Window Balance replacement

The metal part of the balance is 21" long. It has a string coming down from the bottom of the metal part to the pivot part that the window bottom fits into. One of the pictures above shows the broken one with the string loose from the pivot part. The top screw holding the metal part is 3 1/2 inches down from the top. The bottom screw is just dow from the bottom of the metal. The sash weighs 18.5 lbs.

The metal part of the balance measure 9/16 from inside to the outside of the window or building. The side of the metal piece measures 0.675 inches.

I ordered 4 series 770 balances because they look the same as mine. Notice the pivot shoe has a knot holding the end of the string from the balance. I can't remove the balance because there isn't a notch to take it our. The window frame is all aluminum. I tried to cut a notch but it is very difficult.

Most of the pivot shoe is plastic except the part that turns. If I cut the plastic to remove the shoe can the 795 pivot shoe be inserted without a notch.

Thank you that is what I had hoped.