Topological structure synthesis is the most original part of mechanical system design. Aiming at the problems in the existing theories on type synthesis of robot mechanisms, such as incompleteness of synthesis results, inapplicability to bending translation mechanisms and so on, the method of type synthesis and classification for parallel mechanisms with bending translation motion characteristic was proposed. First of all, lines, curves, planes and surfaces were regarded as independent spaces based on the Gauss non-Euclidean intrinsic geometry, which can be used to describe the translation characteristics of the end-effector. Then a motion characteristic model of bending translation was established, which included motion type (translation and rotation), motion direction, dimension and overall geometric shape of motion space. Secondly, the forming mechanism of bending translation was studied, and the relevant operation rules of bending translation motion characteristics were formulated, which made the intersection of all limbs’ motion characteristics for parallel mechanism relatively straightforward and simple. After that, according to the geometric morphological features of space curves, the space curve translation mechanisms can be divided into nine basic types. Finally, the method of type synthesis for space curve translation mechanisms was illustrated by two examples, and the complete procedures for structural synthesis of cylinder-cylinder intersection line translation mechanism and cylinder-cone intersection line translation mechanism were shown by using this method.