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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.
Lineare und nichtlineare FEM
(2022)
Einführung in die lineare FEM - Mechanische Größen der Strukturmechanik - Mathematische Modellierung über Energieprinzipien - Diskretisierung mit Finiten Elementen - Finite-Elemente-Klassen - Mathematische und numerische Aspekte der FEM - Geometrische Nichtlinearität - Materielle Nichtlinearität - Kontaktmodellierung - Gleichungslösung bei nichtlinearen statischen Problemen - Zeitintegration von nichtlinearen dynamischen Problemen - Blechumformsimulation - Anhang: Mathematische Hilfsmittel - Einführung in die Simulation mit LS-DYNA®
Die Zielgruppen- Studierende aus Bachelor- und Masterstudiengängen der Ingenieurwissenschaften an Hochschulen und Technischen Universitäten - Ingenieure und Techniker
A novel type of a vibration driven motion system based on a compliant tensegrity structure with multiple stable equilibrium states is considered. These equilibrium configurations correspond to different prestress states with different dynamical properties. Therefore, the motion characteristics can be varied by changing the equilibrium state. For the application in the fields of mobile robotics, these discrete adjustable dynamics are advantageous. The vibration modes of the structure as well as the corresponding motion characteristics of the system can be adapted to the given environmental conditions in order to ensure a reliable motion. In this paper, dynamical investigations of an exemplary two-dimensional multistable tensegrity structure are considered. For the chosen parameter values the structure features two relevant equilibrium configurations. The resulting motion system is in contact to a horizontal plane due to gravity and the actuation is realized by the harmonic variation of the length of a single tensioned member. The motion of the system is simulated for various actuation frequencies with the different equilibrium states as an initial configuration. A uniaxial or a planar movement occurs depending on the selection of the actuated member within the tensegrity structure. The steady state motion is evaluated regarding motion characteristics like the steady state velocity. Moreover, the influences on the motion behavior caused by the different equilibrium states as an initial condition are emphasized. (C) 2018 Elsevier Ltd. All rights reserved.
Magnetorheological elastomers are a type of smart hybrid material which combines elastic properties of a soft elastomer matrix with magnetic properties of magnetic micro particles. This leads to a material with magnetically controllable mechanical properties of which the magnetorheological effect is the best known. The addition of electroconductive particles to the polymer mix adds electrical properties to the material behaviour. The resulting electrical resistance of the sample can be manipulated by external magnetic fields and mechanical loads. This results in a distinct interplay of mechanical, electrical and magnetic effects with a highly complex time behaviour. In this paper a mechanical characterisation on multiple time scales was conducted to get an insight on the short and long-term electrical and mechanical behaviour of this novel material. The results show a complex resistivity behaviour on several timescales, sensitive to magnetic fields and strain velocity. The observed material exhibits fatigue and relaxation behaviour, whereas the magnetorheological effect appears not to interfere with the piezoresistive properties.
Properties of Polydimethylsiloxane and Magnetoactive Polymers with Electroconductive Particles
(2018)
Magnetoactive polymers are intelligent materials whose mechanical and electrical characteristics are reversibly influenced by external magnetic stimuli. They consist of a highly elastic polymer matrix in which magnetically soft and/or hard particles are distributed by means of special fabrication processes. In addition to ferromagnetic particles such as carbonyl iron powder, electrically conductive particles may also be embedded into the polymer matrix. After characterizing a range of compounds, this work focuses on a comparison of the electrical properties and the suitability of various materials for applications, with particular emphasis on integration into 3D and 6D printing processes. 6D printing is based on the selective positioning of particles in a 3D polymer matrix with a further three degrees of freedom for a graduated dispersion of the particles at certain points and in desired directions. The aim is therefore to ensure that the polymers containing electroconductive tracks have the best possible electrical properties, that is, low resistivity but are still capable of being printed. A comparison between the traditionally used compounds containing graphite and carbon black is made for the first time. This latter is found to be greatly superior both in terms of electrical conductivity and applicability to 3D printing and 6D printing.
