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.

Flexible Bio-tensegrity Manipulator with Multi-degree of Freedom and Variable Structure

Conventional manipulators with rigid structures and sti ness actuators have poor flexibility,limited obstacle avoidance capability,and constrained workspace.Some developed flexible or soft manipulators in recent years have the characteristics of infinite degrees of freedom,high flexibility,environmental adaptability,and extended manipulation capability.However,these existing manipulators still cannot achieve the shrinking motion and independent control of specified segments like the animals,which hinders their applications.In this paper,a flexible bio-tensegrity manipulator,inspired by the longitudinal and transversal muscles of octopus tentacles,was proposed to mimic the shrinking behavior and achieve the variable motion patterns of each segment.Such proposed manipulator uses the elastic spring as the backbone,which is driven by four cables and has one variable structure mechanism in each segment to achieve the independent control of each segment.The variable structure mechanism innovatively contains seven lock-release states to independently control the bending and shrinking motion of each segment.After the kinematic modeling and analysis,one prototype of such bionic flexible manipulator was built and the open-loop control method was proposed.Some proof-of-concept experiments,including the shrinking motion,bending motion,and variable structure motion,were carried out by controlling the length of four cables and changing the lock-release states of the variable structure mechanism,which validate the feasibility and validity of our proposed prototype.Meanwhile,the experimental results show the flexible manipulator can accomplish the bending and shrinking motion with the relative error less than 6.8%through the simple independent control of each segment using the variable structure mechanism.This proposed manipulator has the features of controllable degree-of-freedom in each segment,which extend their environmental adaptability,and manipulation capability.

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.

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.

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.

Examples of Cable-Bar Modular Structures Based on the Class-Theta Tensegrity Systems

The relationship between forms and forces is one of the main topics of structural morphology. This harmonious coexisting link is very strong for systems in tensegrity state, commonly called ＂tensegrity systems＂. It is currently apparent that, among the tensegrity systems, there also exist cable-bar cells with a discontinuous network of cables. It is possible to design a separate set of cables inside the cable-bar elementary cell and to establish a self-stress state of equilibrium. In this connection, the author of this paper suggested to assume a new Class-Theta tensegrity systems. Each of the basic tensegrity systems termed Class-Theta possesses an external and internal set of tension components. The shape of Greek capital letter 69 （Theta） reflects two sets of such components （two sets of tendons, cables, etc.）. This notation corresponds to Skelton＇s Class-k tensegrity structure. As shown in this paper, the Class-Theta tensegrity cell can exemplify a geometrically and practically useful form for the lightweight and long-span modular structures, mainly but not only in view of civil engineering and architecture.

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.

Carbon star CGCS 673 identified as a semi-regular variable star

This study reports that the carbon star CGCS 673 is a semi-regular(SR)variable star with a period of 135 d and an amplitude of 0.18mag in the V-band.The light curve obtained by this study correlates well with the SR classification as the photometric data obtained show noticeable periodicity in the light changes of CGCS 673 that is occasionally interrupted by a period of irregular variability.The derived period and colour index obtained from our data and those from professional databases indicate that the attributes of this star fall within the parameters of the SR class of variable stars.Following our notification of the discovery that this star is a variable source,CGCS 673 has received the AAVSO Unique Identifier of(AAVSO UID)000-BMZ-492.

Tiling a Plane with Semi-Regular Equilateral Polygons with 2m-Sides

In this paper, tiling a plane with equilateral semi-regular convex polygons is considered, and, that is, tiling with equilateral polygons of the same type. Tiling a plane with semi-regular polygons depends not only on the type of a semi-regular polygon, but also on its interior angles that join at a node. In relation to the interior angles, semi-regular equilateral polygons with the same or different interior angles can be joined in the nodes. Here, we shall first consider tiling a plane with semi-regular equilateral polygons with 2m-sides. The analysis is performed by determining the set of all integer solutions of the corresponding Diophantine equation in the form of , whereare the non-negative integers which are not equal to zero at the same time, and are the interior angles of a semi-regular equilateral polygon from the characteristic angle. It is shown that of all semi-regular equilateral polygons with 2m-sides, a plane can be tiled only with the semi-regular equilateral quadrilaterals and semi-regular equilateral hexagons. Then, the problem of tiling a plane with semi-regular equilateral quadrilaterals is analyzed in detail, and then the one with semi-regular equilateral hexagons. For these semi-regular polygons, all possible solutions of the corresponding Diophantine equations were analyzed and all nodes were determined, and then the problem for different values of characteristic elements was observed. For some of the observed cases of tiling a plane with these semi-regular polygons, some graphical presentations of tiling constructions are also given.

