Search

An optimization approach to the computation of the boundaries of different dextrous workspaces of parallel manipulators is presented. A specific dextrous workspace is the region in space in which, at each position of the working point, a manipulator can control the orientation of its upper working platform through a specified range of orientation angles. Here the dextrous workspace is determined from the intersection of suitably chosen fixed orientation workspaces, which are found by application of a constrained optimization algorithm. The procedure is simple and has the considerable advantage that it may easily be automated. The method is illustrated by its application to both a planar and spatial Gough–Stewart platform. Copyright © 2001 John Wiley & Sons, Ltd.

This paper describes the use of Computational Fluid Dynamics (CFD) and mathematical optimization to determine the optimum operating conditions and geometry of a continuous quenching process. The pump power as well as the quench rate of the steel plate in this process is influenced by many parameters. These include the nozzle and header geometry, plate speed, water flow rate, etc. Since an experimental approach is time consuming and costly, use is made of numerical techniques. Furthermore, it is sometimes impossible to measure certain values in this manufacturing process (e.g. the quench rate at a certain depth in the plate). These quantities can be obtained by CFD techniques. Using CFD without optimization on a trial-and-error basis, however, does not guarantee optimal solutions. A better approach, that has until recently been too expensive, is to combine CFD with mathematical optimization techniques, thereby incorporating the influence of the variables automatically. The current study investigates a simplified two-dimensional continuous quenching process. The first part of the study investigates the operating conditions required to quench a plate at a specific quench rate. The second part of the study minimizes the pump power to quench a plate at a specific quench rate. The CFD simulation uses the STAR-CD code to solve the Reynolds-Averaged Navier–Stokes equations with the k–ε turbulence model. The optimization is carried out by means of Snyman's DYNAMIC-Q method, which is specifically designed to handle constrained problems where the objective or constraint functions are expensive to evaluate. The paper illustrates how this optimization technique can be used to obtain the operating conditions needed for a manufacturing process with complex flow and heat transfer phenomena. The paper also illustrates how these techniques can be used in the design phase of such a manufacturing process to determine the optimum geometry and process parameters. Copyright © 2000 John Wiley & Sons, Ltd.