This is the subject of the next page to go up on my website at Paternoster-Row, but briefly, it seems that the disks are threaded through their center holes, like beads, onto a string or ribbon, which is then tied or sewed down between each disk to some kind of sturdier backing.
I've seen these in a variety of sizes: there are several surviving examples, probably from the 19th century, of a bracelet-sized version in Germany and Austria, including this one:
There's also a larger version that can be seen in this painting (both this and the above are from REALonline). It's what the lady in the back pew is holding:
These are some of the donors (shown in a side wing) of the Altarpiece of Saint George by Herlin Friedrich, from 1462. It's quite common, by the way, in paintings like this that include donor portraits, to see all the women and girls of the family grouped on one side -- usually the right as we face the painting, as here -- and all the men and boys over on the left.
There's also some sort of similar disk-thing -- it's not carved with a lot of detail -- on a statue of Saint Christopher I discussed a while back. And Saint Jerome is shown holding a medium-sized example down by his knees in this 1440s Italian painting, though you can't see the detail at this scale.
So you might say I'm on a "drive" to collect more images. (You can stop groaning now.) The news is that I've found three more examples in the last couple of months, so the range of dates and places is getting a bit broader.
The first discovery is this painting by the Master of the Albrecht Altars in Vienna:
This shows the presentation of the infant Jesus at the Temple in Jerusalem (required for all first-born sons). Saint Joseph is standing in the back, holding a betschnur (literally "prayer-string") or disk-rosary. What's particularly interesting is that this painting dates to 1438-1440, considerably before the first Rosary Societies and the "modern" rosary became popular a generation or so later.
Unfortunately the only enlarged detail of this painting that they've chosen to post online is of a corner of the altar, a candlestick, and the Infant's and part of the priest's heads -- not of Saint Joseph with the betschnur.
The second discovery is one I can't show you, because while I do have a detail photo, it was sent to me privately and I had to agree not to post it. And the image of the original painting at the Web Gallery of Art (another terrific website, BTW) doesn't show the relevant side panel. Saint Francis in ecstasy (the WGA image) is the main panel of the painting, but you will have to imagine that standing on St. Francis's right (our left as we face him) is a portrait of another friar, Blessed Rainer of Borgo San Sepulcro, who is holding in his hand a disk rosary very much like Saint Joseph's above. If you ever see me in person, I can show you the closeup. The painting itself, by Sassetta, is in the rather small and out-of-the-way museum at the Villa I Tatti in Settignano, Italy (run by Harvard University).
And just this past week, I took a closer look at this silver panel from an altarpiece in Salzburg -- it's from the Mariapfarr (Church of Saint Mary) and it's dated in the catalog to 1443 (on what evidence I'm not sure).
I am not sure who she is, but the woman on the far left is holding a disk-rosary. (She has a halo, so she must be a saint.) The peculiar spiral column she's embracing with her other arm seems to be a very large, burning candle -- rather too close to everyone's clothes, in my opinion! -- and we can just see Saint Joseph's head peeping over the women's shoulders in the background.