This work focuses on compliant joints in autonomous cells. These cells preserve the underlying geometry of a triangular mesh and enable self-reconfiguration using six-bar linkages. The six-bar linkages, essential for maintaining mesh geometry, are realized as 3D-printable compliant mechanisms. However, compliance in the hinges and deviations from the desired remote center of rotation results in positioning errors. Detailed multibody models have been developed using nonlinear beam elements to accurately represent the compliant mechanisms. In order to meet the required computational real-time performance, we propose surrogate models that can accurately predict positioning errors during self-reconfiguration. Finally, these errors are corrected by solving the inverse kinematics of a hyper-redundant manipulator using the static solution of a linearized model. Our study illustrates the benefits of utilizing a surrogate model, which reduces CPU time compared to beam elements. For the first time, we have successfully corrected positioning errors within a system of cells.

Remote center of motion (RCM) mechanisms are widely used because their center of rotation is outside the mechanical device. Usually, compliant RCM mechanisms use a linkage-based design with flexure hinges to achieve relative motion. It is still an open question to design a distributed compliant RCM mechanism using flexural beams. Addressing this, the paper proposes a generalized optimization approach for the design. The optimization approach is implemented in two steps. First, we use beams to establish a dual-layer ground structure. Using a genetic algorithm and considering the relative density of beams as variables, we obtain the optimized topology. Second, based on the topology and employing curved beams for size-shape optimization, we achieve optimized distributed compliant RCM mechanisms. Based on this approach, we explore and identify four distinct topologies and four detailed distributed compliant RCM mechanisms. With the comparison of stiffnesses and rotational axis shift, two kinds of optimized distributed compliant RCM mechanisms are considered. For verification, the commercial finite element software ABAQUS and experimental testing were utilized, demonstrating excellent alignment. Ultimately, this approach can be generalized for optimizing distributed compliant RCM mechanisms.

Modular self-reconfigurable robots hold the promise of being capable of performing a wide variety of tasks. However, many systems fall short of either delivering this promised functionality due to constraints in system architecture or validating it on functional hardware prototypes. This paper demonstrates the functional capabilities of the Planar Adaptive Robot with Triangular Structure (PARTS) and documents the versatility of this robot system using a holistic approach that combines simulations and hardware demonstrations on a prototype with nine fabricated modules. PARTS is a two-dimensional modular robot consisting of modules with a shape-shifting triangular geometry capable of forming adaptable space-covering structures. Meta-modules and mesh restructuring techniques are presented as methods for achieving topological self-reconfiguration. The feasibility of these methods is demonstrated by applying them on a simulated reconfiguration example of 62 modules. The paper showcases the versatility of PARTS on the hardware prototype using task-specific configurations, including locomotion using a meta-module and a walker configuration, module-module interaction by establishing a bridge between two separated module clusters, and interaction with the environment using a gripper and supporting structure configuration. The results validate the versatility and emphasize the potential of the system’s design concept, motivating the transfer of the hardware architecture to the third dimension.

Computational models are conventionally created with input data, script files, programming interfaces, or graphical user interfaces. This paper explores the potential of expanding model generation, with a focus on multibody system dynamics. In particular, we investigate the ability of Large Language Model (LLM), to generate models from natural language. Our experimental findings indicate that LLM, some of them having been trained on our multibody code Exudyn, surpass the mere replication of existing code examples. The results demonstrate that LLM have a basic understanding of kinematics and dynamics, and that they can transfer this knowledge into a programming interface. Although our tests reveal that complex cases regularly result in programming or modeling errors, we found that LLM can successfully generate correct multibody simulation models from natural-language descriptions for simpler cases, often on the first attempt (zero-shot). After a basic introduction into the functionality of LLM, our Python code, and the test setups, we provide a summarized evaluation for a series of examples with increasing complexity. We start with a single mass oscillator, both in SciPy as well as in Exudyn, and include varied inputs and statistical analysis to highlight the robustness of our approach. Thereafter, systems with mass points, constraints, and rigid bodies are evaluated. In particular, we show that in-context learning can levitate basic knowledge of a multibody code into a zero-shot correct output.

