operating mechanism of vinyl casement window ( arm operater?)

If all you need is the operator, see our 39-187. This closely matches the part I see in your photo.

I think you're confusing the hinge for the operator. The "V" shaped arms that are under your operator are an entirely separate part and not connected to the operator in any way. Did you need the hinge or the operator?

If you did need a hinge1, that's a little trickier. I can't get a great look at it while it's still installed, but it looks like it might be similar to our 36-048. Look it over and see what you think. I can make a more confident recommendation if I can see a picture of it out of the window. See the video below for more information on how this can be done.

We don't have a video on the 39-187 specifically, but the video below covers the basic principle of removal. I know the operator in the video is different, but don't worry about that, it's still the same process. You just disconnect the link arm from the stud bracket, then unscrew the base from the sill. After that, the should just come out. I believe you've already seen this video but I'll post it again just in case.