RJNeal said:
https://www.starrett.com/metrology/product-detail/KA19-N
They are pretty slick...in the 15 years or more that I've owned one, I've used it about 6-10 times. As others have noted there are work-arounds, however, for the small amount of space it takes up amongst the hole saws and for the few $$ it costs it's a great option to have.
They appear to be pretty goofy looking but they do make sense because they are so simple. Their only purpose is to replace the 1/4" diameter pilot drill in the arbor with a hole saw that's then used as the pilot to center the oversize hole saw. There are no extreme loads being put on the Oops arbor as it is only being used as a method to center the undersized hole saw and all of the forces that the larger holesaw incurs is still being directed to the original arbor.
For example L to R:
1 3/8" hole saw with a 5/8-18 internal thread for an arbor.
Standard arbor having a 5/8-18 external thread and a 1/4" pilot drill.
Oops arbor having both 1/2-20 and 5/8-18 external threads.
3/4" hole saw with a 1/2-20 internal thread.
[attachimg=1]
The 1/4" pilot drill is removed so that the Oops arbor can be installed in its place. The Oops arbor will accept hole saws that have both 1/2-20 and 5/8-18 internal threads.
[attachimg=2]
The new enlarged hole saw is threaded onto the original arbor while the original sized hole saw is threaded onto the Oops arbor.
[attachimg=3]
The Oops arbor with the pilot hole saw is inserted into the original arbor which holds the larger holesaw and is secured with the original setscrew.
[attachimg=4]
Holesaw arbors with both 1/2-20 and 5/8-18 external threads can be utilized.
[attachimg=5]