Abstract
In this short article we will discuss methods of finding and classifying singularities of planar mechanisms. The key point is to observe that the configuration spaces of the mechanisms can be understood as analytic and algebraic varieties. The set of singular points of an algebraic variety is itself an algebraic variety and of lower dimension than the original one. The singular variety can be computed using the Jacobian criterion. Once the singular points are obtained their nature can be investigated by investigating the localization of the constraint ideal at the local ring at this point. This will tell us if the singularity is an intersection of several motion modes or a singularity of a particular motion mode. The nature of the singularity can be then analyzed further by computing the tangent cone at this point.
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Notes
- 1.
This could have been done by transforming the analytic variety to algebraic variety but let us do that later.
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Piipponen, S., Arponen, T., Tuomela, J. (2014). Classification of Singularities in Kinematics of Mechanisms. In: Thomas, F., Perez Gracia, A. (eds) Computational Kinematics. Mechanisms and Machine Science, vol 15. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-7214-4_5
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DOI: https://doi.org/10.1007/978-94-007-7214-4_5
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