Deployment of a tensegrity footbridge

Deployable structures are structures that transform their shape from a compact state to an extended in-service position. Structures composed of tension elements that surround compression elements in equilibrium are called tensegrity structures. Tensegrities are good candidates for deployable structures since shape transformations occur by changing lengths of elements at low energy costs. Although the tensegrity concept was first introduced in 1948, few full-scale tensegrity-based structures have been built. Previous work has demonstrated that a tensegrity ring topology is potentially a viable system for a deployable footbridge. This paper describes a study of a near-full-scale deployable tensegrity footbridge. The study has been carried out both numerically and experimentally. The deployment of two modules (one half of the footbridge) is achieved through changing the length of five active cables. Deployment is aided by energy stored in low stiffness spring elements. Self-weight significantly influences deployment, and deployment is not reproducible using the same sequence of cable- length changes. Active control is thus required for accurate positioning of front nodes in order to complete deployment through joining both sides at center span. Additionally, testing and numerical analyses have revealed that the deployment behavior of the structure is nonlinear with respect to cable-length changes. Finally, modeling the behavior of the structure cannot be done accurately using friction-free and dimension- less joints. Similar deployable tensegrity structures of class two and higher are expected to require simulation models that include joint dimensions for accurate prediction of nodal positions. DOI: 10.1061/(ASCE)ST.1943-541X.0001260 . © 2015 American Society of Civil Engineers

Toward development of a biomimetic tensegrity footbridge

Biomimetic structures interact with their environment, change their properties, learn and self-repair, thereby providing properties that are similar to living organisms. Interactions with the environment involve unique challenges in the field of computational control, algorithms, damage tolerance, and structural analysis. Tensegrity structures are pin-jointed structures of cables and struts in a self-stress state. Tensegrity structures are suitable for active control since the shape of the structure can be changed by changing the length of the elements. Consequently, they are good candidates for biomimetic structures. This paper describes research that is moving toward a case study of biomimetic behaviour of a deployable tensegrity footbridge. This footbridge is made of four modules. Each module is composed of pentagonal circuit-pattern including interconnected struts in a ring configuration that can be folded if cable lengths are changed. Various actuator combinations can be selected for deployment. This property is particularly interesting for biomimetic structures since a single shape change can be achieved many ways. Methodologies for deployment and folding of tensegrity footbridge via combinations of spring and cable clustered actuation are described. Analytical predictions are compared with test results of a near-full-scale tensegrity footbridge. Strategies for folding and deployment are different. A continuous cable and spring configuration is feasible for deployment of tensegrity footbridge. Since the deployment behaviour is non-linear and since deformed geometry as well as joint friction influences the deployment pattern, pre-defined control commands cannot provide the desired deployed position. Active deployment control is thus justified

Stiffness and vibration properties of slender tensegrity structures

The stiffness and frequency properties of tensegrity structures are functions of the pre-stress, topology, configuration, and axial stiffness of the elements. The tensegrity structures considered are tensegrity booms, tensegrity grids, and tensegrity power lines. A study has been carried out on the pre-stress design. It includes (i) finding the most flexible directions for different pre-stress levels, (ii) finding the pre-stress pattern which maximizes the first natural frequency. To find the optimum cross-section areas of the elements for triangular prism and Snelson tensegrity booms, an optimization approach is utilized. A constant mass criterion is considered and the genetic algorithm (GA) is used as the optimization method. The stiffness of the triangular prism and Snelson tensegrity booms are modified by introducing actuators. An optimization approach by means of a GA is employed to find the placement of the actuators and their minimum length variations. The results show that the bending stiffness improves significantly, but still an active tensegrity boom is less stiff than a passive truss boom. The GA shows high accuracy in searching the non-structural space. The tensegrity concept is employed to design a novel transmission power line .A tensegrity prism module is selected as the building block. A complete parametric study is performed to investigate the influence of several parameters such as number of modules and their dimensions on the stiffness and frequency of the structure. A general approach is suggested to design the structure considering wind and ice loads. The designed structure has more than 50 times reduction of the electromagnetic field and acceptable deflections under several loading combinations. A study on the first natural frequencies of Snelson, prisms, Micheletti, Marcus and X-frame based tensegrity booms has been carried out. The result shows that the differences in the first natural frequencies of the truss and tensegrity booms are significant and not due to the number of mechanisms or pre-stress levels. The tensegritybooms of the type Snelson with 2 bars and prism with 3 bars have higher frequencies among tensegrity booms.QC 20120904</p