Programmable mechanical structures are formed by autonomous and adaptive cells and can reproduce meshes known from the finite element method. Furthermore, they can change their structure not only through morphing, but also by self-reconfiguration of the cells. A crucial component of the cells, which can preserve the underlying geometry of a triangular mesh, are six-bar linkages. The main part of the present contribution concerns the six-bar linkages as a fully 3D-printable compliant mechanism where each revolute joint of the six-bar linkage is replaced with a notch flexure hinge with the circular contour. The utilization of notch flexure hinges presents two significant drawbacks. First, notch flexure hinges do not maintain the center of rotation. Second, although compliance is an inherent and desirable characteristic of flexural hinges, it gives rise to secondary or parasitic motion. The compliance subsequently lead to alterations in the underlying geometry of a triangular mesh. For self-reconfiguration of the cells, an efficient model is needed to predict the positioning errors. Therefore, the flexure hinge is represented by three distinct models, namely a finite element model, a beam model, and a simplified linearized model based on translational and rotational spring elements. These models are compared and evaluated in succession first to identify the parameters of the simplified model and later on, the simplified model is used to show the deviations of a medium-scaled programmable structure with respect to the idealized behavior. The current work brings us closer to both the development of programmable mechanical structures and the prediction of positioning errors during self-reconfiguration.

This work focuses on the modeling of contact between sheaves and flexible axially moving beams. A two-dimensional beam finite element is employed, based on the absolute nodal coordinate formulation (ANCF) with an improved selective reduced integration for the virtual work of elastic and viscous damping forces. For the efficient modeling of contact between flexible axially moving beams and sheaves in systems such as belt-drives or reeving systems, a number of newly developed algorithms is presented. The computation of normal contact is based on a penalty formulation using a spring-damper model, while for the efficient contact detection a bounding box which fits the exact dimensions of the finite elements is employed. For the detection and computation of contact, the beam elements are divided into linear segments. The modeling of tangential contact is based on a bristle model for friction extended for being compatible with an implicit time integration. A numerical example of a belt drive showed good convergence and agreement with analytical solutions.

This paper presents the approach of the RoboCup@Work team tyrolics of the university of Innsbruck to design, develop and build a mobile manipulator with 10 degrees of freedom. The mobile manipulator LeoBot uses Mecanum wheels to enable omnidirectional movement and includes a Franka Emika Panda serial manipulator. This paper focuses on hardware development and provides information on mechanical, electronic, and mechatronic system components. Basic algorithms developed and used for the competition are briefly described.

This work addresses pipes conveying fluid and axially moving beams undergoing large deformations. A novel two-dimensional beam finite element is presented, based on the absolute nodal coordinate formulation (ANCF) with an extra Eulerian coordinate to describe axial motion. The resulting formulation is well known as the arbitrary Lagrangian Eulerian (ALE) method, which is often used to model axially moving beams and pipes conveying fluid. The proposed approach, which is derived from an extended version of Lagrange's equations of motion, allows for the investigation of the stability of pipes conveying fluid and axially moving beams for a certain axial velocity and stationary state of large deformation. Additionally, a multibody modeling approach allows us to extend the beam formulation for comoving discrete masses, which represent concentrated masses attached to the beam, e.g., gondolas in ropeway systems, or transported masses in conveyor belts. Within numerical investigations, we show that axially moving beams and a larger number of discrete masses behave similarly as in the case of beams with evenly distributed mass.

The present paper addresses axially moving beams with co-moving concentrated masses while undergoing large deformations. For the numerical modeling, a novel beam finite element is introduced, which is based on the absolute nodal coordinate formulation extended with an additional Eulerian coordinate to represent the axial motion. The resulting formulation is well known as Arbitrary Lagrangian Eulerian (ALE) method, which is often used for axially moving beams and pipes conveying fluids. As compared to previous formulations, the present formulation allows us to introduce the Eulerian part by an independent coordinate, which fully incorporates the dynamics of the axial motion, while the shape functions remain independent of the beam coordinates and are thus constant. The proposed approach, which is derived from an extended version of Lagrange’s equations of motion, allows for the investigation of the stability of axially moving beams for a certain axial velocity and stationary state of large deformation. A multibody modeling approach allows us to extend the beam formulation for co-moving discrete masses, which represent concentrated masses attached to the beam, e.g., gondolas in ropeway systems, or transported masses in conveyor belts. Within numerical investigations we show that a larger number of discrete masses behaves similarly as the case of (continuously) distributed mass along the beam.

