Structural Synthesis, Work Spaces and Direct Kinematic of the one Serial Kinematic Chain with 8 Axes for Industrial Robots

In this paper, for a useful working basis, including for the promotion of new redundant structures, beyond those already implemented, there is a systematization of kinematic chain structures with 8 axes. Representation of corresponding workspaces can help the designer in choosing the structure with maximum functionality for a given application. Exemplifying of the use of these redundant structures, namely a structure with 8 axes, is possible presenting the eight-axes robot CLOOS, of type: T⊥R|| (R⊥R||R)(R⊥R⊥R). For this version the workspace is represented, first sequentially, successively for each coupling, starting with the translation coupling from the kinematic chain base and then the workspace is represented totally by overlapping workspaces obtained for each coupling. Below we present the direct kinematics analysis for this kinematic chain using the homogeneous operators’ method. This method is based on the use of homogeneous translation or rotation operators and covering the kinematic chain from the base to the characteristic point at its end by a mobile reference system. Transition from a coupling to another is associated with a matrix homogeneous operator of translation, rotation, translation-translation, rotation-rotation or combined (rotation-translation or translation-rotation). Based on linear and angular dimensions expressed in matrix by corresponding homogeneous operators we obtain the matrix of the robot characteristic point coordinates in the fixed reference system attached to the robot base. Thus, direct kinematics is solved qualitatively. For a set of numerical values, we obtain a quantitative solution.