A locking hinge design relies on a mechanically-actuated magnetic clutch to selectively disengage first and second gears respectively coupled to first and second members and thereby selectively enable relative rotation between the first and second members about an axis of rotation. The mechanically-actuated magnetic clutch includes first and second magnetic members disposed in an opposing relationship, such that permanent magnets respectively disposed in each magnetic member may be placed into either a mutually attractive or mutually repellant relationship in response to relative movement therebetween. One of the magnetic members is coupled to one of the gears to move the gear along the axis of rotation and thereby selectively disengage or engage the gear from or with the other gear such that the gears are selectively engaged in response to mechanical movement of the magnetic members.