Manipulator synthesis on the given properties of working space. Application of polynomials with linear real parameter

In this work the algorithm and the results of a synthesis problem solving for three-links planar manipulator with anthropomorphous structure according to criterion of a minimum total volume of links movements is resulted at achievement by end effector of set of points in the set area of working space. Research of parameters space is made by the Sobol-Statnikov method. The algorithm of numerical solving of the nonlinear equations system of geometrical connections and kinematic criterion of quality is constructed taking into account properties of set of polynomials with linear real parameter. The results of problem solving are show that, from the point of view of the accepted criterion of quality, optimum relations between lengths of manipulator links depend on an area arrangement most often reached by end effector in working space.