Patent drawing - 1923 wobble board precursor by Robert B. McWhirter Public domain image

These are the two patent drawings for a physical-fitness exercise device.
The inventor was Robert B. McWhirter of Newark, Ohio.
The 1925 U.S. patent for this device was applied for in 1923. Its patent number is 1,565,484
This device (rather than one invented by Bernard L. Coplin, whose 1957 U.S patent was applied for in 1954) would be the first wobble board known to be patented if it could be stood on without the user holding on to some stable external support, but there are two indications in the patent that it couldn't be:
It has footstraps; they would prevent or hinder bailing out (hopping off, in order to avoid falling); and bailing out is occasionally necessary on a wobble board if all of a user's weight is on his/her feet and they are both on the board.
The board's 43-degree maximum incline that is shown by the patent drawing's dotted line is impossible for a user to maintain while standing on a wobble board without holding to something. (An 18-degree wobble board is a challenge for an athletic person. A 24-degree wobble board is a stiff challenge for a trained balancer.) Even without an unstable board under one's feet, standing and not falling when one's feet are at an incline of 43 degrees is impossible without holding to something.

The issue of which device was the first wobble board known to have been patented and the issue of whether a device can be considered a wobble board if its user needs to hold onto an external support are elaborated on at the Image Description Page of the patent drawings of Samuel L. Jordan's 1951 precursor to the wobble board.