Labor Finite-Elemente-Methode (FEM)
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AbstractTensegrity structures are prestressed structures consisting of compressed members connected by prestressed tensioned members. Due to their properties, such as flexibility and lightness, mobile robots based on these structures are an attractive subject of research and are suitable for space applications. In this work, a mobile robot based on a tensegrity structure with two curved members connected by eight tensioned strings is analyzed in terms of deformation in the curved members. Further, the difference in locomotion trajectory between the undeformed and deformed structure after the prestress is analyzed. For that, the theory of large deflections of rod-like structures is used. To determine the relationship between acting forces and the deformation, the structure is optimized using minimization algorithms in Python. The results are validated by parameter studies in FEM. The analysis shows that the distance between the two curved members significantly influences the structure’s locomotion. It can be said that the deformation of the components significantly influences the locomotion of tensegrity structures and should be considered when analyzing highly compliant structures.
The use of intrinsically compliant tensegrity structures in manipulation systems is an attractive research topic. In this paper a 3D compliant robotic arm based on a stacked tensegrity structure consisting of x-shaped rigid members is considered. The rigid members are interconnected by a net of prestressed, tensioned members with pronounced intrinsic elasticity and by inelastic tensioned members. The system's motion is achieved by length-change of the inelastic tensioned members. The operating principle of the system is discussed with the help of kinematic considerations and verified by experiments.
In the early-stage development of sheet metal parts, key design properties of new structures must be specified. As these decisions are made under significant uncertainty regarding drawing configuration changes, they sometimes result in the development of new parts that, at a later design stage, will not be drawable. As a result, there is a need to increase the certainty of experience-driven drawing configuration decisions.
Complementing this process with a global sensitivity analysis can provide insight into the impact of various changes in drawing configurations on drawability, unveiling cost-effective strategies to ensure the drawability of new parts. However, when quantitative global sensitivity approaches, such as Sobol's method, are utilized, the computational requirements for obtaining Sobol indices can become prohibitive even for small application problems. To circumvent computational limitations, we evaluate the applicability of different surrogate models engaged in computing global design variable sensitivities for the drawability assessment of a deep-drawn component.
Here, we show in an exemplary application problem, that both a standard kriging model and an ensemble model can provide commendable results at a fraction of the computational cost. Moreover, we compare our surrogate models to existing approaches in the field. Furthermore, we show that the error introduced by the surrogate models is of the same order of magnitude as that from the choice of drawability measure. In consequence, our surrogate models can improve the cost-effective development of a component in the early design phase.
Preliminary considerations on the form-finding of a tensegrity joint to be used in dynamic orthoses
(2024)
Early motion therapy plays an important role for effective long-term healing of joint injuries. In many cases, conventional dynamic orthoses fail to address the intricate movement possibilities of the underlying joints, limited by their simplistic joint representations, often represented by revolute joints, enabling rotations by only one axis. In this paper, a two-dimensional compliant tensegrity joint for use in biomedical applications is investigated. It consists of two compressed members and five compliant tensioned members. Relative movement possibilities are realized by the intrinsic compliance of the structure. In the development of these systems, the first step is the determination of the static stable equilibrium. This analysis is conducted in this paper by considering the potential energy approach or by using the geometric nonlinear finite element method. The mechanical behavior of the structure is assessed with a specific emphasis on its mechanical compliance. The primary objective of this study is the investigation of the influence of structural parameters on the overall stiffness and movability of the structure. The results underscore the significant effect of member parameters on the stiffness and movability of the compliant tensegrity joint, particularly under varying load magnitudes. These findings provide insights for optimizing the joint’s performance, contributing to its potential application in advanced orthotic and exoskeleton devices.
This paper presents a comprehensive analysis of a three-dimensional compliant tensegrity joint structure, examining its actuation, kinematics, and response to external loads. The study investigates a baseline configuration and two asymmetric variants of the joint. The relationship between the shape parameter and the parameters of the tensioned segments is derived, enabling the mathematical description of cable lengths for joint actuation. Geometric nonlinear static finite element simulations are performed to analyze the joint's response under various load conditions. The results reveal the joint's range of motion, the effect of different stiffness configurations, and its deformation behavior under external forces. The study highlights the asymmetric nature of the joint and its potential for targeted motion restriction. These findings advance the general understanding of the behavior of the considered tensegrity joint and provide valuable insights for their design and application in soft robotic systems.
