If your casement window is not opening properly then the problem may be with your casement window hardware. These are several easy adjustments that you can make.
Adjust the Hinges
If the bottom is dragging then you can take out the hinge and place a shim underneath it. This will raise the sash and allow your window to clear the sill.
Many modern casement windows have hinges that can be adjusted. You can adjust the arm with an Allen wrench and this will give you some movement in the hinges.
Modify the Frame
If you have a sticking window and the frame is wood then you can shave off just enough to let the window clear with a planer. Check for paint buildup and peeling as well because these can cause just enough friction to make the window hard to open.
Clean the Crank
If the problem with the window is that the crank is hard to operate then remove the crank from the window. Unscrew the screws and take off the crank. If it appears the gears are worn down you may need to replace it. Otherwise simply clean and oil gear and replace it on the window, securing it with the same screws.