Multiscale tensegrity model for the tensile properties of DNA nanotubes

DNA nanotubes(DNTs)with user-defined shapes and functionalities have potential applications in many fields.So far,compared with numerous experimental studies,there have been only a handful of models on the mechanical properties of such DNTs.This paper aims at presenting a multiscale model to quantify the correlations among the pre-tension states,tensile properties,encapsulation structures of DNTs,and the surrounding factors.First,by combining a statistical worm-like-chain(WLC)model of single DNA deformation and Parsegian's mesoscopic model of DNA liquid crystal free energy,a multiscale tensegrity model is established,and the pre-tension state of DNTs is characterized theoretically for the first time.Then,by using the minimum potential energy principle,the force-extension curve and tensile rigidity of pre-tension DNTs are predicted.Finally,the effects of the encapsulation structure and surrounding factors on the tensile properties of DNTs are studied.The predictions for the tensile behaviors of DNTs can not only reproduce the existing experimental results,but also reveal that the competition of DNA intrachain and interchain interactions in the encapsulation structures determines the pre-tension states of DNTs and their tensile properties.The changes in the pre-tension states and environmental factors make the monotonic or non-monotonic changes in the tensile properties of DNTs under longitudinal loads.

Geometric and material nonlinear analysis of tensegrity structures

A numerical method is presented for the large deflection in elastic analysis of tensegrity structures including both geometric and material nonlinearities.The geometric nonlinearity is considered based on both total Lagrangian and updated Lagrangian formulations,while the material nonlinearity is treated through elastoplastic stress-strain relationship.The nonlinear equilibrium equations are solved using an incremental-iterative scheme in conjunction with the modified Newton-Raphson method.A computer program is developed to predict the mechanical responses of tensegrity systems under tensile,compressive and flexural loadings.Numerical results obtained are compared with those reported in the literature to demonstrate the accuracy and efficiency of the proposed program.The flexural behavior of the double layer quadruplex tensegrity grid is sufficiently good for lightweight large-span structural applications.On the other hand,its bending strength capacity is not sensitive to the self-stress level.

Active vibration control of tensegrity structures for performance enhancement: A comparative study

This study performs a novel control effi ciency assessment approach that compares performance of optimal control algorithms regarding vibration of tensegrity structures. Due to complex loading conditions and the inherent characteristics of tensegrities, e.g. geometrical nonlinearity, the quantization of control effi ciency in active control of tensegrity constitutes a challenging task especially for diff erent control algorithms. As a fi rst step, an actuator energy input, comprising the strain energy of tensegrity elements and their internal forces work, is set to constant levels for the linearquadratic regulator (LQR). Afterwards, the actuator energy of the linear-quadratic Gaussian (LQG) is iterated with identical actuator energy input in LQR. A double layer tensegrity grid is employed to compare the control effi ciencies between LQR and LQG with fi ve diff erent control scenarios. The results demonstrate the effi ciency and robustness in reducing the dynamic response of tensegrity structures, and a theoretical guideline is provided to search optimal control options in controlling actual tensegrities.

Design methods of rhombic tensegrity structures

As a special type of novel flexible structures, tensegrity holds promise for many potential applications in such fields as materials science, biomechanics, civil and aerospace engineering. Rhombic systems are an important class of tensegrity structures, in which each bar constitutes the longest diagonal of a rhombus of four strings. In this paper, we address the design methods of rhombic structures based on the idea that many tensegrity structures can be constructed by assembling one-bar elementary cells. By analyzing the properties of rhombic cells, we first develop two novel schemes, namely, direct enumeration scheme and cell-substitution scheme. In addition, a facile and efficient method is presented to integrate several rhombic systems into a larger tensegrity structure. To illustrate the applications of these methods, some novel rhombic tensegrity structures are constructed.

Dynamic Similarity of Six Bar Ball Tensegrity Structure in Compression and Expansion Processes

Tensegrity structures have identical members in an orientation that have correlated dynamics under external force.To study this interdependent dynamics in different members in compression and expansion processes,it is vital to analyze the dynamics of the whole structure.In this study,six bar tensegrity structure was studied under compression and expansion,and interdependent movement of different members of the structure in both processes was obtained.First,the relationship between external force and members force densities was analytically developed based on the assumption that each bar moves with the same distance when an external force is applied on the six bar tensegrity ball structure along one plane that either compresses or expands the structure.Then,two individual simulations were carried out to analyze the movement of each bar in compression and expansion under the effect of external force,and elongation in all strings was studied in both processes.Finally,comparative dynamic study of different members in compression and expansion of the structure with the effect of external force was performed,which were categorized according to dynamic symmetry.

