I had a question in another venue about the reels on this dispenser and if any great amount of precision is needed in their construction. That person reasoned that different tape rolls may and probably do have different internal diameters and wondered how to avoid a fit on various rolls of tape that is too tight or too loose. I assured him that this was considered and that a design was devised that did not need a high degree of precision while being fairly easy to construct. It allows different sized reels to be mounted with ease while allowing both larger and smaller diameter reels to be mounted without any adjustments. I have had many different tape reels from many different manufacturers on my dispenser and all of them have fit perfectly.
There are two reel mounts that are each 3/4" wide with a plastic spacer between them. This is how the dispenser can mount either two narrow reels of tape or one wide one. These reel mounts are constructed with four spokes with an "outside diameter" that is just a bit more than the standard tape core inside diameter. So the tape reels are distorted by a small amount when mounted and they hold firmly but are easy to mount and dismount. The details of their construction as well as the construction of a simple fixture for their assembly are included in the plans. They are constructed from rectangular oak strips and held together with glue and dowels.
Incidentally, this means that no lathe work is needed for these or any other parts of the dispenser. These tape reels are constructed from rectangular pieces of oak that I cut on my table saw. Some artful sanding is needed on their tips, but that is not hard to do nor is any great precision needed. So even beginners should be able to construct this project.