Programmable structures are formed by autonomous and adaptive triangular cells. However, they are composed of a large number of parts, specifically bearings, which make them laborious to manufacture and expensive. An essential part of these programmable structures are six-bar linkages, which allow to build cells that can preserve the underlying geometry of a triangular mesh. A major improvement, which is the main part of this paper, is to replace the joints of the six-bar-linkage by a compliant mechanism, which allows to manufacture them as one 3D printable part. A multibody system formulation is setup with the model of the compliant mechanisms, treating every joint either ideal or compliant with the given stiffness parameters. The multi-body formulation furthermore allows to include friction as well as an actuator model in a straight-forward manner. The overall stiffness parameter of the real system is then identified from a comparison with an experimental setup of a real compliant triangular cell. Finally, the model is used to show the deviations of a medium-scaled programmable structure with respect to the idealized behavior. The present paper marks a relevant step towards the realization of larger programmable structures as well as the development of 3D programmable structures.

Für die auditive und visuelle Wahrnehmung bieten sogenannte „Virtual Reality“-Systeme eine hochauflösende Nachbildung der Wirklichkeit bei gleichzeitig niedrigen Kosten. Um digitalisierte Objekte noch näher an die Realität zu bringen, werden in dieser Arbeit programmierbare Strukturen vorgestellt, welche neben der visuellen auch die taktile Wahrnehmung ermöglichen sollen. Die Basis der programmierbaren Strukturen bildet ein zellularer Roboter, dessen Zellen sich sowohl verformen als auch aktiv verbinden können. Die dreieckigen Zellen besitzen an jeder Seitenkante einen Aktuator, wodurch es möglich ist, aus mehreren Zellen unstrukturierte Dreiecksnetze aufzubauen. Aufgrund der speziellen Gestalt der Gelenke können die von der Finite-Elemente-Methode bekannten Netze – abgesehen von der Limitierung der Aktuatoren – ohne Einschränkungen nachgebildet werden. Im Vergleich zum Stand der Technik, aus dem bereits durch Knoten und Aktoren aufgebaute Strukturen bekannt sind, ist es hier erstmals gelungen, autonome formbare Zellen zu entwerfen, welche sich aktiv an den Seitenkanten verbinden können. In der vorliegenden Arbeit werden der mechatronische Aufbau und die Kinematik des Systems beschrieben. Aufgrund der vielen Drehgelenke und der 3D-gedruckten Bauteile aus Kunststoff sind eine merkliche Nachgiebigkeit und etwas Spiel vorhanden. Aus diesem Grund wurde ein Modell entwickelt, welches die Abweichungen der Bewegungen des zellularen Roboters von der Soll-Bewegung nachbildet und somit die Ansteuerung der einzelnen Zellen während des Bewegungsvorgangs erleichtert. Vergleiche zwischen dem Modell und Messungen am realen System mithilfe eines Motion-Tracking-Systems werden dargestellt. Der vorgestellte Ansatz liegt in weiten Teilen bereits auch in der räumlichen Form als Tetraeder vor, jedoch können mit diesem noch keine geschlossenen 3D-Strukturen realisiert werden.

A new approach for cellular robots is presented. The single elements of the robot are triangular cells, which can change their shape by means of linear actuators at each edge. The novelty concerns the connection of autonomous cells at their edges rather than at the vertices. In this way, unstructured triangular meshes can be formed. The robot can self-reconfigure and thus can reproduce almost arbitrary planar shapes. In a similar way, the system has been realized with tetrahedrons in a simplified way within a previous work. The self-reconfigurable system shall serve as a basis for programmable matter. The present paper includes the mechatronic design, its components and the kinematic model of the cellular robot. In order to reduce positioning errors, a model is developed, which considers compliance and clearance in the links and joints. Based on a simplified mechanical model using elastic trusses, the positioning errors can be predicted. The parameters of these models are identified from simple motion sequences. Furthermore, the nonlinearity of actuators is identified and corrected. In this way, the desired triangular shapes can be prescribed without measuring the position of the cells.

