Generating tooth geometry…
3.500:1
ring held · sun drives · carrier out
Nothing here is a scaled picture of a gear. Every tooth flank is the involute of its own base circle, generated from inv α = tan α − α each time you change a number. The ratio below is measured from the rotation actually on screen and printed next to the ratio the closed form predicts.
Ring teeth follow: Nr = Ns + 2Np = 60. That is the condition for the ring and the sun to share an axis.
Equally spaced planets only fit when (Ns + Nr) / k is a whole number. The tool refuses to draw a set that cannot be built and says which rule it broke.
Tooth size. The ratio does not depend on it — only the physical size, the forces and the pitch line speed do.
The angle of the line of action. Raising it makes a stronger, stubbier tooth and lowers the contact ratio. Watch both numbers move.
Twist the teeth and each pair comes into mesh gradually instead of all at once — quieter, and it starts pushing the gears sideways. The axial force appears in the drive panel.
The standard reduction. Largest ratio this set can produce.
The left column is what the closed form predicts. The right column is measured from the geometry and the rotations actually on screen — the scene graph is read, not the model. A tool that cannot show its own working is an animation.
| Quantity | Closed form | Measured | Δ |
|---|
Reference values read live on 2026-09-07: ORNL/TM-2010/253 (Toyota power-split tooth counts) · Elements of Metric Gear Technology (contact ratio, assembly conditions) · KHK involute reference
Built by James Lorenz Santos · LinkedIn · HDRI: Poly Haven, CC0
A planetary gearset generated from involute mathematics. This page needs JavaScript and WebGL to generate and render the tooth geometry.
Built by James Lorenz Santos · LinkedIn