When slider 1 moves along fixed guides a-a, pinion 2 rolls along fixed straight rack 3. Any point K of pinion 2 describes cycloid q-q. The parametric equations of the cycloid are x=r(ϕ-sin(ϕ)) and y=r(1-cos(ϕ)) where r=O͞K, and ϕ is the angle of rotation of pinion 2. In rectangular coordinates xOy, the equation of cycloid q-q in the explicit form is x=r arccos(((r-y)/r)±sqrt((2r-y)y)).
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