Rodents use their mystacial vibrissae, e.g., to recognize the shape or determine the surface texture of an object. The vibrissal sensory system consists of two components: the hair shaft and the follicle-sinus complex (FSC). Both components affect the collection of information, but the impacts of the different properties are not completely clear. Borrowing the natural example, the goal is to design a powerful artificial sensor. The influence of a continuous visco-elastic support is analyzed for an artificial sensor following hypotheses about the FSC. Starting with a theoretical treatment of this scenario, the vibrissa is modeled as an Euler-Bernoulli bending beam with a partially continuous visco-elastic support. The numerical simulations are validated by experiments. Using a steel strip as a technical vibrissa and a magneto-sensitive elastomer (MSE) as representation of the artificial continuous visco-elastic support, FSC respectively, the first resonance frequency is determined.
A feasible possibility to develop planar reconfigurable mechanisms is introduced in this work. Applying the tensegrity principle to common four-bar linkages allows a controllable change between two configurations of the mechanism. These two states correspond to different working spaces which vary regarding to the kinematic and mechanical properties. Therefore, the reconfiguration of the mechanism enables two different operation modes. Hence, this kind of mechanism enables the advantageous properties of conventional linkages with an additional enhanced adaptability of the kinematic and mechanic behavior. Beside the conceptual design of such tensegrity-based mechanisms, a reconfigurable four-bar parallel linkage is considered exemplarily. Numerical simulations are evaluated focusing on the kinematic behavior and the structural mechanics of this mechanism. Especially the reconfiguration of the mechanism by changing between two different working spaces is considered. The simulation results clarify the benefit of utilizing the tensegrity principle in mechanism theory. Adding only a few members to the original linkage enables a reconfigurable mechanism with comparable complexity.
Often, the operating range of mobile robots is limited by environ- mental circumstances like obstacles or gaps. Therefore, an adaptation of the motion principle is required to enable an operating continuation of such robots. A jumping motion is a promising approach. This motion type allows to cross gaps or to overcome obstacles where common motion principles which bases on wheels or legs fail. However, especially during landing large forces occur as a consequence of the impact with the ground. This issue encourages the use of compliant tensegrity structures which feature a great shock resistance. In this paper a tensegrity structure with multiple equilibrium configurations is considered. The two-dimensional structure is equipped with two actuators to vary the prestress of the system. The tensegrity structure is in contact to a horizontal plane due to gravity. Two actuation strategies are derived. Beside varying the prestress state of the structure, a jump can be realized by changing the equilibrium configuration. Both actuation strategies and the corresponding motion characteristics are evaluated by numeric simulations. The results emphasize the advantageous properties of tensegrity structures for a jumping motion system. In particular, the multistabilty of the structure allows a simple actuation strategy for a reliable jumping motion.
In this work, a tensegrity structure with spatially curved members is applied as rolling locomotion system. The actuation of the structure allows a variation of the originally cylindrical shape to a conical shape. Moreover, the structure is equipped with internal movable masses to control the position of the center of mass of the structure. To control the locomotion system a reliable actuation strategy is required. Therefore, the kinematics of the system considering the nonholonomic constraints are derived in this paper. Based on the resulting insight in the locomotion behavior a feasible actuation strategy is designed to control the trajectory of the system. To verify this approach kinematic analyses are evaluated numerically. The simulation data confirm the path following due to an appropriate shape change of the tensegrity structure. Thus, this system enables a two-dimensional rolling locomotion. The use of mechanically compliant tensegrity structures in mobile robots is an attractive research topic, due to the possibility to adjust their mechanical properties reversibly during locomotion. In this paper rolling locomotion of mobile robots based on simple tensegrity structures, consisting of three compressed spatially curved members connected to a continuous net of prestressed tensional members, is discussed. Planar locomotion of these robots is induced by the movement of internal masses. The movement direction can be changed by changing the robot's shape between a cylinder and a truncated cone. The paper focuses on the description of the kinematics of these systems with respect to the shape change.
This paper presents a multi-mode motion system based on a compliant tensegrity structure with multiple stable equilibrium configurations. The motion system is in contact to an arbitrarily shaped rigid ground due to gravity. The movement is realized by changing successively between different equilibrium states. Depending on the strategy of changing the equilibrium configuration, different motion types occur. The reachable area of the motion system can be enlarged by adapting the motion type depending on the given environmental characteristics. Furthermore, the efficiency of the motion can be improved by choosing the most suitable motion mode. Theoretical studies regarding the change of the equilibrium states are introduced. Moreover, simulation results for the different motion modes tilting, vibration driven and jumping are illustrated. The resulting motion characteristics emphasize the advantageous adaptability of the motion system regarding to varying environmental conditions.
