While Assistant Driller was tightening up the pull-down lines on the floating crown, he gave the hand signal to the Floorman to convey to the driller (also by hand signal) to hoist up the top drive. At this time he lost his balance and accidently placed his right hand on the line while the driller was raising the Top Drive System (TDS). His index finger got caught between the sheave wheel and the pull-down line resulting in partial amputation of his right-hand index finger.