CASEMENT WINDOW OPERATOR
Your window operator can be replaced with the 39-439B Encore Dual Arm Operator. It doesn't come with a cover and handle so you'll need either the 39-376 or the 39-452. The opposite versions of these parts can be found tagged below.
Both operators are compatible with the 39-566 SS 14-1/2" Track. The link arm on the operator connects to a bracket on the window sash, yours has come off. I'll need to see a photo of the bracket to confirm its replacement match.
Attached is a photo of the under sash. Would I need to replace the metal bracket in this picture as well - in order to mount the new link arm?
The bracket is the smaller piece at the end of the sash, the pin on that would be what the link arm connects to. If this is still in good, working condition, you shouldn't need to replace it.
It appears to be similar to the 39-508, but I can't really see a clear view of it in the photo.
This long piece is the track, which is the 39-566 mentioned. This is what the black nylon slider, at the end of the straight arm, attaches to.