Singularity and kinematic bifurcation analysis of pin-bar mechanisms using analogous stiffness method

Based on the analogy between bifurcation of equilibrium paths in structures and kinematic bifurcation of mechanisms, this paper proposes an analogous stiffness method to detect the singularity and kinematic bifurcation of mechanisms. The analogous stiffness in mechanisms is first defined as the derivative of the state variable with respect to the controlling variable. By investigating the value of analogous stiffness, the singularity can be classified into output singularity, input singularity and architectural singularity. And the kinematic characteristics of free joints at corresponding singularity configurations are expounded. The singular and kinematic bifurcation points of mechanisms can then be determined by solving analogous stiffness equations and compatibility equations simultaneously. Following that, the analytical criterion for finite motion of corresponding free joints at singularity configurations is derived from the second-order analysis of compatibility equations. The efficiency of the proposed method is finally illustrated by three typical examples.