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Investigation of haptic manipulators with linear equations of motion

Kızılbey, Aras
In this thesis, linearization of the equations of motion of haptic interfaces and the effects of such linearization on haptic applications are examined. Three and six DOF configurations of the Phantom Premium™ 1.5 have been selected as the haptic manipulators to be investigated. By utilizing the generic computer code that has been developed for hybrid manipulators composed of revolute and prismatic joints, the equations of motion for the aforementioned two haptic manipulator types are derived in symbolic form. Using the concept of Linearity Number (LN), linearization of the equations of motion of the three and six DOF haptic interfaces have been attempted. It has been already shown that there exist completely linear three DOF serial spatial manipulators. Since Phantom Premium 1.5 contains a parallelogram mechanism, however, it is a hybrid manipulator. To the author’s knowledge, the existence of linear six DOF spatial manipulators, on the other hand, is uncertain. In this study, complete linearization of the three DOF haptic interface is achieved. To the author’s knowledge, such a result does not exist in the literature. Furthermore, non-existence of fully linear equations of motion for the selected six DOF configuration is shown. The effects of linearization on the performance of three DOF haptic interfaces are investigated by considering two performance criteria of a haptic interaction which are Stable Impedance Range and Transparency Bandwidth. Mathematical models and specific simulation environments are formed for Stable Impedance Range and Transparency Bandwidth simulations. The numerical values of these two performance criteria are calculated via simulations. The relationship between the aforementioned performance criteria and the degree of linearity of the haptic manipulator is also investigated.