Graphical representation of the significant 6R KUKA robots spaces

Trajectory planning for serial 6 degree of freedom (DOF) machinery systems is demanding due to complex kinematic structure which affects the machinery tool fame, position, orientation and singularity. These three characteristics represent the key elements for production planning and layout design of the manufacturing systems. Both, simple and complex machine trajectory is defined as series of connected points in 3D space. Each point is defined with its position and orientation related to the machine´s base frames. To visualize the machine´s reachable space, the work envelope is calculated and graphically presented as very well known machine´s property. A methodology to predetermine regions of feasible tool orientation (work window) is analytically and graphically presented. The work envelope boundary is generated using the filtering points algorithm, while work window is generated using either empirical or analytical methods. The singularity regions are calculated by finding the determinant of the reconfigurable Jacobian matrix. These three tool path characteristics represent three different spaces which are identified both analytically and graphically and plotted in Cartesian space using MATLAB tools. The singularity regions will be represented within the workspace and work window for a single machinery kinematic structure. The KUKA KR robot family is used as a case study.