Movement of a piece along the axis of rotation (the Z axis).
Ornamental Turning with the Lindow White Rose Engine Side Pumping
There are two YouTube videos showing this is below. The first one is on a Lindow-White Rose Engine (which was purchased).
Pump Cutting on the MDF Rose Engine
The second one shows pumping on an MDF Rose Engine (which Pat Miller made). This is a very innovative approach that Pat made, using the rosette designed to move the object in a rocking motion, and converting motion that into a pumping action.
Disclaimer : eMail comments to me at OTBookOfKnowledge @ Gmail.com. The process of woodturning involves the use of tools, machinery and materials which could cause injury or be a health hazard unless proper precautions are taken, including the wearing of appropriate protective equipment.