The development of actuator and sensor systems with complex adaptive behavior and operating sensitivity is one of the actual scientific challenges. Smart materials like magneto-sensitive elastomers (MSEs) offer great potential for designing such intelligent devices, because they possess unique magnetic-field-dependent properties. The present paper deals with investigations of the free and forced vibrational behavior displayed by cantilever beams of MSEs containing magnetically soft particles in a uniform magnetic field. It is shown experimentally as well as theoretically that the first bending eigenfrequency of MSE beams depends strongly on the strength of an applied magnetic field. The proposed magneto-mechanical model is based on the vibrational dynamics of thin rods and predicts reliably the amplitude–frequency characteristics depending on the geometric configuration of the MSE and its material parameters. It is found that the vibration response of an MSE beam under kinematic excitation of its base can be modified indirectly by a magnetic field control due to the change of the vibration characteristics. As a result, the resonance can occur in different ranges of the excitation frequency. The dependencies of the amplification ratio on the excitation frequency are obtained experimentally and compared with the result provided by the theoretical model. Moreover, investigations on the potential use of the field-induced plasticity effect of MSEs in form-fit gripper applications are presented. This effect can be used to realize shape adaptable system parts. It is found that the mechanical properties of each component and its concentration within the mixture have an impact on the mechanical behavior of the whole MSE compound. Such parameters as the strength of magnetic field and geometry of the MSE sample have influence on the quality of shape adaptation. The evidence presented provides a good basis for the realization of MSE-based actuator and sensor systems with adaptable sensitivity.
In this paper a novel approach to realize a uniaxial bidirectional vibration driven motion system with controllable direction of motion is investigated. The considered motion system bases on a tensegrity structure with multiple stable equilibrium configurations. The structure is in contact with a horizontal plane due to gravity and the actuation is realized by the harmonic change of the length of a selected member. Beside varying the actuation parameters, the direction of motion can be controlled by changing the equilibrium configuration of the tensegrity structure. In this paper the topology of the tensegrity structure and the parameter values are chosen appropriately to provide two symmetric equilibrium configurations. A change of the equilibrium state yields a novel configuration of the entire motion system which is symmetric to the original state. Utilizing the symmetry of the system the same actuation yields an opposite motion. This approach represents a reliable opportunity to control the direction of motion by changing the equilibrium state for constant actuation parameters. This paper focuses on the parameter selection and the design of the actuation of the vibration driven motion system. The working principle of the vibration driven motion system is verified by numerical simulations. This contribution represents the theoretical investigation for the further development of a prototype.
Towards Magneto-Sensitive Elastomers Based End-Effectors for Gripping Application Technologies
(2019)
Nowadays, the demands in engineering systems become more challenging and the use of conventional materials for certain applications is not suitable. This issue encourages the investigation of novel and innovative materials in soft robotics field. A promising approach is the consideration of magneto-sensitive elastomers (MSE). These materials enable a useful adaptability responding to their mechanical properties. By applying a static magnetic field, the static and dynamic characteristics can be tuned. However, currently the knowledge about the correlations are not satisfying and the resulting material properties can only be predicted approximately with the use of time-expensive simulations regarding to the nano scale. Therefore, feasible material simulations of the description of the mechanical behavior are necessary. In this paper experimental studies of the influence of a static magnetic field on the mechanical properties and shape adaptability of MSE are presented. Furthermore, based on these results a simulation for the material behavior is executed. These results can be implemented into further simulations for various MSE exemplars.
This work presents a novel concept to develop mobile robots enabling crawling locomotion in tubular environment. Chain-like systems are designed by serial cascading a uniform tensegrity module. Inspired by the movement of worms in nature, an undulating shape change of the system is targeted to generate locomotion. The shape changeability of an exemplary tensegrity module due to internal actuation is examined in simulations and experiments. A prototype consisting of these tensegrity modules is manufactured and the locomotion principle is verified in experiments. Comparing to existing prototypes this approach enables an enhanced compliance due to the modular assembly of tensegrity structures.
