Urbanic, R. and Djuric, A., "Methods for Evaluating the Functional Work Space for Machine Tools and 6 Axis Serial Robots," SAE Int. J. Mater. Manf. 9(2):465-473, 2016, doi:10.4271/2016-01-0338.
The ‘boundary of space’ model representing all possible positions which may be occupied by a mechanism during its normal range of motion (for all positions and orientations) is called the work envelope. In the robotic domain, it is also known as the robot operating envelope or workspace. Several researchers have investigated workspace boundaries for different degrees of freedom (DOF), joint types and kinematic structures utilizing many approaches. The work envelope provides essential boundary information, which is critical for safety and layout concerns, but the work envelope information does not by itself determine the reach feasibility of a desired configuration. The effect of orientation is not captured as well as the coupling related to operational parameters. Included in this are spatial occupancy concerns due to linking multiple kinematic chains, which is an issue with multi-tasking machine tools, and manufacturing cells. This research presents methodologies to predetermine regions of feasible operation for multiple kinematic chain mechanisms, such as multi-spindle/multiaxis machine tools and industrial serial 6 degree of freedom robots, and manufacturing cells.