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The reconfigurability and unified analytical kinematics analysis of a type of 3(Ra)PS metamorphic parallel mechanism were studied. According to the constraint screw system, in one configuration, the (Ra)PS chain had no constraint on the platform, while in another configuration, it can provide a constraint by changing the position of the inner axis of the Ra joint. The two configurations of the limb made the 3(Ra)PS metamorphic parallel mechanism have four kinds of topological structures, which had the ability to move between 2R1T (two rotations and one translation), 3R1T (three rotations and one translation), 3R2T and 6 DOF. The basic principles of metamorphic of such reconfigurable axis joint were revealed by investigating the correlation of the corresponding screw systems consisted of line vectors. A limb that can be used to construct a type of parallel mechanism was proposed. The subphases of the limb that accompanied the phase change of a specific reconfigurable axis joint were enumerated and the constraints corresponding to each phase were analyzed based on the reciprocity of the screw. Based on the analysis of the driving scheme, a unified kinematic modelling method with one configuration as a special case of the other was proposed through the difference between the two configurations of the limb. Four kinds of driving schemes and four kinds of unified kinematic models covering 3(Ra)PS metamorphic parallel mechanism were established. The drive selection scheme of 3(Ra)PS metamorphic parallel mechanism and the unified kinematic model covering four configurations were established. The inverse kinematics and forward kinematics were solved analytically, and the theoretical results were verified by numerical examples. The proposed metamorphic parallel mechanism laid a foundation for the workspace, path planning and control of the metamorphic mechanism.