What the hell do they mean by 'locomotion'?

In current mechanics literature one very frequently encounters the concepts locomotion and locomotion system. Unfortunately, strong definitions of these seemingly intuitively clear notions are generally missing. The following paper tries to fill this gap

On a class of biomorphic motion systems

In this paper we consider the dynamics of certain worm-like motion systems with finite degree of freedom. The masspoints of the systems are equipped with runners (steerable in the plane) that, caused by scales, admit motion only in a distinc

A continuum model of passive vibrissae

A passive vibrissa is modeled as an elastic bending rod that interacts with a rigid obstacle in the plane. Aim is to see details of what happens in quasistatically scanning the obstacle. To this end the differential equations emerging from Bernoulli's rod theory are solved by elliptiv integrals followed by numerical evaluations

About mathematical models in mechanics

This paper must not be seen as a report on actual investigations nor as a stroll along stringent analytical mechanics. It is just a revision of a lecture recently given by the author during a seminary of students, pre- and postdocs in the mechanics departments at Technical University Ilmenau. Focussing on current research fields it is to enlighten the general connections of any real object and the hierarchy of models which form the base for theoretical investigations. Therefore the paper should primarily be understood as a pragmatic support of actual scientific meditations and activities by theoretically engaged young people at TU Ilmenau. The readers are supposed to have knowledge in elementary analysis and applied mechanics

Quasistatic inflation processes within rigid tubes

In this paper the authors consider mechanical devices that can be seen as segments of an artificial worm or as a balloon for angioplasty. Continuing former work \cite{St 2003} the segment is now placed within a cylindrical or constricted rigid tube that will be touched or pressed during inflation of the segment. Both the segment's shape and the forces of contact are investigated. The main mathematical tool is the Principle of Minimal Potential Energy - handled as an optimal control problem with state constraint. The necessary optimality conditions are carefully analyzed and simulation results for characteristic examples are presented.\\ The treatment of the problem is primarily mathematical but aiming at application

Ein Optimalsteuerproblem mit einem speziellen Zielfunktional und Zustandsbeschränkungen in einem Teilintervall bei beliebigem Relativgrad

Ausgangspunkt für die Untersuchungen sind zwei klassische Optimalsteuerprobleme mit verschiedenen Integrationsintervallen. Die Zustände sind einer Ungleichungsrestriktion mit beliebigem Relativgrad auf einem gemeinsamen Teilintervall unterworfen. Für dieses Problem werden notwendige Optimalitätsbedingungen hergeleitet. Die Anregung für diese Aufgabenstellung kommt aus der Mechanik: Die äußere Form von zwei elastischen Röhren unterschiedlicher Länge wird durch das Variationsprinzip der minimalen potentiellen Energie bestimmt. Steckt eine Röhre in der anderen, ergibt sich eine Ungleichungsbeschränkung für die Formen in einem Teilintervall

Quasistatic inflation processes within compliant tubes

Continuing former work [8], [9] the authors consider a mechanical system that models a segment of a live or artificial worm or a baloon for angioplasty that is placed within a cylindrical compliant tube (vein). The statics of the inflation process is based on the Principle of Minimal Potential Energy. This is handled as an optimal control problem with state constraint. Certain peculiarities make the necessary optimality conditions go beyond those from classical textbooks. A careful analysis of the conditions leads to a boundary value problem describing the shape of the inflated system and to the determination of the contact forces between balloon and vein. Simulation results are to be presented in a forthcoming Part 2

Optimalsteuerprobleme unter Zustandsrestriktionen

In this paper, the authors consider a class of finite dimensional optimal control problems with state restrictions. These investigations are aimed at utilizable necessary optimality conditions. The purpose of the paper is twofold: first, to prepare a starting point for further investigations on a topic from mechanics begun in [11] and, second, finally to have a written material that can be used in teaching this somewhat unwieldy subject. The optimality conditions are derived by transforming the control problem into a Bolza-type variational problem and then using techniques coming from classical literature in Calculus of Variations. The results are applied to some modified and generalized problems of Dido type. The concluding chapter addresses variational problems and integral principles from Analytical Mechanics under state constraints

A vibrissa-inspired highly flexible tactile sensor: scanning 3D object surfaces providing tactile images

Just as the sense of touch complements vision in various species, several robots could benefit from advanced tactile sensors, in particular when operating under poor visibility. A prominent tactile sense organ, frequently serving as a natural paragon for developing tactile sensors, is the vibrissae of, e.g., rats. Within this study, we present a vibrissa-inspired sensor concept for 3D object scanning and reconstruction to be exemplarily used in mobile robots. The setup consists of a highly flexible rod attached to a 3D force-torque transducer (measuring device). The scanning process is realized by translationally shifting the base of the rod relative to the object. Consequently, the rod sweeps over the object’s surface, undergoing large bending deflections. Then, the support reactions at the base of the rod are evaluated for contact localization. Presenting a method of theoretically generating these support reactions, we provide an important basis for future parameter studies. During scanning, lateral slip of the rod is not actively prevented, in contrast to literature. In this way, we demonstrate the suitability of the sensor for passively dragging it on a mobile robot. Experimental scanning sweeps using an artificial vibrissa (steel wire) of length 50 mm and a glass sphere as a test object with a diameter of 60 mm verify the theoretical results and serve as a proof of concept