An exercise machine having infinite range limiting capability comprises: a frame; a pivotable exercise arm mounted to the frame configured to engage an exercising user and moveable along a stroke path having a fully extended position and a fully flexed position; a movement-resisting system for resisting movement of the exercise arm along the stroke path; an interconnecting unit for interconnecting the exercise arm and the movement-resisting unit so that movement of the exercise arm causes a portion of the movement-resisting unit to move in response thereto; and a range-limiting unit for limiting the distance the exercise arm moves along the stroke path during exercise. The range-limiting unit is connected to the interconnecting unit and is configured to enable a user of the exercise machine to select a first partially flexed position at any desired location along the stroke path such that the exercise arm moves between the first partially flexed position and the fully extended position serving during exercise. The range limiting unit is also configured so that movement of the exercise arm away from the fully extended position past the first partially flexed position by the user selects a second partially flexed position such that the exercise arm moves between the second partially flexed position and the fully extended position during exercise.