Buy a square hole clamp collar and screw it to the face of your pulley. Turn a pilot on the collar to match the ID of the pulley if concentricity is critical.
McMaster stocks the collars:
3325K12 Steel Square-Bore Two-Piece Clamp-on Collar 5/16" Bore, 1-1/16" Outside Diameter, 5/16" Width In stock at $13.13 Each
Broached adapters are available from Browning, Martin, Gates etc
Gunner
Political Correctness is a doctrine fostered by a delusional, illogical liberal minority, and rabidly promoted by an unscrupulous mainstream media, which holds forth the proposition that it is entirely possible to pick up a turd by the clean end.
A two-piece split adapter should be easy to make. Set the stock at a
45 degree angle to mill the vee grooves, cut down the mating surfaces until they almost meet, drill and tap for two clamp screws, then assemble it on the square stock to turn the round pulley mount and a flange to keep it square. You could make the flange large enough for screws to fasten the adapter to the pulley.
If the blanks aren't exactly at 45 degrees when you mill them both, turn one piece around and it will fit.
I made a wrench for rusted brake line fittings this way except that the groove is half a hexagon. The corners don't have to be perfect on a wrench like this because it won't be used unless a flare nut wrench has already mangled the fitting.
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