On the orientation of plane tensegrity cytoskeletons under biaxial substrate stretching

Two different simple cases of plane tensegrity cytoskeleton geometries are presented and investigated in terms of stability. The tensegrity frames are used to model adherent cell cytoskeletal behaviour under the application of plane substrate stretching and describe thoroughly the experimentally observed reorientation phenomenon. Both models comprise two elastic bars (microtubules), four elastic strings (actin filaments) and are attached on an elastic substrate. In the absence of external loading shape stability of the cytoskeleton is dominated by its prestress. Upon application of external loading, the cytoskeleton is reorganized in a new direction such that its total potential energy is rendered a global minimum. Considering linear constitutive relations, yet large deformations, it is revealed that the reorientation phenomenon can be successfully treated as a problem of ma- thematical stability. It is found that apart from the magnitude of contractile prestress and the magnitude of extracellular stretching, the reorientation is strongly shape–dependent as well. Numerical applications not only justify laboratory data reported in literature but such experimental evidence as the concurrent appearance of two distinct and symmetric directions of orientation, indicating the cellular coexistence of phases phenomenon, are clearly detected and incorporated in the proposed mathematical treatment.

Tensegrity applied to modelling the motion of viruses

A considerable number of viruses’structures have been discovered and more are expected to be identified.Different viruses’symmetries can be observed at the nanoscale level.The mechanical models of some viruses realised by scientists are described in this paper,none of which has taken into consideration the internal deformation of subsystems. The authors’models for some viruses’elements are introduced,with rigid and flexible links,which reproduce the movements of viruses including internal deformations of the subunits.

Multi-locomotion transition of tensegrity mobile robot under different terrains

Knowing how to make a multi-locomotion robot achieve locomotion transition under different terrains is a challenging problem,especially for tensegrity robots with multi-locomotion modes.In this study,a motion planning method for the transition of a multi-locomotion tensegrity robot(hereafter TJUBot)under different terrains is proposed.The robot can achieve four locomotion modes:earthworm-like,inchworm-like,tumbling,and sliding locomotion with only two motors.Kinematic models of the four locomotion modes under five typical terrains,including flat ground,confined space,obstacle,gap,and descending slope,are established using the energy method.Meanwhile,the kinematic characteristics(driving law and initial position)of the robot under these terrains are obtained.On this basis,motion planning for the locomotion transition of TJUBot is conducted,which includes a perception strategy based on three laser sensors and a transition strategy under different terrains.The driving laws of the two motors that can ensure the effective locomotion transition of TJUBot under different terrains are naturally obtained.Finally,experiments are conducted.Results demonstrate that the robot can achieve effective locomotion transition when the motion planning method is used.

Design and Experimental Validation of a Worm-Like Tensegrity Robot for In-Pipe Locomotion

Traditional rigid-body in-pipe robots usually have complex and heavy structures with limited flexibility and adaptability.Although soft in-pipe robots have great improvements in flexibility,they still have manufacturing difficulties due to their reliance on high-performance soft materials.Tensegrity structure is a kind of self-stressed spatial structure consisting discrete rigid struts connected by a continuous net of tensional flexible strings,which combines the advantages of both rigid structures and soft structures.By applying tensegrity structures into robotics,this paper proposes a novel worm-like tensegrity robot for moving inside pipes.First,a robot module capable of body deformation is designed based on the concept of tensegrity and its deformation performance is analyzed.Then,the optimal parameters of the module are obtained based on the tensegrity form-finding.The deformation ability of the tensegrity module is tested experimentally.Finally,the worm-like tensegrity robot that can crawl inside pipes is developed by connecting three modules in series.Motion performance and load capacity are tested on the prototype of the worm-like tensegrity robot by experiments of moving in horizontal pipe,vertical pipe,and elbow pipe.Experimental results demonstrate the effectiveness of the proposed design and suggest that the robot has high compliance,mobility,and adaptability although with simple structure and low cost.

Experimental Investigation on the Vibration Attenuation of Tensegrity Prisms Integrated with Particle Dampers

Tensegrities made of tensile strings and compressed struts possess large strength-to-mass ratio values but tend to experience non-negligible vibration in dynamic environments because of poor structural damping.Here,we introduce particle dampers into a tensegrity prism to attenuate vibration,with the goal of establishing a lightweight and efficient approach of vibration suppression.To integrate the particle dampers and the tensegrity,a novel strut structure formed by assembling a solid strut and a hollow strut is devised,in which granular materials are inserted to develop a particle damper.The vibration attenuation performance of the tensegrity prism is investigated through exciter tests.According to the experimental parametric study,the influences of system parameters including excitation magnitude,the filling height of particles,particle size and the configuration of tensegrity prism on the vibration attenuation performance is analyzed.In addition,the experimental results regarding the dependence of the vibration attenuation on the system parameters are interpreted by the mechanism of collisions and frictions between particles and between particles and struts.The maximal vibration attenuation ratio of 76%can be achieved in the experiments.Thus,this research can provide insights into the design of lightweight tensegrity structures where vibration suppression is important,particularly in some dynamic environments.

