This paper presents a novel metamorphic 8R linkage extracted from a kirigami-fold with pregrooved creases and two overconstrained 6R linkages evolved from the 8R linkage by taking the concept of metamorphosis in the sense of structural evolution. The geometric characteristics and the parametric constraints of the evolved 6R linkages are identified following the structural evolution of the 8R linkage. The paper reveals that the evolved 6R linkages are special line-symmetric Bricard 6R loops characterized by the rotational symmetry of order two. The joint space of the overconstrained 6R linkages is analyzed and the relationship between motion parameters of the evolved 6R linkages and reconfiguration parameters of the metamorphic 8R linkage are derived. The motion characteristics of the overconstrained 6R linkages are further verified in terms of screw theory. The bifurcation and trifurcation associated with various transitory positions of the evolved 6R linkages having distinct parametric constraints are consequently identified based on constraint analysis.