Right. Very sorry about the confusion. The vid was "pre-hook"...there were no hooks yet when that was made.
I've made a fairly important change since the video was made. See this (image) The rod and sliding "hooks" replaced the screw eyes so as to distribute the yarn more evenly on the drum.
On most spinning wheels, there is a gadget called a flyer. The flyer has two arms, one on either side of the bobbin. Traditionally, these arms have had screw hooks, or cup hooks fairly close together. Without the hooks, the newly spun yarn would pile up in one place, rather than evenly distributed throughout the whole of the bobbin. In the last 5 years or so, small, modified spring-like devices called sliding hooks began replacing the traditional hooks because they are faster, and distribute the yarn more evenly on the bobbin.
In the image, you'll see a metal rod with 4 of these sliding hooks attached. Neither the rod, nor the sliding hooks were in the vid. They replace the row of static screw eyes, and that's a marked improvement. However, every time I need to stop to slide the hooks, I'm not cranking. The cranking mechanism needs to remain a manual operation because one's hand can feel when something needs immediate attention.
In the video, for example, there is a yarn ball hanging from an inverted U at the top of which is a sealed bearing which allows it to rotate easily so as to keep the plied yarn's twist from accumulating. The yarn travels from there to a screw eye, and then is split into it's 4 plies by the other 4 screw eyes. From there, it is wound around the drum. Plies were breaking with this method, however, because the yarn didn't wind evenly around the drum. In some places, it was thicker than others, and where it was thicker, more yarn was needed to wrap around the total circumferance at each revolution of the drum. Sooner rather than later, that ply would break. That doesn't happen with the sliding hooks.
Yes; I have thought about a number of different mechanical mechanisms to move those sliding hooks back and forth. Little levers from model railroading which are used to switch tracks could also be used to switch the rotation of the motor. Place one at each end of the rod, and you have an endless looping of rotational changes of the motor. I haven't considered an oscillating mechanism, but it sounds intriguing. I'd like to hear more of your thinking with that.
There's something I find very satisfying, and rewarding about simple, basic mechanical devices. Cars, and household appliances like sewing machines worked beautifully before printed circuit boards. Quite a number of them are still in service. Jane & John Homeowner didn't need a degree in electrical engineering to service them, either. That said, I'm looking for practical applications to learn Arduino, and about electronics in general. This contraption seems like one of those practical applications.