Modelling of kinematics of the IRb-6 manipulator

The fundamental problem in industrial robots control concerns algorithms generating reference trajectories. Papers [1–4] suggest generating algorithms of a reference trajectory, which are based on an arbitrary discretization of the manipulators internal coordinates. Each point of discretization in the external space approximating a reference trajectory corresponds with known discretized internal coordinates of the manipulator. In papers [5–7], iteration methods of determining the internal coordinates corresponding to external coordinates of the reference trajectory point have been suggested. In this method of internal coordinates, determining the point of the reference trajectory is being approached in successive steps of iterative computation. In paper [5], a modified iterative method of generating a reference trajectory straight segment has been presented. Analytic formulas which are the solution of an inverse problem of manipulator kinematics enable designing of trajectory generating algorithms which compute, in one step only, internal coordinates of points lying exactly on the reference trajectory, with the accuracy resulting from the computer register length. This paper presents equations of links and actuators kinematics of the IRb-6 manipulator in matrix form. Also, solutions of equations of link kinematics, as well as formulas joining link and actuator natural coordinates of the manipulator, have been presented.