This reversing mechanism, shown in Newark Museum model 70, uses three members: a concentric internal ring and central mutilated external gear alternately drive one offset pinion.
External/internal Mutilated Gear Reverse Interactive Calculator
Explore an ideal equal-stroke slow-forward/quick-return arrangement with exact pitch-circle closure between the concentric driver members and the fixed output pinion.
Equation Used
- The external sector and internal ring are concentric and rotate together at constant entered speed.
- The fixed pinion centre distance is Re+rp, which also equals Ri-rp after deriving Ri=Re+2rp.
- The internal-sector arc is derived for equal-magnitude forward and return displacement; it is not a separately entered tooth design.
- Two equal dwell arcs divide the unused angular budget.
- No module/DP, integer tooth counts, pressure angle, involute profile, entry modification, locking face, backlash, interference, contact ratio, load, inertia, stress, wear, lubrication or manufacturability model.
The entered master radius is the external-sector pitch radius. A compatible internal pitch radius is derived as Ri=Re+2rp, and the internal-sector arc is shortened so its ideal return displacement equals the forward displacement.
Three gears, two mesh directions
The mechanism has three members: a large internal ring, a smaller concentric mutilated external gear, and one offset output pinion. The ring and central gear rotate together. Their toothed sectors reach the pinion at different times.
External mesh turns the pinion opposite the driver; internal mesh turns it in the same direction. That alternating sign produces reversal. For one fixed pinion centre, ideal pitch closure requires Ri-rp=Re+rp, hence Ri=Re+2rp.
Historical slow-forward, quick-return teaching model
The Newark Museum catalogue describes model 70 as usable where advance is slow and return fast, or vice versa. This calculator demonstrates that kinematic principle only; it does not claim a specific modern machine application.
Equal forward and return travel
Forward turns are alpha Re/(360rp). With Ri=Re+2rp, equal return travel requires beta=alpha Re/Ri. The larger internal radius gives a higher ideal pinion speed during return, while the shorter beta arc brings the pinion back by the same number of turns.
Example
For alpha=120 degrees, Re=90 mm and rp=30 mm, Ri=150 mm and beta=72 degrees. Forward and return are each 1.00 pinion revolution. At 40 rpm driver speed, ideal forward speed is 120 rpm, ideal return speed is 200 rpm, and each of the two equal dwell intervals is 0.35 s.
Scope and limitations
This is not a gear design. Real construction requires a selected module or diametral pitch, compatible integer tooth counts, pressure angle and involute forms, sector entry and exit modification, locking faces or detents, backlash, interference and contact-ratio checks, shaft and bearing design, dynamic impact and load analysis, materials, strength, wear, lubrication, tolerances, guarding and validation.
Questions
Why can one fixed pinion mesh with both drivers?
Because the internal and external pitch radii are different and satisfy Ri-rp=Re+rp.
Why is return faster?
The internal ring has the larger pitch radius, so ideal pinion speed is higher during that mesh.
Do the sector bands define gear teeth?
No. They locate the active pitch-circle sectors. Tooth profiles, entry transitions and a physical dwell lock are not modeled.
Historical references
Primary historical basis: The Newark Museum, Mechanical Models: A Series of Working Models on the Art and Science of Mechanics (1930), model 70, ‘Reverse from rotary motion.’ This source supports the three-gear arrangement and slow-forward/quick-return purpose, not the displayed dimensions or tooth design.
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