Low-degree-of-freedom (Low-DOF) parallel manipulators (PMs) have drawn extensive interests, particularly in type synthesis in which two main formal approaches were established by using the reciprocal screw system theory and Lie group theory. This paper aims at numeration and type synthesis of orthogonal translational parallel manipulators (OTPMs) by resorting to an integration of the group- based method and graphical representation of the topology. For this purpose, the concept of Cartesian DOF-characteristic matrix, orig- inated from displacement subgroup and displacement submanifold, is proposed. A new approach based on the combination of the atlas of Cartesian DOF-characteristic matrix and the displacement group-theoretic method is addressed for both exhaustive classi cation and type synthesis of OTPMs. The proposed approach is prone to construct an orthogonal structure and is easy to realize the complete clas- si cation and exhaustive enumeration of this class of low-DOF PMs. Low-degree-of-freedom (Low-DOF) parallel manipulators (PMs) have drawn extensive interests, particularly in type synthesis in which two main formal approaches were established by using the reciprocal screw system theory and Lie group theory. This paper aims at numeration and type synthesis of orthogonal translational parallel manipulators (OTPMs) by resorting to an integration of the group-based method and graphical representation of the topology. For this purpose, the concept of Cartesian DOF-characteristic matrix, orig-in from displacement subgroup and A new approach based on the combination of the atlas of Cartesian DOF-characteristic matrix and the displacement group-theoretic method is addressed for both exhaustive classi cation and type synthesis of OTPMs. The proposed approach is prone to construct an orthogonal structure and is easy to realize the complete clas-si cation and exhaustive enumeration of this class of low-DOF PMs.