Cari and Steve,
I can't get to the needlebar page, but have read information before on Wittier and his mechanism. It works so nicely that one wonders why it wasn't adopted more widely.
The definitions seem a bit contrived from all sources - both transverse and vibrating shuttles 'vibrate' if vibrate means to move back and forth. Words change meanings over the years, and applying a term used for modern cars to 19th century sewing machines might not be accurate. Context can also change the meaning of a word. The Wikipedia information is specific to these 'obsolete' sewing machines. Possibly the terms used were chosen initially to simply differentiate between the mechanisms involved, but not necessarily accurately define them.
It's something to puzzle over but not argue about, and most machines fit one category or the other. The Jones Hand and similar machines are also unusual, but with a straight line and a boat shuttle, they appear closer to transverse than vibrating in the way they function, even though the shuttles move front to back.
Dianne in Colorado