Classification of compatibility paths of SDOF mechanisms

The compatibility paths of mechanisms with a single degree-of-freedom typically form sets of curves in the global representation space. We classify the different cases of compatibility by introducing an energy function. The result obtained also depends on which element of the mechanism is regarded as driven. The different singularity types are demonstrated by examples (split-vanish point, limit point, asymmetric bifurcation, infinitely degenerate bifurcation, hilltop point, compatibility surface).