Building on the analytical results presented in Part I, the issue of multiple singularity is explored. The attained understanding is applied to the analysis and synthesis of compound infinitesimal mechanisms illustrated in several examples. Employing power expansion techniques, higher-order mechanisms are investigated, revealing, in particular, the existence of even-order mechanisms and their peculiar nature. The equivalence condition is established between prestressability and kinematic immobility of underconstrained structural systems with one singularity. A previously unidentified class of systems—unprestressable infinitesimal mechanisms—is revealed. It complements the conventional source of infinitesimally mobile systems associated with a strict constrained extremum and the resulting feature of prestressability.

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