Agile bionic leg mechanism (ABLM) has attracted more and more attention in the development of jumping robots and high-speed running robots. However, theoretical study of the global structure for motility characteristics and its evolution is few. By using the modern mathematical tools such as singular theory, geometric topology, and group theory, a global scale analysis method for kinematic performance of mechanisms is proposed. Taking 6-bar with two rings mechanism as an example, a detailed analysis process is studied. The 6-bar ABLM designed by this theory is verified by virtual prototype simulation experiment. The global scale analysis of 4-bar linkage is also carried out by using this method, and the result is compared with the “Grashof criterion” to verify the correctness of this method. It provides a general theory and method for innovative design and global scale analysis of ABLM.