Analytical and numerical analysis of mobility and kinematic bifurcation of planar linkages

Mobility analysis of linkage systems remains a topic of extensive research. Some criteria were proposed to determine whether a system is a moveable mechanism, such as the Maxwell criterion. However, the most frequently used criteria at a given configuration are not sufficient and necessary conditions for a finite mechanism. For the kinematic analysis, many researchers proposed numerical methods rather than using analytical approaches. In this paper, the mobility and kinematic bifurcation of mechanisms can be determined by analytical and numerical analysis of system constraint equations. If the solution of system constraint equations exists and the system constraint equations are continuous, the system is moveable. The kinematic bifurcation and the limit point in the kinematic path of mechanisms are also discussed. Finally, all the motion paths can be obtained by this method considering bifurcation and limit point in the kinematic paths at any configurations.