A drain cleaning machine for moving a snake in a drain includes a rotating shell, a motor to rotate the rotating shell, and a radial drive mechanism coupled for rotation with the rotating shell and including a plurality of collets. The radial drive mechanism is switchable between an engaged state in which the one or more collets move toward a snake axis to engage the snake, and a disengaged state. A translate mechanism is coupled for rotation with the rotating shell and includes a plurality of wheels. The translate mechanism is switchable between an engaged state in which the wheels move toward the snake axis to engage the snake, and a disengaged state. A selection mechanism is configured to switch the radial drive mechanism from the disengaged state to the engaged state and configured to switch the translate mechanism from the disengaged state to the engaged state.