This thesis presents the design and development of a novel two-axis micromirror utilizing electrostatic, repulsive-force rotational actuators for laser scanned vector display systems. The micromirror consists of a 1.0 mm reflective mirror plate that can be rotated at high speeds to steer a laser beam to generate images. Fabricated using PolyMUMPs, the micromirror is operated in a non-resonant mode between 0 V and 200 V and can achieve a maximum optical scanning angle of ±2.6° in each axis with a settling time as fast as 2.75 ms and a first resonant frequency of 1400 Hz. Open-loop control methods were developed for image correcting and improving image quality. The micromirror was integrated into a portable, handheld vector display device which included designing and developing driving circuits, device firmware, mechanical components and optical components.

This thesis describes the development of a MEMS repulsive actuator capable of producing a large out-of-plane force. Existing MEMS repulsive actuators are low out-of-plane force actuators that are unable to support or lift a mass of 1 mg. A high force MEMS repulsive actuator was developed to overcome this limitation. The design was optimized employing parameters of the actuator’s fingers to increase the out-of-plane force. A design was developed based on the analytical results derived from extending the mathematical model of an existing actuator. A commercial manufacturing process, PolyMUMPs, was used to fabricate a prototype which was tested to validate the analytical and computational results. The prototype achieved an out-of-plane displacement of 15 µm and a 0.2° angular rotation. The resonance frequency was 120 Hz, and the rise and fall times were measured as 14.5 ms and 3625 ms (3.6 sec), respectively. The estimated out-of-plane force is 40 µN.

This thesis presents the design and development of a novel two-axis micromirror utilizing electrostatic, repulsive-force rotational actuators for laser scanned vector display systems. The micromirror consists of a 1.0 mm reflective mirror plate that can be rotated at high speeds to steer a laser beam to generate images. Fabricated using PolyMUMPs, the micromirror is operated in a non-resonant mode between 0 V and 200 V and can achieve a maximum optical scanning angle of ±2.6° in each axis with a settling time as fast as 2.75 ms and a first resonant frequency of 1400 Hz. Open-loop control methods were developed for image correcting and improving image quality. The micromirror was integrated into a portable, handheld vector display device which included designing and developing driving circuits, device firmware, mechanical components and optical components.

This thesis describes the development of a MEMS repulsive actuator capable of producing a large out-of-plane force. Existing MEMS repulsive actuators are low out-of-plane force actuators that are unable to support or lift a mass of 1 mg. A high force MEMS repulsive actuator was developed to overcome this limitation. The design was optimized employing parameters of the actuator’s fingers to increase the out-of-plane force. A design was developed based on the analytical results derived from extending the mathematical model of an existing actuator. A commercial manufacturing process, PolyMUMPs, was used to fabricate a prototype which was tested to validate the analytical and computational results. The prototype achieved an out-of-plane displacement of 15 µm and a 0.2° angular rotation. The resonance frequency was 120 Hz, and the rise and fall times were measured as 14.5 ms and 3625 ms (3.6 sec), respectively. The estimated out-of-plane force is 40 µN.

Force fields of 3d objects are used for different purposes in computer graphics as skeletonization and collision detection. In this paper we present a novel method to approximate the force field of a discrete 3d object in linear time. Similar to the distance transformation we define a rule that describe how the forces associated with boundary points are propagated into the interior of the object. The result of this propagation depends on the order in which the points of the object are processed. Therefore we analyze how to obtain an order-invariant approximation formula. For a chosen iteration order (i, j, k) the set of boundary points that influence the force of a particular point p of the object can be described by a spatial region Rijk. The geometries of these regions are characterized both for the Cartesian and the body-centered cubic grid (bcc grid). We show that in the case of the bcc grid these regions can be combined in such a way that E3 is uniformly covered which basically means that each boundary point is contained in the same number of regions. Based on the covering an approximation formula for the force field is proposed that has linear complexity and gives good results for standard objects. We also show that such a uniform covering can not be built from the regions of influence of the Cartesian grid. With our method it becomes possible to use features of the force field for a fast and topology preserving skeletonization. We use a thinning strategy on the bcc grid to compute the skeleton and ensure that critical points of the force field are not removed. This leads to improved skeletons with respect to the properties of centeredness and rotational invariance.

The master thesis is focused on the calculation of electrodynamic forces acting on the contacts of the moulded case circuit breaker Siemens 3VA5 from OEZ Letohrad. This work is divided into ten chapters. In the introductory chapter it is described why it is important to deal with the calculation of the electrodynamic forces and the design of the current path. The second chapter describes the problem of the origin and effect of electrodynamic forces on individual parts of the electrical device. The third chapter describes the parameters, properties and design of the 3VA5 Siemens circuit breaker. The fourth chapter describes the Finite Element Methods. The fifth chapter describes how to create a 3D current path model in Solidworks. The sixth to ninth chapter is focused on the stationary calculation of moments in the program Ansys Maxwell by means of Magnetostatic Analysis and on the calculation of the total repulsive force between contacts with the influence of ferromagnetic materials. The last chapter is focused on dynamic calculation of moments and forces acting on contacts in a certain time interval.

The thesis is focused on the calculation of electrodynamic forces that counterwork on moving contacts of compact circuit breaker BL1600 from the company OEZ Letohrad. The thesis is divided into separates chapters that build on themselves. In the introduction the reason why we deal with calculation of dynamic forces and structural arrangement of current carrying path is described. In the following chapter there is a theoretical analysis of electrodynamic forces that conterwork on individual parts of circuit breaker´s element. The third part is devoted to structural arrangement of the circuit breaker BL1600. In this part we can find an example of using the circuit broker Modeion in practice. Two next chaptures deal with adjustment of the model of current carrying path which then serves for the calculation of electrodynamic forces. The rest of the thesis is devoted to my own calculations. These calculations are mainly stationary where we try to find the forces that conterwork on the contacts in a steady current and in a point in time. There are also dynamics calculation when we can watch the forces that counterwork on contacts in a certain time interval. The last chapter is devoted to a stationary calculation of forces that counterwork on the electrical arc which arises while turning the short-circuit current off. The obtained results are evaluated in partial conclusions of this thesis.

Force fields of 3d objects are used for different purposes in computer graphics as skeletonization and collision detection. In this paper we present a novel method to approximate the force field of a discrete 3d object in linear time. Similar to the distance transformation we define a rule that describe how the forces associated with boundary points are propagated into the interior of the object. The result of this propagation depends on the order in which the points of the object are processed. Therefore we analyze how to obtain an order-invariant approximation formula. For a chosen iteration order (i, j, k) the set of boundary points that influence the force of a particular point p of the object can be described by a spatial region Rijk. The geometries of these regions are characterized both for the Cartesian and the body-centered cubic grid (bcc grid). We show that in the case of the bcc grid these regions can be combined in such a way that E3 is uniformly covered which basically means that each boundary point is contained in the same number of regions. Based on the covering an approximation formula for the force field is proposed that has linear complexity and gives good results for standard objects. We also show that such a uniform covering can not be built from the regions of influence of the Cartesian grid. With our method it becomes possible to use features of the force field for a fast and topology preserving skeletonization. We use a thinning strategy on the bcc grid to compute the skeleton and ensure that critical points of the force field are not removed. This leads to improved skeletons with respect to the properties of centeredness and rotational invariance.