Square peg in round hole.

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I am building a rotating machine. Think BBQ
The centre shaft will be timber (because there isn't a BBQ)
At one side , I have a shaft (8mm) that goes into a bearing block for smooth movement.
That's simple

The timber end is this type
https://www.amazon.co.uk/Yibuy-8mm-16mm-Flange-Couplings-Joints/dp/B07F7W3D9L


The other end uses a square drive shaft (and BBQ motor) to drive it at 2rpm

I need to drive the timber with a square drive. This is, in fact, a door handle shaft as I am using stuff to hand.
So I need to "machine" an 8mm square shaft into an 8mm round shaft.
I have a bench grinder (my first choice) a drill press, vice and files
I am tempted to grind the corners off the square?

What would you do?
 
Funnily enough, I was going the file one end of the square shaft into a point, then cut a series of cross cuts on the now tapered end, then hammer it into a penny washer with an 8mm hole.

In theory that would have broached a square hole. But I was worried about keeping it square.

I'd given up looking for a round to square coupler

Will check
 
If the diameter of the hole in the flange drive was that of accros the points of the square shaft could you not either, drill through shaft and flange then roll pin or bolt...
or drill and tap the flange and tighten two grub screws against opposite flats of the flats?
 
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