Um die Leistungsfähigkeit von nachgiebigen Robotersystemen („Soft Robotics“) zu verbessern, werden immer neue Möglichkeiten zur Realisierung dieser Systeme gesucht. In vielen Anwendungen ist der Einsatz von mechanisch vorgespannten nachgiebigen Strukturen in diesen Systemen von Vorteil. Die Steifigkeit dieser Strukturen kann gezielt und gegebenenfalls reversibel variabel eingestellt werden. Die Formveränderung kann nur durch wenige Aktuatoren erzeugt werden.
Nachgiebige Tensegrity-Strukturen, die auf hochelastischen Materialien basieren, entsprechen einer speziellen Klasse von mechanisch vorgespannten Strukturen. Sie werden durch druck- und zugbelastete Segmente gebildet, wobei die druckbelasteten Segmente untereinander nicht direkt verbunden sind. Die resultierende Form dieser Strukturen wird durch ihre Vorspannung bestimmt. Weiche Roboter, die auf diesen Strukturen basieren, bieten mehrere vorteilhafte Eigenschaften, wie z. B. Faltbarkeit/Entfaltbarkeit, geringe Masse, hohes Festigkeits-Gewichts-Verhältnis und stoßdämpfende Fähigkeiten [1]. Diese Strukturen haben eine ausgeprägte Fähigkeit, sowohl ihre Form als auch ihre Steifigkeit zu verändern. In den letzten Jahren hat das Interesse an der Erforschung von Robotersystemen, die auf diesen Strukturen basieren, zugenommen. Aktuelle Arbeiten konzentrieren sich auf die Entwicklung von mobilen Robotern [2]–[7] und Manipulatoren, die auf diesen Strukturen basieren [8]–[10]. Tensegrity-Manipulatoren werden typischerweise durch Kaskadierung von gleichartigen elementaren Einheiten gebildet, die nach dem Tensegrity-Prinzip untereinander verbunden werden. Die elementaren Einheiten sind entweder selber konventionelle Tensegrity-Strukturen oder einteilige planare bzw. räumliche Strukturen. In klassischen Tensegrity-Manipulatoren werden starre Drucksegmente und nicht elastische Zugsegmente verwendet. Die Formänderung dieser Systeme wird durch Änderung der Längen ausgewählter Zugsegmente realisiert. Dem gegenübergestellt können nachgiebige Tensegrity-Manipulatoren realisiert werden, indem die Zugsegmente der Struktur eine hohe Nachgiebigkeit aufweisen. Um die mechanische Nachgiebigkeit und Formänderungsfähigkeit von diesen nachgiebigen Manipulatoren zusätzlich
zu erhöhen, ist auch der Einsatz von Tensegrity-Strukturen auf der Basis nachgiebiger Drucksegmente denkbar.
Im vorliegenden Beitrag werden zwei nachgiebige Tensegrity-Manipulatoren vorgestellt und in Hinblick auf ihre mechanischen Eigenschaften und Formänderungsfähigkeit gegenübergestellt. Sie unterscheiden sich in ihrer Topologie, in der Art der Aktuierung und auch in der mechanischen Nachgiebigkeit. Die mechanische Nachgiebigkeit des ersten Systems beruht auf der Elastizität der Zugsegmente, die Drucksegmente sind starr. Die elementaren Einheiten bilden einteilige Strukturen. Das zweite System beruht auf elementaren Einheiten, die selbst räumliche Tensegrity-Strukturen sind. In diesem System sind sowohl die Zug- als auch die Drucksegmente nachgiebig. Die Aktuierung des ersten Systems erfolgt durch Längenänderung der Zugsegmente. Im zweiten System wird die Formänderung des Gesamtsystems durch Änderung der Form der nachgiebigen Drucksegmente realisiert. Die theoretischen Untersuchungen erfolgen unter Anwendung
der statischen geometrisch nichtlinearen FE-Methode. Mit diesen Untersuchungen wird die Formveränderungsfähigkeit der beiden Systeme unter Variation ihrer Vorspannung untersucht und gegenübergestellt. Die experimentellen Untersuchungen an zwei Demonstratoren bestätigen die theoretischen Ergebnisse und zeigen die Anwendbarkeit von Systemen auf Basis dieser Strukturen als Manipulatoren auf.
Theoretical considerations on a 2D compliant tensegrity joint in context of a biomedical application
(2023)
In this paper, a two-dimensional compliant tensegrity joint was investigated for potential biomedical applications such as orthotics or exoskeletons. The structure consists of two compressed members connected by five compliant tensioned members. The concept is based on the tensegrity principle, which allows the realization of dynamic orthoses without conventional hinge joints. Another advantage is the adaptability to the individual needs of the patient through a suitable design of the structure and the careful selection of the characteristics of the elements. Using geometric nonlinear analysis, the mechanical behavior of the structure was investigated, focusing on mechanical compliance. The main objective was to determine the influence of the initial length and stiffness of the tensioned members and the influence of the magnitude of external forces on the overall stiffness of the movable member of the structure. The results highlight the significant impact of member parameters on the structure's stiffness and movability under varying load magnitudes. The research laid the foundation for future development of dynamic orthoses based on this structure.
