Replace truth window operator/cranks
The broken portion of each mechanism is the rotating center part attached to the hand crank. It has come out, rotating on it's thread. It allows opening of the window but comes out when trying to close.
Thanks for posting. Yes, unfortunately when that gear pops out with the handle it means the entire operator has broken down and should be replaced. Fortunately we should be able to help in both cases. For the awning operator, start by looking at our 39-015. Compare the dimensions below to make sure it matches up.
For the casement operator, I think our 39-032 is what you're looking for; but double check the dimensions in the below diagram, especially that link arm length. You list 4" for this measurement, but on the 39-032 this comes out to 4-7/16". If you indeed measure differently, just confirm that, and we'll see if we can't find something better for you. In either event, for a new cover for this operator, see the 39-107. For both operators, the 39-114L will work as a new handle. Let me know if you have further questions.