Mohile, Ajey Avinash.

When small perturbations in the kinematic parameters of a robot are taken into consideration, the model of a robot no longer contains perfect parallelism and perpendicularity that makes the nominal inverse kinematics so simple. In particular, the effect of joint axis misalignments and small perturbations in the kinematic parameters on the robot singularities is of interest. This aspect is particularly important when planning the workspace of a robot that must undergo calibration. To utilize the work volume most efficiently, one must know exactly what points are permissible as taught points. In other words, reachable workspace must be clearly defined to avoid the robot from entering the singularity zones not only of the nominal robot but also of all future actual robots. Once singularity zones for the actual robot are correctly identified, workspace planning becomes a simple task. In this thesis the relationship between small perturbations in kinematic parameters and singularities of a simple three-revolute articulated arm are studied. It is shown that singularities in such a robot do shift to new locations.