In nature, vibrissae are tactile hairs of mammals used as sensor elements for the exploring the surrounding area. These hairs, also known as whiskers, can be found in different locations on an animals body. Mystacial vibrissae are distributed over a whiskerpad on a muzzle. Carpal vibrissae are located on the downside aspect of the forelimbs of mammals. The vibrissal hair has a conical shape and grows from a special heavily innervated hair follicle incorporating a capsule of blood. As the hair itself has no receptors along its length, the vibrissa may be considered as a system for transmitting forces and torques that arise from the contact between the hair and an object to sensory receptors inside the follicle. The present thesis deals with the vibrational motion of vibrissae dur- ing natural exploratory behaviour from the mechanical point of view. The phenomenon of the parametric resonance of the vibrissa is investigated the- oretically and numerically. In the first part of this thesis, two mechanical models of an elastic beam are presented based on findings in the literature. The first model considers a straight beam with the linearly decreasing radius of the circular cross-section. The second model takes into account the circu- lar natural configuration of the cylindrical beam. Within these models, the small transverse vibration of the beam under a periodic following force at the tip are analysed using the Euler-Bernoulli beam theory and asymptotic methods of mechanics. In the second part of the thesis, the numerical analysis of the problems is performed based on the finite element method using ANSYS 16.2 software. For each model, the dynamical response of the system on the parametric excitation is simulated for different frequency values. It is shown theoretically and numerically that at specific ranges of the excitation frequency the phenomenon of the parametric resonance of the beam takes place. That means that the amplitude of vibrations of the beam increases exponentially with time, when it is stimulated within one of the frequency ranges of the parametric resonance. These ranges depend on the geometrical and material parameters of the beam model, as well as the am- plitude of the periodic excitation. / Tesis

The somatosensory system of mammals includes sensory hairs (vibrissae) for tactile perception during near field exploration. Interacting with the environment, the tactile hair transfers mechanical stimuli to the hair follicle (follicle-sinus complex). The follicle-sinus complex transduces the singnals and transmits them to the central nervous system. Rats, e.g., are able to characterize objects with regard to their surface and geometric shape. Inspired by the biological paragon, the implementation of a vibrissa-like tactile sensor is an object of engineering research. According to the sensory organ, the function of a technical vibrissa is based on the recording of stimuli by the artificial hair shaft and their measurement at the support. This enables the detection of technically relevant information. In this context, the present work focuses on the task of object contour reconstruction. For that purpose, the support reactions are determined during scanning of an object. Previous investigations have been restricted on scanning objects with convex contours. This is due to the limitation of mechanical models to single-point contact scenarios. Goal of the present work is the consideration of multiple contact points between sensor shaft and object contour. The sensor shaft is modelled as a Euler-Bernoulli beam. The mathematical/theoretical description of the deformation of the beam during quasi-static scanning results in a multipoint boundary value problem with switching point. In order to simulate scanning sweeps along two different object types, the corresponding multipoint boundary value problems are solved by applying a shooting method incooperating a Runge Kutta Method of 4th order. The support reactions are calculated during scanning. It shows that multi-point contacts can be identified in the support reactions. The simulation is validated by experiments using selected examples.

