Yellow oval gear engages with a pink input pinion rotating around fixed axis.
Lower end of the pinion is a pin sliding in an oval groove.
The groove center closed curve is shaped by offsetting the rolling curve of the oval gear. The offset is equal to pitch radius of the pinion.
The oval gear has planar motion, 3 degrees of freedom: 1 rotation and 2 translations. The rotation is guaranteed by its revolution joint with green upper slider. The two linear motions are possible thanks to the green upper slider and violet lower slider. Here prismatic joints should be of ball-type linear guideway to ease the motion.
Function of the blue ruler is to assist guiding the oval gear.
The workpiece is mounted on the yellow table fixed to the oval gear.
Blue curve is locus of the center of an end mill (mounted coaxially with the pinion) on the table surface. It is exact copy of the groove center curve.
Change shape of the oval gear for other loci. However it is not easy to create such gear.
This video was made on request of a YouTube user. The mechanism was purely created on computer and needs to be verified in practice.