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...

We apply the technique of complex paths to obtain Hawking radiation in different coordinate representations of the Schwarzschild space–time. The coordinate representations we consider do not possess a singularity at the horizon unlike the standard Schwarzschild coordinate. However, the event horizon manifests itself as a singularity in the expression for the semiclassical action. This singulari...

In this work, we develop an efficient solver based on neural networks for second-order elliptic equations with variable coefficients and a singular source. This class of problems covers general point sources, line the combination point-line sources has broad range practical applications. The proposed approach is decomposing true solution into part that known analytically using fundamental Lapla...

We consider solving the singular linear system arisen from the Poisson equation with the Neumann boundary condition. To handle the singularity, there are two usual approaches: one is to fix a Dirichlet boundary condition at one point, and the other seeks a unique solution in the orthogonal complement of the kernel. One may incorrectly presume that the two solutions are the similar to each other...

Joint-coupling is introduced in the design and control of parallel manipulators for purposes of singularity management. The idea behind joint-coupling is to drive several joints with one single actuator by mechanical or electronic means, while preserving the mobility of the manipulator. Such joint-coupling can affect the condition of direct singularities of parallel manipulators through its cou...

In this paper, we consider the acoustic cloaking based on singular transformations and its approximation in the context of scattering problems in R. The cloaking based on singular transformations can not avoid a singularity of the resulting Laplace–Beltrami operator because singular transformations blow up one point to a sphere. In order to treat the singularity properly, we use the variational...

Parallel mechanisms frequently contain an unstable type of singularity that has no counterpart in serial mechanisms. When the mechanism is at or near this type of singularity, it loses the ability to counteract external forces in certain directions which can lead to arbitrary motion. The determination of unstable singular configurations in parallel mechanisms is not trivial, and is usually atte...

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...

We confront two integrability criteria for rational mappings. The first is the singularity confinement based on the requirement that every singu-larity, spontaneously appearing during the iteration of a mapping, disappear after some steps. The second recently proposed is the algebraic entropy criterion associated to the growth of the degree of the iterates. The algebraic entropy results confirm...