Verschiedene Säugetiere, so auch Ratten, verfügen an ihren Pfoten über Tasthaare, die sog. karpalen Vibrissen. Untersuchungen der Fortbewegung von Ratten haben gezeigt, dass der Kontakt zwischen den karpalen Vibrissen und dem Untergrund Einfluss auf das Fortbewegungsverhalten der Tiere hat. Karpale Vibrissen bestehen aus einem Haarschaft und einem Follikel. Der Haarschaft ist lang, schlank, elastisch und im Follikel gelagert, in dem sich die Mechanorezeptoren befinden. Ausgehend von Vorarbeiten der Fachgebiete BiomechatronikundTechnischeMechanikderTechnischenUniversitätIlmenausowieder Section of Mechanical Engineering, Pontificial Catholic University of Peru, wurde ein mech- anisches Modell einer karpalen Vibrisse erstellt. Zielsetzung der vorliegenden Arbeit ist es, die imFollikelwirkendenKräfteundMomente währendder FortbewegungeinerRatte zu bestimmen. Aus den ermittelten Signalen sollen Rückschlüsse auf die Beschaffenheit des Kontaktes zwischen Haarschaft und Oberfläche gezogen werden. Hierzu wurde die in einer Vorarbeit ermittelte Bewegungsbahn einerRattenpfotemitdem indieserArbeit erstellten mechanischen Modell kombiniert. Die daraus entstandene invers dynamische Analyse wurde im Mehrkörpersimulationsprogramm ALASKA durchgeführt. Da nicht alle Eigenschaften und Parameter des biologischen Vorbilds bekannt sind, wurden z.B. der Reibkoeffizient, die Lagerungseigenschaften oder die Materialeigenschaften des Haarschaftes variiert. Als Ergebnis der durchgeführten Parameterstudien konnten verschiedene Einflüsse bestätigt werden. Hierbei zeigen sich u. a. Effekte wie eine Änderung der Signalstärke sowie Än- derungen in der Kontaktzeit. / Variousmammals, e.g. rats, have tactile hairs on their paws, the so-called carpal vibrissae. Studies of the locomotion ofrats have shown that the contact between the carpal vibrissae and the ground have an influence on the locomotion behaviour of the animals. Carpal vibrissae consist of a hair shaft and a follicle. The hair shaft is long, slender, elastic and is located in the follicle. The follicle includes the mechanoreceptors. A mechanical model of acarpalvibrissawasdesignedonthebasisofpreliminaryworks fromtheBiomechatronics Group and Technical Mechanics Group of the Technische Universität Ilmenau and the Section of Mechanical Engineering, Pontificial Catholic University of Peru. The objective ofthepresent work is to determine the forces and moments acting in the follicle during the locomotion of a rat. From the determined signals, conclusions could be drawn about the nature ofthe contact between hair shaft and surface. Forthis purpose, the in a preliminary work determined trajectory of a rat’s paw was combined with the in this work created mechanical model. The resulting inverse dynamic analysis was performed in the multi-body simulation program ALASKA. Since not all properties and parameters of the biological model are known, e.g.,the coefficient offriction,the support characteristics orthematerial properties of the hair shaft were varied. As a result of the parameter studies, various influences could be confirmed. Amongst other things, effects had been shown, such as a change in signal strength and changes in contact time. / Tesis

Einige Säugetiere verfügen zur taktilen Umgebungserkundung über spezielle Tasthaare, die sog. Vibrissen. Die Verwendung dieses komplexen Sinnesorgans ermöglicht es bspw. Rat-ten Abstände und Orientierungen von Objekten sowie deren Konturen und Oberflächenbe-schaffenheiten auf Basis weniger Berührungen durch ihre Vibrissen zu detektieren. Vibrissen kommen meist in Gruppen an verschiedensten Körperstellen (z.B. im Gesichtsfeld oder den Extremitäten) der Tiere vor. In der Literatur beschränken sich die meisten mechanischen Vibrissenmodelle auf die Betrachtung einer einzelnen Vibrisse, die zumeist als eingespann-ter Biegebalken modelliert wird. An dieser Stelle setzt die vorliegende Arbeit an und leistet einen Beitrag zur Untersuchung realitätsgetreuerer, elastisch gekoppelter Vibrissensysteme. Der Fokus liegt auf der Objektkonturabtastung und der theoretischen Erzeugung der Lager-reaktionen jeder einzelnen Vibrisse. Dabei werden das elastische Gewebe der Tiere, in das die Vibrissen eingebettet sind und die dadurch gegebene mechanische Beeinflussung der Vibris-sen untereinander berücksichtigt. Zunächst erfolgt die Modellierung einer einzelnen Vibrisse durch einen langen, schlanken Balken zylindrischer Form dessen Verformungen mithilfe der nicht-linearen Euler-Bernoulli Theorie beschrieben werden. Das Modell wird anschließend in verschiedenen Abstraktionsstufen zunächst um eine elastische Lagerung und anschließend um eine zweiten Vibrisse erweitert. Die Kopplung der Vibrissen wird durch verschiedene Federstrukturen realisiert. Für die Objektabtastung wird das Vibrissenmodell quasi-statisch und translatorisch an einer exemplarisch betrachteten, streng konvexen Objekt-Profilkontur vorbeigezogen. Während der Abtastung wird zwischen den Kontaktphasen des Spitzen- und Tangentialkontakts unterschieden. Darüber hinaus werden für den Fall der Objektabtastung mithilfe mehrerer Vibrissen verschiedene Szenarien abgeleitet, um zu berücksichtigen, welche und wie viele der Vibrissen sich