Slant-Parallelogram Derailleur — Gap Explorer

Core Ideas — Patents · US 3,364,762 (T. Maeda, filed 1964; the slant parallelogram known as SunTour's) · geometry of the guide-pulley path against the sprocket pack, computed live from the model of the math page

This explorer shows how the elements of the patent work together; it is not a setup tool. Gaps are measured between pitch circles, not tooth tip to tooth tip as in workshop manuals, and the numbers are model assumptions. To set up a real derailleur, follow the maker's instructions.

Sprocket pack?
Parallelogram?
slant angle α
α is the angle of the pulley path in the rear view; "match" joins the lower edges of the largest and the smallest sprocket.
Adjustments?
B-screw: gap on the largest sprocket gB
Set on the largest sprocket, as the manuals prescribe. Gaps here are between pitch circles.
cage position (shift lever)
rear view lateral scale
How to use this explorer — four steps
  1. Keep the 1960s 5-speed 14–24 pack and press Straight (before 1964): the gap grows from the largest to the smallest sprocket.
  2. Press Slanted (Maeda): the pulley path tilts and follows the pack; the gap becomes almost the same everywhere.
  3. Press ▶ Shift across the pack and watch the side view: the free span stays short on every sprocket.
  4. Choose the wide packs (11–34, then 10–50): the slanted line no longer fits, and the gap grows again in the middle — where the idea stops.
Hover or tap the ? buttons for an explanation of each panel; hover a sprocket, the pulley or a chart point for its values.
Rear view — the pulley path against the pack?
pulley path line of the lower edges (patent line 30) gap within 2 mm of gB 2–5 mm more than 5 mm
Side view — the current sprocket?
Free span L: the chain's tangent from the sprocket to the guide pulley. The shorter it is, the more steeply one shift step s tilts it, and the sooner the chain is pushed onto the next sprocket.
Gap on every sprocket — straight vs slanted?
Free span L on every sprocket?
One B-screw setting, the whole pack?
Sprocket by sprocket (current parallelogram)?