A fundamental problem in industrial robots control concerns algorithms generating reference trajectories. In the papers (Gerke, 1985; Gousenes, 1984; Jacak, 1989; Lozano-Perez, 1983) some generating algorithms based on an arbitrary discretization of the manipulators internal coordinates are suggested. Each point of discretization in the external space approximating a reference trajectory is represented by known discretized internal coordinates of the manipulator. ; On the other hand, in papers (Dulęba and Łysakowska, 1990; Jacak and Łysakowska, 1990; Taylor, 1983) iteration methods of determining the internal coordinates corresponding to external coordinates of the reference trajectory point have been suggested. By applying this technique, the point of the reference trajectory is approached in successive steps of an iterative procedure. ; In the paper of Dulęba and Łysakowska (1990) a modified iterative method of generating a straight segment of the reference trajectory has been presented. Analytic formulae which are the solution to an inverse problem of manipulator kinematics enable us to design 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. ; The paper presents equations of links and actuators kinematics of IRb-6 manipulator in a matrix form. Also solution to equations of link kinematics as well as formulae joining link and actuator natural coordinates of the manipulator have been presented.