Endbands are an aspect of bookbinding that has interested me from the outset. Like many, my first attempts were decorative endbands in colourful silks; but during my time working as a professional book conservator in Oxford I became much more interested in the laced-in structural endbands found on medieval bindings. More recently I have experimented with endbands as a less-interventive way of re-attaching loose or detached boards. I’d like to share this little sketch with you as I believe that this distils much of what I’ve learnt about the mechanics of how endbands work.
Back-bead: this structure of endband offers great flexibility combined with great strength. The back bead locks the outer tie-down thread (the one down the spine of the book) in place stopping the endband from dropping off the back, as well as keeping the core neatly aligned flush with the spine. Because the tie-downs sit snugly up against the spine-folds the endband flexes without inhibiting the opening of the leaves.
Figure-of-eight: the mechanics of a figure-of-eight endband are very similar to that of the back-bead – it is strong yet flexible. The tie-downs are against the spine folds so there is no restriction on opening; however, there is no back bead to stop the core shifting backwards so the endband will tend to sit over the spine edge rather than up against it.
Front-bead: Although more decorative, the front-bead endband is mechanically problematic. The inner tie-down thread comes over the front of the core so is positioned away from the spine-fold, the result of this is either one of two things: 1) the opening of the book is inhibited; a more extreme version of this effect can be observed on Islamic style endbands that have wide flat supporting cores. 2) alternatively the endband drops off the back of the book. If the endband is one that is intended to offer strength and stability, or is one that is to be laced in to boards or covers then it becomes all but useless. One tempting solution to this problem is the endband with a bead one the front and back. The endband core is now held at the both edges so will not drop off the back of the book, but it does not solve the problem of restricted opening. Furthermore, this endband is quite restricted, with much less flexibility. Interestingly, Chris Clarkson also noted ‘the mechanical foolishness of this design’ 
Arthur Green, 28th February 2019