An exercise machine (10, 60, 90, 120, 150) and a method for its use in training selected muscle groups by controlled use of brakes to resist crank movement adjustably at specific and adjustable controlled positions in the rotation of a crank (14, 16, 14', 16', 102, 104, 120, 122, 152, 154). A control system (40, 140, 140') may be incorporated to cause brake mechanisms (32, 80, 82, 96, 128, 129, 156) to apply varying amounts of resistance to a pair of pedal-driven cranks to simulate the efforts required to ride an actual bicycle over a course including various up-slopes and downslopes.