Secondorder Taylor Stability Analysis of Isolated Kinematic Singularities of Closedchain Mechanisms A. Peidro, O. Reinoso, A Gil, J.MĒ Marin, L. Paya, Y. Berenguer Proceedings of the 14th International Conference on Informatics in Control, Automation and Robotics (ICINCO 2017) (Madrid (Spain), 2628 July 2017)
Ed. SCITEPRESS ISBN:9789897582646 DOI:10.5220/0006428503510358  Vol. 2, pp. 351358
Abstract:
When the geometric design of a closedchain mechanism is nongeneric, the singularity locus of the mechanism
may exhibit isolated points. It is well known that these isolated points are unstable since they disappear
or generate/reveal cusps when the geometric design of the mechanism slightly deviates from a nongeneric
design, possibly affecting the ability of the mechanism to reconfigure without crossing undesirable singularities.
This paper presents a method based on secondorder Taylor expansions to determine how these isolated
singularities transform when perturbing the different geometric parameters of a nongeneric mechanism. The
method consists in approximating the singularity locus by a conic section near the isolated singularity, and
classifying the resulting conic in terms of the perturbations of the different geometric parameters. Two nongeneric
closedchain mechanisms are used to illustrate the presented method: an orthogonal 3R serial arm
with specified position for its tip, and the planar Stewart parallel platform.
