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 groupbased method and graphical representation of the topology.For this purpose,the concept of Cartesian DOF-characteristic matrix,originated 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 classification and type synthesis of oTPMs.The proposed approach is prone to construct all orthogonal structure and is easy to realize the complete classification and exhaustive enumeration of this class of low-DOF PMs.