The green slider carries red tool and cyan slider which has revolution joint with the green slider and prismatic joint with pink taper ruler. When the violet power-fed carriage moves along the axis of rotation of the yellow work, the tool moves along a line parallel to the ruler to create inner taper thread on the work.
The lathe is set to get when the chuck turns 1 revolution, the violet carriage moves L mm (thread lead). The tool is retrieved a little during the reverse stroke.