Topological analysis of singularity loci for serial and parallel manipulators

Singularities of robot manipulators have been intensely studied in the last decades by researchers of many fields. Serial singularities produce some local loss of dexterity of the manipulator, therefore it might be desirable to search for singularityfree trajectories in the jointspace. On the other hand, parallel singularities are very dangerous for parallel manipulators, for they may provoke the local loss of platform control, and jeopardize the structural integrity of links or actuators. It is therefore utterly important to avoid parallel singularities, while operating a parallel machine. Furthermore, there might be some configurations of a parallel manipulators that are allowed by the constraints, but nevertheless are unreachable by any feasible path. The present work proposes a numerical procedure based upon Morse theory, an important branch of differential topology. Such procedure counts and identify the singularity-free regions that are cut by the singularity locus out of the configuration space, and the disjoint regions composing the configuration space of a parallel manipulator. Moreover, given any two configurations of a manipulator, a feasible or a singularity-free path connecting them can always be found, or it can be proved that none exists. Examples of applications to 3R and 6R serial manipulators, to 3UPS and 3UPU parallel wrists, to 3UPU parallel translational manipulators, and to 3RRR planar manipulators are reported in the work.

Singularity-Free Fully-Isotropic Translational Parallel Manipulators

Parallel mechanisms show desirable characteristics such as a large payload to robot weight ratio, considerable stiffness, low inertia and high dynamic performances. In particular, parallel manipulators with fewer than six degrees of freedom have recently attracted researchers’ attention, as their employ may prove valuable in those applications in which a higher mobility is uncalled-for. The attention of this dissertation is focused on translational parallel manipulators (TPMs), that is on parallel manipulators whose output link (platform) is provided with a pure translational motion with respect to the frame. The first part deals with the general problem of the topological synthesis and classification of TPMs, that is it identifies the architectures that TPM legs must possess for the platform to be able to freely translate in space without altering its orientation. The second part studies both constraint and direct singularities of TPMs. In particular, special families of fully-isotropic mechanisms are identified. Such manipulators exhibit outstanding properties, as they are free from singularities and show a constant orthogonal Jacobian matrix throughout their workspace. As a consequence, both the direct and the inverse position problems are linear and the kinematic analysis proves straightforward.

El depósito irregular de dinero: una aproximación teórica, histórica y ética

El análisis económico de las instituciones jurídicas ha adquirido una importancia considerable en los últimos años. Precisamente, el objetivo esencial de este trabajo se centra en el estudio del análisis económico del contrato de depósito irregular de dinero mediante tres enfoques metodológicos diferentes. El primer capítulo de este trabajo analiza la naturaleza jurídica del contrato de depósito irregular de dinero, examinando las principales características respecto al contrato de préstamo o mutuo. Igualmente, este capítulo estudiará la lógica jurídica propia de ambas instituciones, y cómo los principios generales del derecho fueron descubiertos desde el derecho romano clásico. El segundo capítulo trata de analizar la historia de los hechos económicos y, en particular, el proceso histórico de la violación de los principios tradicionales del derecho en relación al contrato de depósito irregular de dinero. Por último, el capítulo tercero examina los distintos intentos doctrinales realizados para elaborar un nuevo tipo de contrato de depósito bancario de dinero, con el único objetivo de legitimar un sistema bancario con un coeficiente de caja de reserva fraccionaria.