Using a Singularity Locus to Exhibit the Number of Geometric Inversions, Transitions and Circuits of a Linkage

The identification of motion characteristics and assembly circuits is fundamental in creating a workable mechanism. A circuit defect prevents a mechanism from moving between desired positions. This paper extends the established methods for analyzing multi-degree-of-freedom platforms to gain insight on single-actuated linkages. Specifically, from a plot of the singularity locus projected onto the input joint space, the number of singularities, number of geometric inversions and circuit regimes are revealed. The input/output motion of the linkage can be inferred from the locus. The methodology to produce the singularity locus is general and does not rely on geometric insights of a particular mechanism. By using the locus, desired operational features can be readily identified, such as a fully rotatable crank. Unique motion characteristics, such as a greater than 360° non-rotatable crank, can be also be detected. Further, it is observed that transition linkages serve as bounds between the regions of circuit change.