In diesem Beitrag erfolgt die theoretische Untersuchung einer zweidimensionalen nachgiebigen Tensegrity-Struktur in Hinsicht auf ihre potenzielle Eignung als Basisstruktur für eine dynamische Handorthese. Translatorische und rotatorische relative Bewegungsmöglichkeiten zwischen den Drucksegmenten der Struktur sind möglich, da diese Segmente durch nachgiebige Zugsegmente miteinander verbunden sind. Die Form der Struktur und ihre Vorspannung in einer statisch stabilen Gleichgewichtskonfiguration werden mit Hilfe der Minimierung des Kräfte- und Momentenungleichgewichts, der Betrachtung der potentiellen Energie der Struktur und einem Ansatz mittels statischer Finite-Elemente-Methode (FEM) in Abhängigkeit der Segmentparameter untersucht.
In this paper, the movement behavior of amoeboid locomotion system is investigated and the theoretical proof of the locomotion of the system is provided with the finite element method. It is shown that not only the speed of locomotion but also its direction can be influenced by the drive frequency. Depending on the drive frequency, a movement from the home position and a subsequent movement in opposite directions can be achieved. In addition, high speeds of movement can be achieved in a limited frequency range.
In the treatment of hand injuries in the context of orthopedic care, movable hand orthoses are used in many cases. Early motion therapy is in most cases advantageous for adequate, rapid, and successful long-term healing of the hand. Conventional mobile hand orthoses can only be used for movement therapy to a limited extent since they represent the wrist as a simple rotating joint and neglect the complexity of the movement possibilities of the hand. In this paper, a novel concept for movable hand orthoses based on prestressed compliant structures is presented. The advantage with this concept is that it replicates the multiaxial motion capabilities without the need for conventional joints. Besides the derivation and description of the concept, a first three-dimensional CAD design is shown. Additionally, the next planned steps in the development of such a novel dynamic hand orthosis are described.
In the treatment of hand injuries in the context of orthopedic care, movable wrist hand orthoses are used in numerous instances. Early motion therapy is in most cases advantageous for adequate, rapid and successful long-term healing of the hand. Conventional dynamic wrist hand orthoses can only be used for movement therapy to a limited extent since they represent the wrist as a simple rotating joint and neglect the complexity of the hand movement possibilities. In this paper, a preliminary concept for dynamic wrist hand orthoses based on prestressed compliant structures is presented. The distinctive feature of this concept lies in the enabling of multiaxial motion capabilities of the human hand without applying conventional joints. According to the concept the wrist region is surrounded by a prestressed compliant structure. Besides the derivation and description of the concept, a first three-dimensional computer-aided design is shown. Additionally, the necessary steps in the development of such a novel dynamic wrist orthosis are discussed.
The laminated steel core of transformers is one of the main sources of the generated sound, as it is excited by different electromagnetic effects during its normal operation. If the core is excited in its eigenfrequencies, the sound generated by a transformer will increase significantly. Therefore, knowledge of the core’s eigenmodes and -frequencies in an early design stage can decrease expenses by avoiding costly modifications that might be required to avoid the sound levels exceeding the specified values after the final factory acceptance test. The current study focuses on developing a core resonance model to determine the eigenmodes and -frequencies of a transformer core. The core’s geometry was simplified to a connected-beam structure and a numerical-based approach was applied. The accuracy of the developed model was validated against finite element method (FEM), using ANSYS on a reference core model.
During the factory acceptance test, the sound levels are measured. If the measured sound levels exceed pre-specified values, modifications on the transformer’s active part and/or tank need to be conducted. Tank resonance, if occurs, at twice main power frequency and its higher harmonics is one of the main reasons of amplifying the generated sound levels. Therefore, it is preferable to know already in the design stage about the occurrence of the tank resonance and propose reliable tank solutions. The current study presents a newly developed model for calculating the mode shapes and its corresponding eigenfrequencies of the tank.
In practical use cases, simulation engineers are confronted with uncertainties in the simulation parameters. Normally, trust in a model is built from experience, practical assumptions, and parameter studies. This approach, though, is based on the assumption that few parameter combinations are sufficient to represent the whole design space. This lacks an appraisable mathematical basis.