All known locomotion principles are limited respective to environmental conditions. Often, the occurrence of obstacles or gaps means the break-off for the operating motion systems. For such circumstances, a controllable jumping locomotion is required to cross these barriers. However, this locomotion demands sophisticated requirements to the actuation. The abrupt actuation is commonly realized by high dynamic actuators or complex mechanisms. In this work, a simple solution utilizing the multistability of a compliant tensegrity structure is described. Therefore, a two-dimensional tensegrity structure featuring four stable equilibria is considered. Based on bifurcation analyses a feasible actuation to control the current equilibrium configuration is derived. Changing between selected equilibrium states enables a great difference in potential energy, which yields a jumping motion of the structure. Based on numerical simulations a suitable actuation strategy is chosen to overcome obstacle and steps by jumping forward or backward, respectively. The theoretical approach is examined experimentally with a prototype of the multistable tensegrity structure.
(c) 2020 Elsevier Ltd. All rights reserved.
All known locomotion principles are limited respective to environmental conditions. Often, the occurrence of obstacles or gaps means the break-off for the operating motion systems. For such circumstances, a controllable jumping locomotion is required to cross these barriers. However, this locomotion demands sophisticated requirements to the actuation. The abrupt actuation is commonly realized by high dynamic actuators or complex mechanisms. In this work, a simple solution utilizing the multistability of a compliant tensegrity structure is described. Therefore, a two-dimensional tensegrity structure featuring four stable equilibria is considered. Based on bifurcation analyses a feasible actuation to control the current equilibrium configuration is derived. Changing between selected equilibrium states enables a great difference in potential energy, which yields a jumping motion of the structure. Based on numerical simulations a suitable actuation strategy is chosen to overcome obstacle and steps by jumping forward or backward, respectively. The theoretical approach is examined experimentally with a prototype of the multistable tensegrity structure.
The development of reconfigurable planar four-bar linkages by applying the tensegrity principle is considered. Conventional quadrilateral linkages enable two operation modes differing in the kinematic behavior. However, a change between these states is not possible due to the geometric constraints. To enable a reconfiguration between the different modes one-sided limited nonholonomic constraints are introduced in this work. This issue is realized by applying ropes that cannot resist compression. However, to guarantee an appropriate load case in operation a prestress within the mechanism is required. Hence, the linkage is extended to a tensegrity-based mechanism. The structural dynamics are derived using the LAGRANGE formalism and the structural behavior is evaluated using numerical simulations. Furthermore, a prototype of an exemplary tensegrity-based mechanism is manufactured and experiments regarding the mechanical properties, in particular the reconfiguration, are performed. The results suggest the potential benefit of applying the tensegrity principle within conventional planar four-bar linkages.
The use of non-conventional materials is nowadays of much interest in scientific community. Magneto-rheological elastomers are hybrid materials, which in presence of magnetic fields state a change in their mechanical properties. They are composed by an elastomeric matrix with embedded magnetic particles. One of the most attractive features of these materials is that as soon as the magnetic field is removed from the material, the original mechanical properties are completely recovered, with negligible differences in comparison to the original state. This paper focuses on the study of magnetic characteristics of these smart materials, such as relative permeability and demagnetizing factors, for samples with different volume concentration of ferromagnetic particles.
The paper deals with the investigation of magneto-sensitive elastomers (MSE) and their application in technical actuator systems. MSE consist of an elastic matrix 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, conductivity and thermoelasticity, respectively. The focuses of investigations are the beneficial properties of MSE in prototypes for locomotion and manipulation purposes that possess an integrated sensor function. The research follows the principle of a model-based design, i.e. the working steps are ideation, mathematical modelling, material characterization as well as building first functional models (prototypes). The developed apedal (without legs) and non-wheeled locomotion systems use the interplay between material deformations and the mechanical motion in connection with the issues of control and stability. Non-linear friction phenomena lead to a monotonous forward motion of the systems. The aim of this study is the design of such mechanical structures, which reduce the control costs. The investigations deal with the movement and control of ‘intelligent’ mechanisms, for which the magnetically field-controlled particle-matrix interactions provide an appropriate approach. The presented grippers enclose partially gripped objects, which is an advantage for handling sensitive objects. Form-fit grippers with adaptable contour at the contact area enable a uniform pressure distribution on the surface of gripped objects. Furthermore, with the possibility of active shape adaptation, objects with significantly differing geometries can be gripped. To realise the desired active shape adaptation, the effect of field-induced plasticity of MSE is used. The first developed prototypes mainly confirm the functional principles as such without direct application. For this, besides the ability of locomotion and manipulation itself, further technological possibilities have to be added to the systems. The first steps are therefore being taken towards integrated MSE based adaptive sensor systems.
