That looks like a very interesting book Frances.
I’ll try and add the little I might know. Today the term engine turning doesn’t mean the same thing as it was once used for ornamental or those guilloche straight line machines. I guess technically it’s still correct and that’s how your book describes it, but it creates confusion about what’s actually being described without further context. Dave’s last picture of what’s meant today by engine turning or it’s sometimes described as jeweling by gun smiths is a completely different, much simpler and easier process since very good work can even be done using little more than a pillar drill, a flat faced wooden dowel of the correct diameter, abrasives and some basic spacing marks. A mill makes it even easier for the regular spacing and swirl overlaps. I’ve done a little of it, and it’s simple, but not quite as intuitive as one would think for some of it. For the best effect, the work piece needs to be highly polished first, and the abrasives should never be wiped off. Instead they need to be washed off so the surface isn’t affected by straight line scratching any wiping would cause. For the best results, how much down feed pressure is applied and for how long almost to the exact second is also highly important to get the same depth and level of light reflection from each swirl mark in the metal. Any minor errors in technique show up as something that’s instantly and easily noticeable. Engine turning by today’s definition does have one thing common to it and ornamental turning or straight line work. They all use the light reflections in the same way to catch someones attention. So in my opinion, there loosely related, but still not the same thing since straight line or ornamental turning uses in general much deeper cuts and much more precision.
For any that don’t know of them, there were also geometric chucks. As an example, visualize the usual line drawing of what a snow flake crystal can look like. Those Geometric chucks can allow something much the same plus thousands of different designs with even more complexity to be cut into dense hardwoods or softer metals in one single and continuous line. That T.D. Walshaw book Bazyle mentioned has a pretty good description and line drawings of how a two stage geometric chuck works. Ornamental turning as a craft was invented sometime around the 1500’s and got progressively more expensive and complex. It started out as mostly a hobby for the ultra wealthy and royalty. It’s generally thought that a decently equipped ornamental lathe cost roughly the same as what two new modest to average sized homes would during the same time period. Later on one common use for those rose engines, ornamental lathes, straight line machines and those geometric chucks were all used before cnc for the printing dies producing high value bonds, money and even post office stamps in most countries as an attempt to prevent counterfeiting. To make it even tougher, small added hand engraved details plus multi stage dies that fit tightly together that also used different dye colors on each die segment during the printing process were also fairly common. I believe most or maybe all of the famous Faberge eggs have some evidence that all of this type of equipment helped to produce some of the intricate designs on them. For some higher priced goods and jewelry, watches etc, straight line and rose engine designs seemed to be fairly common in the mid to late 1800’s and even into the early 20th century. Only for the very wealthy of course, but today’s high end mechanical watch making has started a resurgence in the use of this equipment that’s now quite rare, hard to find and expensive when you do. A well equipped Holtzapffel ornamental lathe recently sold in a U.S. auction for roughly $250,000.
Rose Engine lathes were also built with one or two extra motions our lathes can’t do. They used rosettes or more descriptive, multi lobed cams attached to the spindle and the head stock could rock the amount the different cams had for lobe design and the high and low offsets each of those different shaped rosettes had. Some rose engine lathes could also follow cams that forced the lathe spindle and work piece to move back and forth in a lateral direction. A pumping action would be used by ornamental turners to describe it.
The Lathes UK site, https://www.lathes.co.uk/page21.html has a fair amount about the equipment and tooling accessories multiple manufacturers produced under the heading of Ornamental Turning. But I’ve not found much about those straight line machines anywhere other than a few YT videos and some very short written descriptions. Ornamental turning and how it’s done is also fairly strange for whatever reason. It’s either appealing and interesting to some, or and it seems for most, it isn’t.