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.

满约束轴向拼接张拉整体结构的自稳定性分析

为获得更多张拉整体构型和拓扑结构,本文基于平衡方程,研究张拉整体拼接结构自稳定条件下的结构参数关系的求取方法。基于三杆张拉整体单元轴向拼接形成的臂状张拉整体结构,以减少结构节点约束数为目的去除索构件,获得一种新型满约束轴向拼接张拉整体结构;分析此结构的节点坐标、构件向量的求取方法,推导结构的平衡方程;依据节点和构件之间的连接关系,以获得方阵形式的平衡矩阵为目标,提出了平衡方程缩减原则;根据平衡方程有非零解,平衡矩阵行列式为零的原则,获得保证张拉整体结构自稳定的结构参数关系。通过具体实例分析,证明此方法正确,获得的结构参数关系能够保证确定的满约束轴向拼接张拉整体结构的自稳定性。

基于奇异值分解张拉整体结构找形方法

张拉整体结构是由一组不连续的受压单元包含于连续受拉单元组成的稳定自平衡结构,为了寻找自平衡状态下的构型,引入奇异值分解的方法,将寻找张拉整体结构的自平衡构型问题转化为最小奇异值的判定。通过广义节点坐标和构件之间的连接关系建立结构的数学模型;引入力密度的概念,对张拉整体结构进行受力分析,列写包含平衡矩阵的平衡方程;对平衡矩阵进行奇异值分解,利用分解获得的最小奇异值判断平衡方程是否有解,对张拉整体结构是否存在自平衡构型进行初步判定,再依据获得的力密度的均匀性(同组构件力密度大小相等)和正负属性(杆的力密度小于0,索的力密度大于0)对结构自平衡状态进一步判断;通过实例分析对该找形方法的可行性进行了验证,结果表明:该方法可以找到张拉整体结构自平衡构型。本文为寻找自平衡张拉整体结构提供了一种思路。

考虑预应力松弛的张拉整体机械臂可靠性分析

柔性张拉整体结构可应用于桥梁、机械臂和深空探测等多种工程场景。以张拉整体机械臂为例,应力松弛导致的绳索预应力水平下降可能带来驱动变形响应的不确定性,从而造成结构功能失效。因此,研究绳索预应力松弛不确定性在张拉整体结构中的传播对机械臂作动位移的定量控制十分必要。然而,张拉整体机械臂可能包含数十甚至上百根绳索,采用Monte Carlo方法对设计变量进行随机抽样时将面临“维度灾难”。通过对机械臂工作服役时间引入概率模型,并结合独立同分布假设,该文从钢索预应力设计规范出发,将随机发生的预应力松弛引入了基于共旋坐标法的结构可靠性分析。该文采用基于最小角回归的稀疏混沌多项式展开(polynomial chaos expansion,PCE)方法,对张拉整体机械臂作动位移进行不确定性传播分析,实现了对结构响应概率密度分布的快速预测。针对该文研究的12杆、36绳结构,稀疏PCE方法在仅使用500次有限元模拟结果作为训练数据的情况下便能获得足够高的预测精度,很好地解决了“维度灾难”问题,提高了分析效率。在此基础上,对设计变量进行灵敏度分析,准确找出对机械臂作动位移影响最大的绳索。研究结果表明,只需对该绳索进行材料选型改进,便能够大幅提高机械臂的长时作动可靠度。该文方法可应用于张拉整体机械臂的动力学问题不确定性量化及可靠性结构优化设计。

