Structural synthesis of LEMs based on planar kinematic chains

This paper proposed a structural synthesis method of LEMs both with prismatic joint and revolute joint, which can solve the problem of frame and driver link transformation. First, equate the LEMs in the plane with the planar kinematic chains, and then construct the group-based adjacent matrix of the planar kinematic chains, and to solve all possible connection mode of planar mechanism which is given the number of bars and degrees of freedom. According to the number of bars and degree of freedom, analysis all the combination of Assur group, set up the frame of the group-based adjacent matrix, assemble the first stage and later groups to driver link and frame or former groups, and identify the isomorphism in synchronism, get all the connections of planar mechanism with only revolute pair, and then plug the joint types of driver link and all the different types of groups into the above planar mechanism connections, get all the connections with prismatic joint and revolute joint and the transformation of frame and driver link. Finally, restore the obtained planar kinematic chains to LEMs in the planar. Taking eight-bar planar mechanism for example, 102 kinds of different types of structures with revolution joint have been obtained.