A leg exercise machine (10) for bilateral and unilateral leg exercising. Machine (10) preferably includes an electromagnetic brake unit (44) coupled to a side-mounted exercise arm (68) through a planetary drive assembly (51). A longitudinally-adjustable leg pad support (70) is slidably mounted on exercise arm (68). Leg pad support (70) can carry a long rod (78) suitable for supporting a pair of leg pad assemblies (84) or a short rod (93) suitable for carrying a single leg pad assembly (84), depending on whether bilateral or unilateral exercising, respectively, is desired. Rods (78, 93) are sufficiently long to allow for lateral play in the leg pad assemblies (84) relative to the exercise arm (68) so as to accommodate various hip widths and so as not to create a side load on the knees during flexion and extension.