Tensegrity: A Novel Conceptual Framework for Rehabilitation of Functional Deficits for Breast Cancer Survivors

The current approach to breast cancer rehabilitation is currently narrowly focused on addressing resultant problems such as lymphedema or shoulder pain.Referrals to rehabilitation are reactive responses to these problems.Taking a step back and looking at the breast cancer intervention in totality,it becomes apparent that steps could be taken to minimize or actu-ally prevent some of the ensuing functional problems by proactively treating a breast cancer survivor.Rather than waiting for problems to arise,immediately post-intervention or ideally pre-intervention and throughout intervention referral of an individual to rehabilitation could provide a supportive role in the functional progression of the patient.Furthermore,while most orthopedic rehabilitation focuses on the function of a particular joint,with the extensive impact of the breast cancer treatments on the soft tissue of the body without any specific intervention at a joint,it is imperative that we begin to shift our rehabilitation approach to focusing on the alterations of the soft tissue prior to addressing any functional limitations in the joints,with the most common victim being the shoulder joint.This novel approach to breast cancer rehabilitation sug-gests initially addressing soft tissue limitations.As these limitations begin to resolve as optimally as possible,secondary consideration is then given to functional limitations of a joint such as the shoulder joint.

The dynamic relaxation form finding method aided with advanced recurrent neural network

How to establish a self‐equilibrium configuration is vital for further kinematics and dynamics analyses of tensegrity mechanism.In this study,for investigating tensegrity form‐finding problems,a concise and efficient dynamic relaxation‐noise tolerant zeroing neural network(DR‐NTZNN)form‐finding algorithm is established through analysing the physical properties of tensegrity structures.In addition,the non‐linear constrained opti-misation problem which transformed from the form‐finding problem is solved by a sequential quadratic programming algorithm.Moreover,the noise may produce in the form‐finding process that includes the round‐off errors which are brought by the approximate matrix and restart point calculating course,disturbance caused by external force and manufacturing error when constructing a tensegrity structure.Hence,for the purpose of suppressing the noise,a noise tolerant zeroing neural network is presented to solve the search direction,which can endow the anti‐noise capability to the form‐finding model and enhance the calculation capability.Besides,the dynamic relaxation method is contributed to seek the nodal coordinates rapidly when the search direction is acquired.The numerical results show the form‐finding model has a huge capability for high‐dimensional free form cable‐strut mechanisms with complicated topology.Eventually,comparing with other existing form‐finding methods,the contrast simulations reveal the excellent anti‐noise performance and calculation capacity of DR‐NTZNN form‐finding algorithm.

Snapping instability in prismatic tensegrities under torsion

Tensegrities are a class of lightweight and reticulated structures consisting of stressed strings and bars. It is shown that each prismatic tensegrity can have two self-equilibrated and stable states, leading to a snapping instability behavior under an applied torque. The predicted mechanism is experimentally validated, and can be used in areas such as advanced sensors and actuators, energy storage /alsorption equipments, and folding/unfolding devices.

Tensegrities and Tensioned Structures

“Push-and-pull”efficient structures have been inconceivable between XVIII centuries.It is because of the incapacity of obtain an efficient behaviour of tensioned material.Since XVIII centuries,architecture developed some structural knowledge generating novel structural forms in the architecture and engineering that were not known before.Tensegrities and tensioned structures were studied due to the knowledge of geometry and tension.Some investigations about tensegrities and tensioned structures have been developed since that moment.Tensegrities are bar and cable structures that work only in compression or tension efforts.Bars and cables are balanced,but in appearance the growth is disorderly.Most of deployable structures are based on tensegrity systems.The research is focused in presenting a summary of tensegrities and tensioned architectures that have been used in the structural design of novel patterns.The research of adequate materials to tension efforts will be crucial in this study.The investigation presents an important state of the art that provides technical solutions to apply on novel architectures based on tensegrities and tensioned structures.The research is useful to produce the current constructive solutions based on these constructive systems.

预应力张拉网壳的几何稳定性分析

介绍一种新颖实用的张拉网壳，这种网壳由柔性缆索和刚性杆件组成，按照“拉力连续、压力间断”的思想设计，以最大限度地利用工程材料．本文讨论了这类网壳的几何造型和几何形状的稳定性条件，举例说明了张拉网壳内预应力的确定方法．

In Situ Reconfiguration of Assembling Pattern for Modular Continuum Robots

Modular continuum robots possess significant versatility across various scenarios;however,conventional assembling methods typically rely on linear connection between modules.This limitation can impede the robotic interaction capabilities,especially in specific engineering applications.Herein,inspired by the assembling pattern between the femur and tibia in a human knee,we proposed a multidirectional assembling strategy.This strategy encompasses linear,oblique,and orthogonal connections,allowing a two-module continuum robot to undergo in-situ reconfiguration into three distinct initial configurations.To anticipate the final configuration resulting from diverse assembling patterns,we employed the positional formulation finite element framework to establish a mechanical model,and the theoretical results reveal that our customizable strategy can offer an effective route for robotic interactions.We showcased diverse assembling patterns for coping with interaction requirements.The experimental results indicate that our modular continuum robot not only reconfigures its initial profile in situ but also enables on-demand regulation of the final configuration.These capabilities provide a foundation for the future development of modular continuum robots,enabling them to be adaptable to diverse environments,particularly in unstructured surroundings.