A geometric approach for determining inner and exterior boundaries of workspaces of planar manipulators

In this paper a method to determine the internal and external boundaries of planar workspaces, represented with an ordered set of points, is presented. The sequence of points are grouped and can be interpreted to form a sequence of curves. Three successive curves are used for determining the instantaneous center of rotation for the second one of them. The two extremal points on the curve with respect to the instantaneous center are recognized as singular points. The chronological ordering of these singular points is used to generate the two envelope curves, which are potentially intersecting. Methods have been presented in the paper for the determination of the workspace boundary from the envelope curves. Strategies to deal with the manipulators with joint limits and various degenerate situations have also been discussed. The computational steps being completely geometric, the method does not require the knowledge about the manipulator's kinematics. Hence, it can be used for the workspace of arbitrary planar manipulators. A number of illustrative examples demonstrate the efficacy of the proposed method.

An Outward-Wave-Favouring Finite Element-Based Strategy for Exterior Acoustical Problems

This work presents a finite element-based strategy for exterior acoustical problems based on an assumed pressure form that favours outgoing waves. The resulting governing equation, weak formulation, and finite element formulation are developed both for coupled and uncoupled problems. The developed elements are very similar to conventional elements in that they are based on the standard Galerkin variational formulation and use standard Lagrange interpolation functions and standard Gaussian quadrature. In addition and in contrast to wave envelope formulations and their extensions, the developed elements can be used in the immediate vicinity of the radiator/scatterer. The method is similar to the perfectly matched layer (PML) method in the sense that each layer of elements added around the radiator absorbs acoustical waves so that no boundary condition needs to be applied at the outermost boundary where the domain is truncated. By comparing against strategies such as the PML and wave-envelope methods, we show that the relative accuracy, both in the near and far-field results, is considerably higher.

Postsynthetic Exterior Decoration of an Organic Cage by Copper(I)-Catalysed A(3)-Coupling and Detection of Nitroaromatics

A new synthetic protocol based on one-pot, copper(I)-catalysed multicomponent reaction of formaldehyde, secondary amine and terminal alkyne has been employed to postsynthetically modify a self-assembled nanoscopic organic cage. By employing this synthetic strategy, three new cages appended with phenyl-, xylyl-and naphthyl-acetylene moieties have been synthesised. The resulting modified cages were characterised by using a range of spectroscopic techniques. The synthesised cages were fluorescent and thus one of them was tested to explore the potential use of such compounds as chemosensors for the detection of nitroaromatics. Experimental findings suggest a high selective quenching of initial fluorescence intensity in the presence of nitroaromatic compounds. Furthermore, it has been observed that among the various nitroaromatics tested, nitrophenolic compounds have better quenching ability.