Magnetoactive elastomers (MAEs) are a special type of smart materials consisting of an elastic matrix with embedded microsized particles that are made of ferromagnetic materials with high or low coercivity. Due to their composition, such elastomers possess unique magnetic field-dependent material properties. The present paper compiles the results of investigations on MAEs towards an approach of their potential application as vibrating sensor elements with adaptable sensitivity. Starting with the model-based and experimental studies of the free vibrational behavior displayed by cantilevers made of MAEs, it is shown that the first bending eigenfrequency of the cantilevers depends strongly on the strength of an applied uniform magnetic field. The investigations of the forced vibration response of MAE beams subjected to in-plane kinematic excitation confirm the possibility of active magnetic control of the amplitude-frequency characteristics. With change of the uniform field strength, the MAE beam reveals different steady-state responses for the same excitation, and the resonance may occur at various ranges of the excitation frequency. Nonlinear dependencies of the amplification ratio on the excitation frequency are obtained for different magnitudes of the applied field. Furthermore, it is shown that the steady-state vibrations of MAE beams can be detected based on the magnetic field distortion. The field difference, which is measured simultaneously on the sides of a vibrating MAE beam, provides a signal with the same frequency as the excitation and an amplitude proportional to the amplitude of resulting vibrations. The presented prototype of the MAE-based vibrating unit with the field-controlled “configuration” can be implemented for realization of acceleration sensor systems with adaptable sensitivity. The ongoing research on MAEs is oriented to the use of other geometrical forms along with beams, e.g. two-dimensional structures such as membranes.
This paper describes the development of a tilting locomotion system based on a compliant tensegrity structure with multiple stable equilibrium configurations. A tensegrity structure featuring 4 stable equilibrium states is considered. The mechanical model of the structure is presented and the according equations of motion are derived. The variation of the length of selected structural members allows to influence the prestress state and the corresponding shape of the tensegrity structure. Based on bifurcation analyses a reliable actuation strategy to control the current equilibrium state is designed. In this work, the tensegrity structure is assumed to be in contact with a horizontal plane due to gravity. The derived actuation strategy is utilized to generate tilting locomotion by successively changing the equilibrium state. Numerical simulations are evaluated considering the locomotion characteristics. In order to validate this theoretical approach a prototype is developed. Experiments regarding to the equilibrium configurations, the actuation strategy and the locomotion characteristics are evaluated using image processing tools and motion capturing. The results verify the theoretical data and confirm the working principle of the investigated tilting locomotion system. This approach represents a feasible actuation strategy to realize a reliable tilting locomotion utilizing the multistability of compliant tensegrity structures.
In this work, a tensegrity structure with spatially curved members is applied as rolling locomotion system. The actuation of the structure allows a variation of the originally cylindrical shape to a conical shape. Moreover, the structure is equipped with internal movable masses to control the position of the center of mass of the structure. To control the locomotion system a reliable actuation strategy is required. Therefore, the kinematics of the system considering the nonholonomic constraints are derived in this paper. Based on the resulting insight in the locomotion behavior a feasible actuation strategy is designed to control the trajectory of the system. To verify this approach kinematic analyses are evaluated numerically. The simulation data confirm the path following due to an appropriate shape change of the tensegrity structure. Thus, this system enables a two-dimensional rolling locomotion.
Thermomechanical shape memory materials have certain disadvantages when it comes to 3D volumetric reproduction intended for rapid prototyping or robotic prehension. The need to constantly supply energy to counteract elastic retraction forces in order to maintain the required geometry, together with the inability to achieve conformal stability at elevated temperatures, limits the application of thermal shape memory polymers. Form removal also presents problems as most viscoelastic materials do not ensure demolding stability. This work demonstrates how magnetoactive boron−organo−silicon oxide polymers under the influence of an applied magnetic field can be used to achieve energy free sustainable volumetric shape memory effects over extended periods. The rheopectic properties of boron−organo−silicon oxide materials sustain form removal without mold distortion.