十二杆张拉整体结构动态分析及路径规划研究

张拉整体因其区别于传统结构的特点在土木和可动结构领域有广泛的发展前景,目前学者对于多步态或更复杂的球形张拉整体研究较少,且一些传统路径规划方法不适用于多面体张拉整体结构.因此,本文采用几何方法找寻了一种多步态的十二杆球形张拉整体结构(Snub-12)的合理构型,并用找形方法进行了验证.定义并分析了Snub-12的多种基本步态和各步态形成的理论路径空间,并将其与单步态的6杆球形张拉整体结构(TR-6)进行对比,明确了两种结构运动的特点和区别.对快速搜索随机树算法进行改进并利用其产生引导路径,结合Snub-12步态组合的情况,生成适合不同场景的合理运动路径,最后通过仿真分析验证了方法的可行性和有效性.分析结果表明:同等条件下,不论是路径空间中盲区占比还是独立滚动步态的翻滚步长,Snub-12均优于TR-6,更适宜开展长距离运动.基于引导策略的路径规划方法可以解决多步态张拉整体结构的路径规划问题,这丰富了球形张拉整体结构的运动理论,可以为该类球形张拉整体可动结构的实际应用提供了理论支撑.

张拉整体机器人杆件后屈曲驱动行走数值仿真

球形张拉整体机器人与传统的轮式、足式机器人相比,具有高强度质量比、缓冲性能好、地形适应力强等优点,在深空探测中有着广阔的应用前景。球形张拉整体机器人常采用绳索驱动模式,但在驱动行走过程中,过多的驱动数目给球形张拉整体机器人的制造与控制带来了困难。提出了一种基于柔性杆件后屈曲变形的新型驱动模式,实现了球形张拉整体机器人行走过程的数值仿真,并对绳索驱动和杆件后屈曲驱动模式的效率进行了比较。通过椭圆积分法,求得单根杆件在后屈曲变形中的精确解。基于该理论在ADAMS中建立考虑杆件后屈曲变形、接触、摩擦的球形张拉整体机器人刚柔耦合动力学仿真模型。通过ADAMS与Simulink软件联合仿真,利用贪心搜索(greedy search)算法,确定了球形张拉整体机器人的基本步态。在Simulink软件中建立控制系统模型,实现了机器人在杆件后屈曲驱动模式下,向任意目标点的行走控制。对比传统绳索驱动,杆件后屈曲驱动模式下,机器人连续行走所需驱动器数目从18个减少到6个,行走速度提高了43.78%。研究结果为新型张拉整体机器人的设计与制造提供了理论指导。

张拉整体机器人构型与运动控制研究现状及进展

研究发现张拉整体结构存在于细胞骨架、肌肉-骨骼系统等生物体,并将其原理广泛应用于建筑、雕塑、空间探测等工程结构中。张拉整体结构具有形态可调性、受力可控性、绳索抗拉性和结构轻质、结构自稳定等优势,因此在机器人领域极具应用前景。而软体机器人作为一种新型、仿生、能与人安全交互的机器人,近年来成为力学、材料学、医学、生物学等多学科交叉领域的研究热点之一。但是,要想实现灵活准确的运动、高效地承受外载、迅速地适应环境等复杂特性和功能,张拉整体机器人在其构型、运动步态及控制研究等方面依旧面临着巨大挑战。本研究选取张拉整体机器人的三大典型类别(棱柱形张拉整体机器人、球形张拉整体机器人及构型较复杂的张拉整体机器人),对其构型、运动步态及控制的国内外相关研究现状和发展趋势进行综述,旨在为机器人的仿生学研究提供科学依据。

基于张拉整体结构的可变形移动机器人的设计与实验研究

移动机器人可以代替人进入火灾、地震现场等高危环境进行地形探索及伤员搜寻等工作,然而大多数机器人难以同时适应障碍、直角墙壁、墙面过渡等多种复杂地形,且其控制系统相对复杂,需要外部能源输入。为此,设计了一款具有多种功能、控制相对简单且无系留的可变形移动机器人。首先,将二杆四索张拉整体结构作为基本单元,设计了可实现弯曲变形的张拉整体结构躯干;其次,基于吸附力及结构参数的分析,设计了负压吸附装置,并将它与可变形躯干结合,形成了机器人整体结构;接着,对机器人进行运动学分析,获得了机器人位姿与电机转角的映射关系,并据此规划了机器人墙面过渡、从墙面穿越狭小空间及翻转上台阶的步态;最后,完成了机器人样机的研制,并针对不同地形开展了机器人运动实验,验证了机器人步态规划的合理性。研究结果为多功能移动机器人的设计与制造提供了一定的参考价值。