Date of Award


Publication Type

Master Thesis

Degree Name



Industrial and Manufacturing Systems Engineering


Applied sciences, Forward kinematics, Functional workspace, Open kinematic chains, Robotic/machine placement, Robotic workspace, Serial manipulators


Jill Urbanic




The work envelope of a robot does not capture the effect of tool orientation. Applications will require the tool to be at a certain orientation to perform the tasks necessary. It is therefore important to introduce a parameter that can capture the effect of orientation for multiple robots and configurations. This is called the functional work space, which is a subset of the work envelope would capture the effect of orientation. This research discusses the development of establishing an assessment tool that can predict the functional work space of a robot for a certain tool-orientation pair thus aiding in proper tool, tool path, fixture, related configuration selection and placement. Several solutions are studied and an analytical and a geometric solution is presented after a detailed study of joint dependencies, joint movements, limits, link lengths and displacements through visual, empirical and analytical approaches. The functional workspace curve for a manipulator with similar kinematic structure can be created using the geometrical solution discussed in this research. It is difficult to derive a general paradigm since different parameters such as, joint limits, angles and twist angles seem to have a different effect on the shape of the workspace. The geometrical solution employed is simple, easy to deduce and can be simulated with a commercial software package. Design decisions pertaining to configuration and reconfiguration of manipulators will benefit by employing the solution as a design/analysis tool. A case study involving an X-ray diffraction technique goniometer is presented to highlight the merits of this work.