The theory of homogenization allows to find for a given system of partial differential equations governing a model with a very complicated internal struc- ture a system governing a model without this structure, whose solution is in a certain sense an approximation of the solution of the original problem. In this thesis, methods of the theory of homogenization are applied to three sys- tems of partial differential equations. The first one governs a flow of a class of non-Newtonian fluid through a porous medium. The second system is utilized for modeling of a flow of a fluid through an electric field wherein the viscosity depends significantly on the intensity of the electric field. For the third system is considered an elliptic operator having growth and coercivity indicated by a general anisotropic inhomogeneous N-function. 1

This project focuses on the design and modeling of a two degree-of-freedom dissipative passive haptic display. Haptic displays are man-machine interfaces that transmit forces to the human operator. A dissipative passive haptic display is one that may only remove energy from the system using actuators such as brakes and dampers, thus ensuring the safety of the human operator. These devices may be used to implement virtual constraints such as desired paths and obstacles. Traditional friction brakes have previously been used as dissipative and coupling elements in a two degree-of-freedom parallel manipulator, resulting in undesired effects such as vibration, stiction, and slow response times. Alternatively, the new robot is actuated by rheological brakes, which feature fast response times and smooth application of torque. This approach aims to improve upon the accuracy and feel of the previous design. A commercial magnetorheological (MR) fluid brake was selected and put through an extensive series of tests. The data was used to develop a model that characterizes MR fluid behavior in low speed braking applications. A parallel five bar linkage was designed and built that has separate configurations corresponding to 3-brake and 4-brake operation. The length of each arm was chosen by means of a geometrical optimization that weighs the size and area of the workspace and actuator effects. A simulation was then developed by incorporating the brake model into the equations of motion of the robot. Next, two forms of path following velocity control were devised and tested in simulation. Finally, the accuracy, workload, and smoothness of both controllers and both configurations were examined in preliminary tests with human operators.

Thesis (Ph. D.)--Ohio State University, 2007. / Title from first page of PDF file. Includes bibliographical references (p. 166-181).

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