Description:
It is central to the control of manipulators to calculate the set/sets of joint-displacements which correspond to a given spatial pose (position and orientation) of the end-effector. This problem, which is referred to as the inverse position problem, represents one of the most difficult mathematical challenges in the field of robotics, particularly when performed for calibrated robots (or robots with general structures). In such cases, closed form solutions are too impractical to implement and iterative solutions suffer from numerical singularities. In the present work a procedure is introduced to obtain multiple inverse position solutions for serial robotic structures. For calibrated robots, the procedure involves a simple iterative technique designed to ensure fast convergence and eliminate the occurrence of singularity. However, inverse position solutions for spherical-wrist manipulators will be obtained in a straight-forward non-iterative fashion. A published kinematic notation, referred to as the phi -model, was used to develop the system equations.
Description:
Liquid effluents that arise in the landfilling of municipal solid wastes, both leachate and gas condensates, can replace some or all of the conventional coal flotation reagents. The waste management industry currently must treat these effluents, to destroy contained organics, prior to their discharge to the environment and hence they are available at no cost, or even with "dollars attached". These landfill-derived liquids contain valuable short-chain fatty acids (e.g. valeric and caproic acids) that act as both frother and collector in flotation processes. They can be further concentrated by membrane filtration to reduce the transport costs of such liquids and the ease of their use in coal recovery systems. This paper will discuss how these liquids are formed in landfills, their typical compositions and how they can be employed to recover fine coal. Data from both conventional flotation feeds (-0.5 mm) and column flotation feeds (-0.1 mm) is presented.