Abstract: The essence of equilibrium-path bifurcations in ideal structural instability was revealed. It was shown that when the generalized tangent stiffness becomes zero, the external forces and structural displacements lose control of each others, which leads to singularity of structures. Based on the analogy between equilibrium-path bifurcations of structures and kinematic bifurcations of mechanisms, the analogous stiffness in mechanisms was defined as the derivative of the state variable on the controlling variable. It was proved that when the analogous stiffness becomes zero, infinite or 0/0 type, the corresponding controlling and state variables lose control of each other and singularity of mechanisms emerges, whose corresponding singularity configurations were classified. After defining the analogous stiffness equations as the analogous stiffness being zero, infinite or 0/0, the analogous stiffness method was proposed to detect kinematic bifurcations of mechanisms by solving analogous stiffness equations and compatibility equations simultaneously. Finally, the validity and advantage of the present method were illustrated by a typical 2-DOF example, based on the method.