Three identical elliptical gears 1, 2 and 3 rotate about fixed axes A, B and C. The transmission ratio between gears 1 and 2 is i₁₂=(1+2e cos(ϕ₁)+e²)/(1-e²) and that between gears 2 and 3 is i₂₃=(1+2e cos(ϕ₂)+e²)/(1-e²) where e=c/A͞B=c/B͞C is the eccentricity of the ellipses, c is the distance between the foci of the ellipses, and ϕ₁, ϕ₂ and ϕ₃ are the angles of rotation of gears 1, 2 and 3 and are related by the conditions and ϕ₂=arcsin((1-e²)/(1+2e cos(ϕ₁)+e²))sin(ϕ₁) and ϕ₃=arcsin((1-e²)/(1+2e cos(ϕ₂)+e²))sin(ϕ₂). Gears 1 and 3 rotate in the same direction.
$2347$SG,4L$