Second-order Taylor Stability Analysis of Isolated Kinematic Singularities of Closed-chain 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), 26-28 July 2017)
Ed. SCITEPRESS - Vol. 2, pp. 351-358
When the geometric design of a closed-chain mechanism is non-generic, 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 non-generic
design, possibly affecting the ability of the mechanism to reconfigure without crossing undesirable singularities.
This paper presents a method based on second-order Taylor expansions to determine how these isolated
singularities transform when perturbing the different geometric parameters of a non-generic 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
closed-chain 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.