Teaching the reduction technique with interactive visualizations: report on a simple automatic tutor

The reduction technique is an important problem solving method often used in computer science and mathematics to solve a new problem by the known solution of another problem. In this paper we investigate the potential of interactive visualization for teaching the reduction method and focus on the following two questions: What part can visualizations play in the presentation and understanding of the reduction technique? and: How can we build systems for teaching the reduction technique that can be used by students in a teleteaching environment? We try to answer the latter question by reporting on a field test of an automatic tutor which we have build for our students

Incremental theory reasoning methods for semantic tableaux

Theory reasoning is an important technique for increasing the efficiency of automated deduction systems. In this paper we present incremental theory reasoning, a method that improves the interaction between the foreground reasoner and the background (theory) reasoner and, thus, the efficiency of the combined system. The use of incremental theory reasoning in free variable semantic tableaux and the cost reduction that can be achieved are discussed; as an example, completion-based equality reasoning is presented, including experimental data obtained using an implementation

Position Determination of a Robot End-Effector Using a 6D-Measurement System Based on the Two-View Vision

A mechatronic system based on the micro-macro-kinematic consists of an industrial robot and a piezoelectric stage mounted on the robot’s end-effector and has to carry out operations like micro-assembly or micro-milling. The piezoelectric stage has to compensate the positioning error of the robot. Therefore, the position of the robot’s end-effector has to be measured with high accuracy. This paper presents a high accuracy 6D-measurement system, which is used to determine the position and orientation of the robot’s end-effector. We start with the description of the operational concept and components of the measurement system. Then we look at image processing methods, camera calibration and reconstruction methods and choose the most accurate ones. We apply the well-known pin-hole camera model to calibrate single cameras. Then we apply the epipolar geometry to describe the relationship between two cameras and calibrate them as a stereo vision system. A distortion model is also applied to enhance the accuracy of the system. The measurement results are presented in the end of the paper

Digital image processing algorithms for automated inspection of dynamic effects in roller bearings

Unstable movement in roller bearings like cage or roller slip can lead to damages or eventually even to an early break of the bearing. To prevent slip, inadequate operating states should be avoided. Therefore, it is necessary to study the dynamic behavior of the bearing. Unfortunately, there is only a limited range of measurement methods for the dynamic of bearing components. Two possible approaches are using solely a high-speed camera or the combination of an optomechanical image derotator and a high-speed camera. This work focuses on a proposal which is suitable for both. Initially, the influence of the rotational velocity in the images is eliminated. In the next step the measurement data is reduced to a region of interest which displays a particular rolling-element. A rolling element is equipped with a linear marker which, in the next stage, is segmented by a thresholding method to multiple regions. The region representing the marker is extracted from the background and the position is calculated by a Principle Component Analysis. Depending on the shift of the angular position and the lag time between two images, the rotational velocity of the rolling element is calculated. Thus, it is possible to determine whether the rolling element is operating under ideal conditions. In conclusion, it can be said that this approach enables a simple and flexible non-invasive method to depict the occurrence of roller slip in roller bearings. © 2017 SPIE

Wavefront predictions for the automated assembly of optical systems

Industrial assembly of optical systems is still a tedious and cost-intensive task that is mostly dominated by manual labor. Positional fine-adjustment of optical components is pivotal to ensure a desired performance of the optical device at hand. In this paper, we use wavefront predictions to aim for fully automated assembly procedures. Wavefront measurements along with position identification methods can be utilized to continuously update a simulation model which in turn allows for predictions on future wavefront errors. This enables to take according correction measures during the assembly process if a certain wavefront tolerance specification is not met. In order to demonstrate the efficacy of the proposed approach and methods, a beam expander is sequentially assembled. The setup consists of a laser, two bi-convex lenses, and a Shack-Hartmann wavefront sensor and has to satisfy a certain wavefront tolerance specification after its assembly. © 2018 SPIE

Predictive tolerance bands for the correction-less assembly of optical systems

When assembling optical systems, uncertainties of the positioning system and overall mounting tolerances lead to the deterioration of performance due to resulting misaligned optical components. In this paper, we present a novel methodology for the correction-less assembly of optical systems based on predictive tolerance bands. By running a simulation model in parallel to the assembly process, performance predictions can be made during the assembly that take into account the uncertainties of the positioning system. Typically, optical performance can be assessed by a variety of criteria. In this paper, we utilize the Marechal criterion based on the root mean square (RMS) error as it allows to verify if the optical system is defraction-limited. The extension with Monte Carlo methods enables the prediction of mean values and standard deviations for the chosen metric. This is done for the entire optical system yet to be assembled by integrating uncertainties of the positioning system within the simulation framework. Before assembly, a desired threshold (here the RMS value derived from the Marechal criterion) can be specified which is predicted and monitored throughout the assembly process. For verification, we analyze a two-lens system in simulation to demonstrate our proposed framework

Vergleich und Analyse von Ordnungseinschränkungen für freie Variablen Tableau

In dieser Arbeit untersuchen wir einige Erweiterungen geordneter Tableaus: die Ordnung auf Atomen wird durch das allgemeinere Konzept einer Auswahlfunktion ersetzt; die Substitutivitt, welche fžr das liften notwendig ist, kann fžr bestimmte Varianten des Kalkžls durch eine schwchere Eigenschaft ersetzt werden; und eine ersten Version geordneter Tableaus mit Theorien wird eingefžhrt. Wir zeigen die Korrektheit und Vollstndigkeit der resultierenden Kalkžle. Desweiteren berichten wir žber unsere Experimente, welche wir mit einer prototypischen Implementierung durchgefžhrt haben, und zeigen fžr welche Problemklassen sich geordnete Tableaus sinnvoll einsetzen lassen