An adaptive tetrahedral element (ATE) has been designed, which can attach to and detach from other ATEs along their deformable faces. The goal is to obtain any configuration or shape autonomously. The tetrahedrons edges represents six actuators and each ATE has its own microcontroller, battery and wireless transceiver module. Several connected ATEs are forming an adaptive robot with tetrahedral structure (ARTS) which is intended to represent any geometric form with a piecewise flat surface. Contrary to existing cellular and tetrahedral robots ARTS combines the advantages of selfreconfigurable modular robots and tetrahedral robots which have the ability to change their shape.

In diesem Beitrag wird zuerst eine elektromechanisch gekoppelte Theorie für dünne Schalen mit piezoelektrischen Wandlern im Rahmen einer geometrisch nichtlinearen Formulierung vorgestellt. Hierbei wird eine Schale als materielle Fläche mit mechanischen und elektrischen Freiheitsgraden modelliert. Eine Finite Elemente Implementierung beschließt den ersten Teil der Arbeit. Im zweiten Teil des Beitrags wird die vorgestellte Theorie mit Hilfe von Vergleichsrechnungen mit dem kommerziell erhältlichen Finite Elemente Programm Abaqus sowie mit Ergebnissen aus der Literatur verifiziert, um dann im dritten Teil der Arbeit zur Schwingungsreduktion zur Anwendung gebracht zu werden. Der vorliegende Beitrag endet mit einer experimentellen Untersuchung der passiven Schwingungsreduktion einer dünnen Schale mit piezoelektrischen Wandlern unter Verwendung der Methode des passiven Shunt Dampings.

For the modelling of thin elastic shells with attached piezoelectric transducers, we consider a material surface with certain mechanical degrees of freedom in each point. Additionally, electrical unknowns are present within the domain, where the piezoelectric transducers are attached, such that the sensing and actuating behavior can be properly accounted for. The modelling is done in the geometrically nonlinear regime, but the electromechanically coupled constitutive relations are treated within the framework of Voigt’s linear theory of piezoelectricity. Owing to the assumed thinness of the shell the influence of shear is neglected in the modeling. A Finite Element scheme for the solution of the resulting model is implemented and the solutions computed with the present theory are compared to results computed with the commercially available FE code Abaqus. Different examples are presented ranging from large deformations, to snap through instability and to a linear analysis. A very good agreement between the results is obtained, from which the accuracy of the thin shell formulation as a material surface is concluded. Next, an existing physical shell is modeled within the linearized version of the present theory and the computational results are compared to measurement results from the physical experiment. The agreement is reasonably good; natural frequencies as well as eigenmodes are considered for the comparison. Concerning the eigenmodes the MAC criterion is used. Finally, the resulting linear time invariant dynamical system for the simulation of the physical shell is imported into Mathematica and different strategies for passive and active control are tested and compared to each other. Concerning passive control methods classical single mode shunt-damping using an optimized RL-network is studied.

In der vorliegenden Arbeit wird ein vollstandig neuer Ansatz fur zellulare Roboter vorgestellt. Die einzelnen Elemente des Roboters sind dreieckige, veranderliche Zellen, welche jeweils drei aktuierbare Seitenkanten besitzen. Die wesentliche Neuerung ist die Verbindung der veranderlichen Zellen an den Seitenkanten, wodurch aufgrund der speziellen Kinematik der Zellen allgemeine unstrukturierte Dreiecksnetze nachgebildet werden konnen. Der zellulare Roboter ist dadurch in der Lage, nahezu beliebige Gestalten anzunehmen und er kann sich selbst rekonfigurieren. Der Roboter, welcher auch als programmierbare Struktur verstanden werden kann, wurde in einer fruheren Arbeit mit vereinfachter tetraedrischer Kinematik auch als raumliches System entwickelt und soll eine Grundlage fur ein programmierbares Material dienen. In der vorliegenden Arbeit werden die Komponenten des mechatronischen Prototyps sowie dessen Kinematik vorgestellt. Modelle fur die Aktoren und die Dreieckselemente werden verwendet um Positionierungsfehler zu reduzieren. Aus den gemessenen Positionen und den Sollpositionen werden die Positionierungsfehler des zugrundeliegenden (idealisierten) Dreiecksnetzes berechnet. Der Einsatz vereinfachter Modelle der realen Kinematik des adaptiven Roboters liefert die Moglichkeit zur Korrektur der Linearaktoren um die Positionierungsfehler zu minimieren. Die Parameter dieser Modelle werden aus einfachen Bewegungsablaufen identifiziert.