We define the notion of a finite-time singularity of a vector field and then discuss a technique suitable for the asymptotic analysis of vector fields and their integral curves in the neighborhood of such a singularity. Having in mind the application of this method to cosmology, we also provide an analysis of the time singularities of an isotropic universe filled with a perfect fluid in general...

We analyse the classical model of competition between three species studied by May and Leonard (SIAM J Appl Math 29 (1975) 243-256) with the approaches of singularity analysis and symmetry analysis to identify values of the parameters for which the system is integrable. We observe some striking relations between critical values arising from the approach of dynamical systems and the singularity ...

this paper presents the kinematic analysis and the development of a 4-degree-of-freedom serial-parallel mechanism for large commercial vehicle driving simulators. the degrees of freedom are selected according to the target maneuvers and the structure of human motion perception organs. several kinematic properties of parallel part of the mechanism under study are investigated, including the inve...

Instantaneous kinematics and singularity analysis of a class of three-legged, 6-DOF parallel manipulators are addressed in this paper. A generic method of derivation of reciprocal screw and consequently, the instantaneous kinematics model is presented. The advantage of this formulation is that the instantaneous kinematics model possesses well-defined geometric meaning and algebraic structure. S...

This paper extends a recently proposed singularity analysis method to lower-mobility parallel manipulators having an articulated nacelle. Using screw theory, a twist graph is introduced in order to simplify the constraint analysis of such manipulators. Then, a wrench graph is obtained in order to represent some points at infinity on the Plücker lines of the Jacobian matrix. Using GrassmannCayle...

Toby Walsh in “The Singularity May Never Be Near” gives six arguments to support his point of view that technological singularity may happen but that it is unlikely. In this paper, we provide analysis of each one of his arguments and arrive at similar conclusions, but with more weight given to the “likely to happen” probability.