Through the application of Assur bar groups method and graph theory

the link classification and link composition are finished to get the most basic kinematic chain’s structure of the planar 3-DOF mechanism with full revolute pairs which has three symmetrical branched chains.Then topological embryonic graph is drawn using the interpolation point method of the topological embryonic graph.The classification of the branched chains is done and the chains are inserted in the topology embryonic graph.Through the isomorphism analysis

the 6 configurations of kinematic chains are obtained.Finally

using a new graph theory description method based on the link’s relationship the hybrid configuration of planar 3-DOF is obtained

then the application research is proceeded.Doing these can lay the foundation for the study of the planar 3-DOF mechanism with non full revolute pairs.At the same time

the study of the planar 3-DOF mechanism is also more conducive to the research of the spatial lower-freedom mechanism.