An Undulator is a reciprocrator "on steroids". The key difference is that one of the cams is replaced with another which is not round. There are many shapes, many with shapes like a rosette.

These cams are similar to the oddly shaped cams or gears in a Spirograph, and similarly amazing shapes can be thusly produced.

More Information

John Edwards compiled a great amount of information about this device in Hotzapffel, Volume VI, starting on pg. 521.

The drawings of various cams and associated waves produced explain this topic far better than I could.

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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.