This paper presents a unique feature of geometric constraint of adjacent axes of the variable-axis (vA) joint and analyses the effectiveness in the constructed limb, resulting in variation of mobility configuration of two 3SvPSv metamorphic parallel mechanisms. The underlying principle of the metamorphosis of this vA joint is unravelled by investigating the dependence of the corresponding screw system comprising of line vectors, leading to evolution of the vA joint from the source phase Sv to the variable Hooke’s joint phase Uv and the variable revolute-joint phase Rv. The kinematic chain installed with the vA joint forms a reconfigurable limb and is then used to construct two 3SvPSv metamorphic parallel mechanisms proposed in this paper. The phase change of the vA joints incurs the constraint change of the SvPSv limb and subsequently results in the change of mobility configuration of the metamorphic parallel mechanisms. The paper further addresses the geometrical condition for constructing 3SvPSv metamorphic parallel mechanisms following the constraints delivered by the reconfigurable limbs, leading to the analysis of mobility change of the mechanisms induced by the phase change of the limbs.