You have the concept correct. I am curious though if you are refering to a manual duplicator or a computer controllerd machine. I have owned several different manual trace duplicators of two different designs. The most common is the one like you describe where the z axis is mounted on a pivot that allows the up and down motion. there are other designs though that don't use that concept. One machine is a 4 axis Don Allen built using a parallelogram. The other is a Honeig 3 axis machine that is built much like a moving gantry based cnc router except all the xyz movement is suppliet by human arms and hands.
No if you are asking about computer controlled carvers, that is a different story. All of the one I have seen are basically a 3 axis cnc machine with a 4th axis mounted to hold the piece to be carved. They work in the same way as a milling machine does. Up, down on the z with no pivoting and no arm.
ps I use a 4 axis wood router as my carving machine now.