Wheel 1 rotates about fixed axis A. Rack 2 slides along fixed straight guides B-B. The outlines of wheel 1 and rack 2 are centrodes in their relative motion. The angle ϕ₁ of rotation and angular velocity ω₁ of wheel 1 are related to the displacement s₂ and velocity v₂ of rack 2 by the equation v₂/ω₁=ds₁/dϕ₁=A͞P where P is the point of contact of the outlines and always lies on line Ay which is perpendicular to the axis of guides B-B. The outline of wheel 1 is composed of a portion of an Archimedian spiral with the equation r₁=2aϕ₁ where r₁ is the radius vector and a is the constant factor of the spiral. The displacement of rack 2 is s₂=aϕ₁² i.e. the mechanism generates a quadratic relationship and the outline of rack 2 is a portion of a parabola.
$2312$SG,3L$