Euclidyne

Instrument-Lab Explorations into Euclid, Ratios, and Rhythm

Applications and Reality Checks

Meshing Reality Check

What Center-Distance Changes Really Do in an Involute Pair

Analogy Only False False False

Ratio

3/5

State

nominal

Working Pressure Angle

20.0 deg

The speed ratio stays 24/40 while the operating pressure angle shifts.
Changing center distance affects engagement conditions; it does not turn the shift into a discrete integer remainder.

Claim Status

Rigour stays visible

Analogy Only False False False
  • Automatic compound-gear or sliding-gear Euclid machines remain a conceptual analogy unless sensing, control, and reconfiguration are added beyond a simple gear train.
  • Changing the center distance of involute gears does not make the shift itself equal the integer remainder.
  • Generic inward-spiral or logarithmic-spiral claims for arbitrary gear or rectangle models are not valid in general.
  • Historical compound gear trains did not themselves implement Euclid as an exact iterative algorithm on arbitrary inputs.