Rear Mount casement operator
Thanks for reaching out! Your casement operator appears to be the 39-022 rear mount operator. The opposite version is part 39-023 and it is available in white. Carefully review and compare the dimensions to your existing operator to determine if this is the right replacement. You'll also want to confirm that the wheel on the same is the same. The compatible crank handle would be part 39-114L.
The roller measures 17/32" in diameter and the arm thickness measures 5/8. Also, the roller is stainless steel.
I would recommend double checking the measurement of your roller. If you are still getting a measurement of 9/16", you might need to consider changing the track on the roller connects to. The two compatible tracks would be 39-504 and 39-520