Variational approach for singularity-free path-planning of parallel manipulators

This paper addresses the problem of singularity-free path-planning for parallel manipulators. Unlike in serial manipulators, where there are only boundary singularities, parallel manipulators also possess singular configurations within the workspace where the manipulators are uncontrollable. Therefore, it is imperative that the generated paths are singularity-free. In this paper, we use a variational approach for planning singularity-free paths for parallel manipulators, based on a Lagrangian incorporating both a kinetic energy term which keeps the path short, and a potential energy term which ensures that the obtained path is singularity-free and the actuator lengths remain within their prescribed limits. The approach is applied to several parallel manipulators to evaluate the performance of this method

Fourth order resonant collisions of multipliers in reversible maps: period-4 orbits and invariant curves

Resonant collision of multipliers at ±i of a symmetric fixed point for a 2-parameter family of 4-dimensional reversible maps is considered. Bifurcation of period-4 orbits from the fixed point and their linear stability characteristics are briefly reviewed. In one of the three possible types of bifurcation (see text), a small angle secondary collision of the Floquet multipliers of the bifurcating periodic orbit takes place, leading to the bifurcation of invariant curves from the orbit. The invariant curves are calculated in a perturbation scheme in the leading order of perturbation. The secondary bifurcation is found to be of superthreshold type. An interesting pattern in the vicinity of the resonant collision, involving families of invariant curves and 2-tori, emerges. Results of numerical iterations, corroborating the picture conjectured on the basis of perturbation calculations, are presented. Corresponding results on resonant collisions at −1 are briefly stated

Calcutta 1981

A city laden with symbolic meaning in the Western mind, Calcutta – with ten million inhabitants today – is much more than the apathetic or violent display of urban destitution in India, as seen by the world at large. This collection tries to reach precisely beyond the cliches, to enable some of those who work in the city as decision-makers, planners or analysts, to speak out and Interpret the multifaceted crisis that has hit this city as it continues to grow, even though its economy is in decline. Their words have all the force as they are derived from first-hand experience. In analysing the laboured evolution of this city, once known as "the most beautiful city east of Suez", we have provided some material on a major case-study for the debate on urban planning and development in the Third World. The planning exercise launched in Calcutta in early 1960s, with support from American experts, hoped also to halt the spread of communism in Bengal. This was a vain expectation, however, as the Communist Party of India-Marxist has been continuously voted into power since 1977. From that date, the Left Front Government has controlled the Calcutta Metropolitan Development Authority, which provides amenities to the city and metropolitan district with support from, among others, the World Bank. What are henceforth the urban development policies of "parliamentary communism"? What are the problems they are up against when action is necessary on all fronts at once? In the final analysis, for what purpose and for whom are they planning? What should be the priorities? To set up the economy to right first? To provide amenities for the city? Or to improve the daily life of the most underprivileged? When confronted with these realities, what the Left is able to achieve in power? These are some of the questions that the contributors to this collection have, in their own way, been concerned with in creating an image of present-day Calcutta, seen through its own eyes.To Pushkar and Subha, to Barun, Ella, Sudhesna, Swamik, and to the memory of M.G. Kutty, a South Indian who choosed to strive for a better Calcutta, for India is one