This paper proposes a new synthesis approach by using constraints for limb synthesis to target mobility-change in the mechanism construction. The limbs therefore produced have the facility to reconfigure the limb twist-system to change the screw system order for reconfigurability. This presents various reconfigurable limbs with geometric constraints of their joints based on the newly invented reconfigurable Hook (rT) joints. The procedure of the limb synthesis is put forward to fully utilize the property of the new joint for generating the reconfigurable limbs. The paper further presents a mobility-change condition to construct a metamorphic mechanism with the reconfigurable limbs. This gives a family of metamorphic parallel mechanisms that have the facility to change mobility in the range of 3– 6. A further family of metamorphic parallel mechanisms is proposed with a central strut. Their topological configuration change is investigated by examining the constraint change stemming from the phase alteration of the reconfigurable Hooke rT joint.