To get insights into which parameters most strongly affect the results, a global sensitivity analysis can be conducted [2, 3]. The results are utilized to rank the most influential parameters and to filter less relevant ones. This gives feedback which improved set of input data will lead to more certainty in the simulation results. To enable this in the framework of multi-fidelity analysis and optimization, we compare here global sensitivities and uncertainties of the implicit One-Step approach (low-fidelity) with those of the explicit multi-step deep drawing approach (high-fidelity).
The paper deals with the investigation of magneto-sensitive elastomers(MSE) and their application in technical actuator systems. MSE consist of an elasticmatrix containing suspended magnetically soft and/or hard particles. Additionally,they can also contain silicone oil, graphite particles, thermoplastic components, etc.,in various concentrations in order to tune specific properties such as viscosity, con-ductivity and thermoelasticity, respectively. The focuses of investigations are thebeneficial properties of MSE in prototypes for locomotion and manipulation purposesthat possess an integrated sensor function. The research follows the principle of amodel-based design, i.e. the working steps are ideation, mathematical modelling,material characterization as well as building first functional models (prototypes). Thedeveloped apedal (without legs) and non-wheeled locomotion systems use the inter-play between material deformations and the mechanical motion in connection with theissues of control and stability. Non-linear friction phenomena lead to a monotonousforward motion of the systems. The aim of this study is the design of such mechanicalstructures, which reduce the control costs. The investigations deal with the movementand control of‘intelligent’mechanisms, for which the magnetically field-controlledparticle-matrix interactions provide an appropriate approach. The presented grippersenclose partially gripped objects, which is an advantage for handling sensitive objects.Form-fit grippers with adaptable contour at the contact area enable a uniform pressuredistribution on the surface of gripped objects. Furthermore, with the possibility ofactive shape adaptation, objects with significantly differing geometries can be gripped.To realise the desired active shape adaptation, the effect of field-induced plasticity ofMSE is used. The first developed prototypes mainly confirm the functional principles assuch without direct application. For this, besides the ability of locomotion andmanipulation itself, further technological possibilities have to be added to the systems.
Field induced plasticity of magneto-sensitive elastomers for gripping technology applications
(2018)
The use of compliant tensegrity structures in robotic applications offers several advantageous properties. In this work the dynamic behaviour of a planar tensegrity structure with multiple static equilibrium configurations is analysed, with respect to its further use in a two-finger-gripper application. In this application, two equilibrium configurations of the structure correspond to the opened and closed states of the gripper. The transition between these equilibrium configurations, caused by a proper selected actuation method, is essentially dependent on the actuation parameters and on the system parameters. To study the behaviour of the dynamic system and possible actuation methods, the nonlinear equations of motion are derived and transient dynamic analyses are performed. The movement behaviour is analysed in relation to the prestress of the structure and actuation parameters.
This paper deals with the locomotion by tilting sequences of shape-variable compliant tensegrity structures. The shape of these structures is controlled by manipulating their prestress state. The tensegrity structure is tilting as consequence of a suitable variation of its shape. By multiple repetition of such tilting sequences a motion is generated. Quasi-static considerations for the considered structures are presented in order to estimate the actuation parameters. For a proper number of actuators this quasi-static approach enables an analytical calculation of the actuation parameters of the structure in order to control the geometrical configuration as required. As an example a two-dimensional tensegrity structure which is in contact with a horizontal plane due to gravity is considered. By successive tilting sequences a uniaxial motion results. The excitation of the structure is calculated for a given change of shape with the quasi-static analysis. The according results are compared with transient dynamic simulations. Qualitative conclusions about the motion behavior and the usability of the quasi-static approach are given.
Dynamical Investigation of Crawling Motion System based on a Multistable Tensegrity Structure
(2018)
The basic idea of this article is the utilization of the multistable character of a compliant tensegrity structure to control the direction of motion of a crawling motion system. A crawling motion system basing on a two-dimensional tensegrity structure with multiple stable equilibrium states is considered. This system is in contact with a horizontal plane due to gravity. For a selected harmonic actuation of the system small oscillations around the given equilibrium state of the tensegrity structure occur and the corresponding uniaxial motion of the system is evaluated. A change of the equilibrium state of the tensegrity structure yields to novel configuration of the entire system. Moreover, the motion behavior of the novel configuration is totally different although the actuation strategy is not varied. In particular, the direction of motion changes. Therefore, this approach enables a uniaxial bidirectional crawling motion with a controllable direction of motion using only one actuat or with a selected excitation frequency.