An exercise machine (2) includes side frame members (6). Electromagnetic brakes (62) supported on movable carriages (66) slide along side frame members (6). Carriage (66) includes a hinge (100) for allowing each brake (62) to pivot between multiple positions. Both types of motion allow the output shafts (64) on brakes (62) to be reoriented relative to a support bench (20) on which a user of machine (2) is located. Various exercise attachments may be coupled to brake shafts (64) for contacting various body members to perform different exercises. A controller (200) regulates the force levels of brakes (62).