You can try with sketches especially for the mates that you need.
Try to make a sketch in part1 (something like a arc in a plane there is in the same "height" like the bore pin) and a sketch point in the bore pin and mate them together. The movement of the bore pin will be limitated of the length of the arc (or line). The same procedure can you use for the other mates too. It's also possible to make parts they are actually only sketches and to use them only to achieve the start and end of the movement.
If don't understand how I mean this, I will try to build tomorrow something with your model.