In this paper, a concept of parallel mechanisms with configurable–structural platforms (CSPs) based on configurable platforms (CP) is proposed. When the self-deformable motion of the configurable platform is constrained by chains, the CP degenerates into the structural platform (SP). The self-deformation motion of CP changes the axis arrangement of the kinematic joints at the end of each chain, and the transformation between the CP and the SP can be realized by combining the constraint change of the chains. Based on the finite displacement screw matrix, virtual kinematic joint motion is used to describe the self-deforming axis motion of Bennett linkage CPs. Then the motion of virtual rigid body is described by Lie group theory. Finally, a type synthesis method of parallel mechanisms with CSPs is established based on Lie group theory. Parallel mechanisms with CSPs can use CPs to grasp, position and cooperate with other functions, and also can use SPs to work as traditional parallel mechanisms.