PARTIAL: the calculator defines an Archimedean polar radius r(θ) = r₀ + bθ over a selected arc and reports r/rp comparisons. It does not solve conjugate tooth profiles, fixed-axis closure or an actual transmission ratio.
PARTIAL · Archimedean Scroll Radius Reference
Explore an Archimedean scroll radius schedule and radius-to-reference-pinion comparisons.
Equation Used
- Radius varies linearly with polar angle over the selected arc.
- The reference circle is placed on the curve's local outward normal.
- Reported r/rp values are dimensionless comparisons only.
- Tooth geometry, rolling closure, center constraints, loads and dynamics are excluded.
The moving pinion is an exact tangent-circle construction, not a fixed-axis gear solution.
Exact local-tangent construction
The visual draws the selected polar curve and places a circular reference pinion on the curve's local normal, so its pitch circle is exactly tangent at the highlighted point.
The pinion center therefore moves with the normal construction. This is a geometry audit reference, not a working fixed-center scroll-gear mechanism.
What the calculator determines
Select start radius, end radius, reference pinion radius and working arc. Outputs are start, midpoint and end radius divided by pinion radius, plus polar slope b.
No angular displacement law, center path constraint, rolling closure, tooth form, contact ratio, interference, force or torque is calculated.
Polar radius schedule
With arc Θ in radians, b = (r₁−r₀)/Θ and r(θ) = r₀+bθ for 0≤θ≤Θ. The reported dimensionless comparisons are r(0)/rp, r(Θ/2)/rp and r(Θ)/rp.
Selected-input arithmetic
For r₀ = 40 mm, r₁ = 80 mm, rp = 20 mm and Θ = 240°, the comparisons are 2, 3 and 4, while b is about 9.55 mm/rad.
Unresolved mechanism boundary
A genuine meshing design requires compatible pitch curves, center constraints, conjugate teeth and rolling/sliding analysis. Simply placing a circular pinion along the radial line does not make it tangent to an Archimedean spiral except in special cases.
Unsupported performance, materials, tolerances, applications and maintenance claims are removed.
Questions
Are the reported values gear ratios?
No. They are radius-to-reference-radius comparisons.
Is the pinion center fixed?
No. The displayed construction follows the local normal.
Do the curves prove a valid tooth mesh?
No.
Can this design a scroll gear?
No.
References & Further Reading
- Wikipedia contributors. Non-circular gear. Wikipedia
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