Design of linear surfaces that restrict the range of permissible positions of links of the manipulator mechanisms in implementation of instantaneous states

Abstract

Linear surfaces are used in various spheres of human activity. One of the most common techniques of designing linear surfaces is based on the three directing curves. In some cases, one of these directing curves is not set, but rather replaced by some geometric condition imposed on the emerging surfaces, which can in form of a certain point correspondence established between the points of the rest two directing curves. The article reviews the example of designing such surfaces, which in an approximate form would restrict the zone that sets the permissible positions of links of the manipulator mechanism of certain given configuration in realization of permissible instantaneous states. The acquired linear surfaces underlie the algorithm for calculation of configurations, which do not intersect the restricted zone in case of a deadlock situation. The result of this research is the computer simulation of the motions of arm and torso mechanism of the Android robot using the obtained algorithm for calculation of configurations. The simulation of motion demonstrates that the use of linear surfaces in analysis of the relative position of the manipulator and restricted zones in the deadlock situations allows reducing the calculation time by 50-60 percent. Such reduction of calculation time is highly demanded in computer control of the arm and torso motions of the Android robot on a real time scale.