Usage patterns
〈物〉の付け根が痛いthe base of X hurts
The base of my arm hurts and I can't move it.
〈物〉の付け根から折れるto break off at the base of X
The branch broke off right at its base.
〈物〉の付け根を押すto press the base of X
There's a pressure point if you press the base of your finger.