In this paper compliant multistable tensegrity structures with discrete variable stiffness are investigated. The different stiffness states result from the different prestress states of these structures corresponding to the equilibrium configurations. Three planar tensegrity mechanisms with two stable equilibrium configurations are considered exemplarily. The overall stiffness of these structures is characterized by investigations with regard to their geometric nonlinear static behavior. Dynamical analyses show the possibility of the change between the equilibrium configurations and enable the derivation of suitable actuation strategies.
Vibrating sensor unit made of a magnetoactive elastomer with field-adjustable characteristics
(2020)
The present work deals with the investigation of the oscillatory behavior displayed by a vibrating sensor unit made of a magnetoactive elastomer (MAE). Since this type of smart materials consists of an elastic matrix and micro-magnetic particles, it reveals exceptional magnetic-field-dependent material properties. The forced vibration response under the bending of the MAE unit subjected to in-plane harmonic kinematic excitation of the housing is studied. It is found that the amplitude-frequency characteristics of the MAE unit can be changed considerably by means of an external homogeneous magnetic field. With and without applied field, the unit displays different steady-state responses for the same excitation, and the resonance occurs at various ranges of the excitation frequency. The nonlinear phenomenon of the resonance hysteresis is observed depending on whether the excitation frequency increases or decreases. It is shown that the MAE vibrations can be detected based on the magnetic field distortion measurements. The presented prototype of the MAE-based vibrating unit with field-adjustable “configuration” can be potentially implemented for realization of acceleration sensor systems with adaptive sensitivity.
The use of mechanically prestressed compliant structures in soft robotics is a recently discussed topic. Tensegrity structures, consisting of a set of rigid disconnected compressed members connected to a continuous net of prestressed elastic tensioned members build one specific class of these structures. Robots based on these structures have manifold shape changing abilities and can adapt their mechanical properties reversibly by changing of their prestress state according to specific tasks.
In the paper selected aspects on the potential use of elastomer materials in these structures are discussed with the help of theoretical analysis. Therefore, a selected basic tensegrity structure with elastomer members is investigated focusing on the stiffness and shape changing ability in dependence of the nonlinear hyperelastic behavior of the used elastomer materials. The considered structure is compared with a conventional tensegrity structure with linear elastic tensioned members. Finally, selected criterions for the advantageous use of elastomer materials in compliant tensegrity robots are discussed.
Because of increased stroke rates the loads on forming tools increase too. To ensure a save design of components, durability analyses are intended. For this, simulation results from FE analyses are necessary. Therefore, it is desirable to use elements with quadratic function, because of a good stress approximation.The goal of the described investigation is to show if calculation results created by LS-DYNA [1] can be used for durability analyses. Especially the use of quadratic elements is investigated. For the evaluation, on the one hand explicit FE analyses of a special durability test are carried out. These analyses are validated by available test data. To create results for later durability analyses further FE analyses with implicit time discretisation are carried out. In this paper results of the investigations are presented and evaluated critically.
In deep-drawing dies for steel sheet parts of car bodies huge masses are moved. To prevent vibrations, which occur by sudden acceleration or stopping of those masses, elastomeric tubular dampers [1] are used. The dampers are made out of carbon filled elastomers. A good knowledge about the material behaviour of metals is available. But for the numerical investigation of complete deep-drawing dies the elastomeric dampers must be taken into account, too. To characterize the material behaviour of the elastomers tensile tests and pressure tests were carried out. The received material data from the tests were read into LS-DYNA [2]. Simulation models of the tensile test and the pressure test were created for LS-DYNA according to the real dimensions and boundary conditions. For validation purposes, calculations of loading cycles were done to enable a comparison between test data and simulation results. For the calculations the implemented material model *MAT_SIMPLIFIED_RUBBER_WITH_DAMAGE (*MAT_183) was used. The comparison shows a good fitting between the test data and the calculation results with respect to the mechanical material behaviour by using this material model in single loading cases. The settings from the simulations of material tests were transferred to simulations of dampers, which are used in deep-drawing dies.