is full-cycle rate not calculated?
Full-cycle rate requires the actual end-loop and transfer kinematics, not only straight pitch speed.
Primary and historical references
- US471369A, Reciprocating mechanism for printing presses: documents upper/lower racks, a continuously driven pinion and guided reversal parts in the mangle/Napier family.
- Henry T. Brown, Five Hundred and Seven Mechanical Movements, movement 197: states that continuous pinion rotation reciprocates the rack frame and the pinion shaft follows the end guides.
- USPTO Class 74 definition, Mangle Connections: defines alternating opposite-side gear engagement producing reciprocating output.
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