Violet slider moves along horizontal runway.
Blue gear pivoted on the violet slider rolls on grey rack.
Pink rotary runway has a revolution joint with the crank of the violet slider. The joint center is always on rolling line of the rack.
Yellow bar slides along the pink runway and has a revolution joint with the blue gear at B. Distance from B to rotary axis of the blue gear is R (gear rolling radius).
Point B traces an cycloid (in black).
Point E and F trace red and green curves.
They are considered as the result of the black cycloid deformation with constant distance along the direction toward the instantaneous center of the gear rotation.
This method of forming curves is used in designing and manufacturing of profiles, non-circular wheels, cams etc.