The crank- group driving mechanism is a kind of underactuated mechanism with redundant characteristics. Based on the topological theory,taking the typical structures of the crank- group driving mechanism（ the single driven crank driving mechanism and the double driven crank driving mechanism） as examples,a preliminary study and exploration of its topological structure is conducted by using kinematic chain and the matrix. To solve the mechanism problems through the topological structure theory,the organic integration of topology and mechanism is achieved. And there’s no doubt that it’s of great importance for the study and the development of interdisciplinary.