Stiffness and vibration properties of slender tensegrity structures

The stiffness and frequency properties of tensegrity structures are functions of the pre-stress, topology, configuration, and axial stiffness of the elements. The tensegrity structures considered are tensegrity booms, tensegrity grids, and tensegrity power lines. A study has been carried out on the pre-stress design. It includes (i) finding the most flexible directions for different pre-stress levels, (ii) finding the pre-stress pattern which maximizes the first natural frequency. To find the optimum cross-section areas of the elements for triangular prism and Snelson tensegrity booms, an optimization approach is utilized. A constant mass criterion is considered and the genetic algorithm (GA) is used as the optimization method. The stiffness of the triangular prism and Snelson tensegrity booms are modified by introducing actuators. An optimization approach by means of a GA is employed to find the placement of the actuators and their minimum length variations. The results show that the bending stiffness improves significantly, but still an active tensegrity boom is less stiff than a passive truss boom. The GA shows high accuracy in searching the non-structural space. The tensegrity concept is employed to design a novel transmission power line .A tensegrity prism module is selected as the building block. A complete parametric study is performed to investigate the influence of several parameters such as number of modules and their dimensions on the stiffness and frequency of the structure. A general approach is suggested to design the structure considering wind and ice loads. The designed structure has more than 50 times reduction of the electromagnetic field and acceptable deflections under several loading combinations. A study on the first natural frequencies of Snelson, prisms, Micheletti, Marcus and X-frame based tensegrity booms has been carried out. The result shows that the differences in the first natural frequencies of the truss and tensegrity booms are significant and not due to the number of mechanisms or pre-stress levels. The tensegritybooms of the type Snelson with 2 bars and prism with 3 bars have higher frequencies among tensegrity booms.QC 20120904</p

A deployable tensegrity footbridge that connects at mid-span

This paper describes a near full-scale deployable tensegrity footbridge that deploys from both sides and connects at mid-span. Tensegrity structures are pre-stressed structures composed of tension elements (cables) surrounded by compression elements (struts) in equilibrium. The deployment of each bridge half is control by five active continuous cables and is assisted by the release of energy in spring elements that are longer when the bridge is folded. Two topologies (uniform and symmetric) that differ in terms of symmetry of elements are compared with respect to serviceability performance and deployed shape prior to mid-span connection. While both topologies have similar performance, the deployed shape of the symmetric topology results in much smaller pre-control distances between mid-span nodes than the uniform topology. This paper presents a two-stage control methodology for determining control commands for mid-span connection of the two bridge halves. The control methodology determines active cable-length changes based on computational control using a simplified analytical model and then, through measurement of the structural response to cable-length changes. Both halves are successfully connected at the end of deployment. Active control strategies provide effective solutions for completing deployment of multi-degree-of-freedom structures

Active control for mid-span connection of a deployable tensegrity footbridge

Tensegrity structures are spatial self-stressed pin jointed structures where compression components (struts) are surrounded by tension elements. This paper describes a near full-scale deployable tensegrity footbridge that deploys from both sides and connects at mid-span. Two topologies that differ in terms of symmetry of elements and paths of continuous cables are compared. Although both topologies behave similarly with respect to serviceability criteria, there is a significant difference in behavior during deployment. A two-stage control methodology for the connection of both halves of the footbridge is presented. The control methodology determines active cable length changes based on computational control and measurement of the response of the structure during deployment. Both halves are successfully connected at the end of deployment. (C) 2016 Elsevier Ltd. All rights reserved

Mid-span connection of a deployable tensegrity footbridge

This paper describes a near full-scale deployable tensegrity footbridge. Tensegrity structures are pre-stressed structures composed of tension elements (cables) surrounded by compression elements (struts) in equilibrium. Deployment of two bridge halves is assisted by the energy stored in spring elements. Five active cables control the deployment of each half. This paper presents a two-stage control methodology for determining control commands for mid-span connection of the two bridge halves. The control methodology determines active cable length changes based on computational control on a simplified analytical model and including measurement of the structural response to cable-length changes. Both halves are successfully connected at the end of deployment. Active control strategies provide effective solutions for completing deployment of multi-degree-of-freedom structures