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Topological structure is the most original part of mechanical system design. The premise of structure synthesis depends on complete description and accurate analysis of the motion characteristics. And the motion characteristic is not only the design objective of type synthesis, but also the judgment whether the obtained mechanism meets the requirements. The existing indexes of motion characteristics only contain three kinds of information: motion type (translation and rotation), motion direction and the dimension of motion space, but they lack the overall geometric shape of motion space, which will lead to insufficient information of motion characteristics and incomplete type expressions. To solve this problem, a geometric description and analysis method for the motion characteristics of robot endeffector was proposed based on Gaussian geometry. Firstly, a geometric description model of motion characteristics was established, which included overall geometric shape of motion space. Secondly, the relevant operation rules of motion characteristics were formulated, which made the intersection of all limbs’ motion characteristics for parallel mechanism relatively straightforward and simple. And a geometric analysis method for the motion characteristics of robot endeffector was presented. Finally, the validity of the geometric description and analysis method was verified by some concrete examples. Compared with the algebraic method, the geometric analysis method for the motion characteristics of the robot endeffector was much simpler and more intuitive, which had obvious advantages especially for mechanisms with bending motion characteristics.