The elementary bifurcation theory is utilized to study the bifurcation of singularities of general parallel mechanisms. Based on constraint equations, some typical motion bifurcation of simple parallel mechanisms are researched and they can be classified into different styles by codimensions of constraint equations at actuator singular points or end-effector singular points. Finally, this paper discusses how the disturbance of mechanism parameters affects the bifurcation diagram of singularities and results show that those nonpersistent bifurcations of parallel mechanisms can be transformed into those persistent bifurcations so that the motion uncertainty at singularities can be overcome.