gleichzeitig in Kontakt mit dem Objekt befinden. Basierend auf dieser Einteilung werden verschiedene Gleichungen zur Ermittlung der Fußpunktpositio-nen aller Vibrissen hergeleitet. Das mechanische Modell dient als Grundlage für die Durch-führung von Parameterstudien, in denen der Einfluss der Lager- bzw. Kopplungselastizität sowie des Objektabstandes auf die Lagerreaktionen der einzelnen Vibrissen untersucht wird. Dabei zeigt sich u. a., dass, im Gegensatz zum Objektabstand, eine Lagerelastizität in Ab-tastrichtung keinen Einfluss auf die Maximalwerte der Lagerreaktionen hat. Im Falle zweier gekoppelter Vibrissen können bestimmte Events, wie das Ablösen einer Vibrisse vom Objekt, in den Lagerreaktionen der jeweils anderen Vibrisse detektiert werden. / Some mammals exhibit special tactile hairs (vibrissae) for tactile exploration of their environment. This complex sensory organ enables, e.g., rats to detect distances and orientations of objects as well as their contours and surface textures. Vibrissae are located in groups at various parts of the animal’s body, e.g., in the snout region or at the extremities. In litera- ture, most mechanical vibrissa models are limited to the consideration of a single vibrissa, usually modelled as a clamped bending beam. The present work contributes to the inves- tigation of more realistic vibrissae systems, which are elastically coupled. The focus is on object contour scanning and a theoretical generation of the support reactions of each vibris- sa. In doing so, a mutual influence of the vibrissae is taken into account. Firstly, a single vibrissa is modeled as a long, slender, cylindrically shaped beam, whose deformations are described using nonlinear Euler-Bernoulli theory. The model is extended in different levels of abstraction. First, the model is adapted for an elastic support. Secondly, it is extended by a further vibrissa. The coupling of the vibrissae is realized by different structures of springs. For object scanning, the vibrissae model is swept along a strictly convex object profile con- tour quasi-statically and translationally. During the scanning process, a distinction is made between tip and tangential contacts. In addition, different scenarios are derived, respecting which and how many of the vibrissae are in contact with the object simultaneously. Based on this classification, the base positions of all vibrissae are determined during scanning. The mechanical model serves as a basis for parameter studies, which clarify the influence of the elasticities as well as the object distance on the support reactions of each individual vibrissa. The results shows that, in contrast to the object distance, a elastic support, which is aligned with the scanning direction has no influence on the maximum values of the support reactions. Due to the elastic coupling, the snap-off of one vibrissa from the object, can be detected in the support reactions of both coupled vibrissae. / Tesis

In nature, vibrissae are tactile hairs of mammals used as sensor elements for the exploring the surrounding area. These hairs, also known as whiskers, can be found in different locations on an animals body. Mystacial vibrissae are distributed over a whiskerpad on a muzzle. Carpal vibrissae are located on the downside aspect of the forelimbs of mammals. The vibrissal hair has a conical shape and grows from a special heavily innervated hair follicle incorporating a capsule of blood. As the hair itself has no receptors along its length, the vibrissa may be considered as a system for transmitting forces and torques that arise from the contact between the hair and an object to sensory receptors inside the follicle. The present thesis deals with the vibrational motion of vibrissae dur- ing natural exploratory behaviour from the mechanical point of view. The phenomenon of the parametric resonance of the vibrissa is investigated the- oretically and numerically. In the first part of this thesis, two mechanical models of an elastic beam are presented based on findings in the literature. The first model considers a straight beam with the linearly decreasing radius of the circular cross-section. The second model takes into account the circu- lar natural configuration of the cylindrical beam. Within these models, the small transverse vibration of the beam under a periodic following force at the tip are analysed using the Euler-Bernoulli beam theory and asymptotic methods of mechanics. In the second part of the thesis, the numerical analysis of the problems is performed based on the finite element method using ANSYS 16.2 software. For each model, the dynamical response of the system on the parametric excitation is simulated for different frequency values. It is shown theoretically and numerically that at specific ranges of the excitation frequency the phenomenon of the parametric resonance of the beam takes place. That means that the amplitude of vibrations of the beam increases exponentially with time, when it is stimulated within one of the frequency ranges of the parametric resonance. These ranges depend on the geometrical and material parameters of the beam model, as well as the am- plitude of the periodic excitation. / Tesis