An exercise arm assembly for mounting on an exercise machine frame has a main arm, a swing arm, and a handle. The main arm has a first end for pivoting on a frame of the machine to pivot about a first pivot axis. The swing arm has a first end pivoted to the second end of the main arm for pivoting about a second pivot axis. The handle is pivoted to the swing arm for pivoting about a third pivot axis, with each pivot axis being perpendicular to the other two pivot axes to form a perpendicular, tri-pivot arm system.