This paper presents an analysis to create a general singularity condition for a mechanism that contains a deformable closed contour. This kinematic architecture is particularly relevant to rigid-link, shape-changing mechanisms. Closed contour shape-changing mechanisms will be shown to belong to the Assur classification because of the pattern of interconnections among the links. The general singularity equations are reduced to a condensed form, which allows geometric relationships to be readily detected. The analysis is repeated for alternative input links. A method for formulating the singularity condition for an Assur Class , knowing the condition for a Class mechanism, is given. This approach is illustrated with several examples.
Singularity Analysis of an Extensible Kinematic Architecture: Assur Class , Order
Myszka, D. H., Murray, A. P., and Schmiedeler, J. P. (August 5, 2008). "Singularity Analysis of an Extensible Kinematic Architecture: Assur Class , Order ." ASME. J. Mechanisms Robotics. February 2009; 1(1): 011009. https://doi.org/10.1115/1.2960542
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