Find here a list of tensegrity applications and simulators that can be accessed online to experiment with virtual tensegrities. See also CAD.

Generic Tools Useful In Tensegrity Research

Form-Finding and Static Analysis of Tensegrity Structures

Researchers at Case Western Reserve University (Cleveland, USA) developed a unified approach through Finite Element Analysis (FEA) and unconstrained non-linear programming for form-finding and static analysis of tensegrity structures. The group distributes an NLP package enabling the unconstrained minimization of a smooth nonlinear real-valued function F(X) as per parameters specified in a configuration file. In their words:

"This text describes a mathematical model for both form finding and static analysis of tensegrity structures. The static analysis can be formulated as an unconstrained nonlinear programming problem, where the objective function is the total potential energy and the displacements of the nodal points are the unknowns. A special line element that can show a constant tension for any displacement of its nodes is used to define a prestressed equilibrium configuration. A quasi-Newton method is used, which avoids the evaluation of the tangent stiffness matrix. Download the complete text as MS-Word and PDF documents, computer source codes written in Ada95 and executable codes for Windows. The computer codes generate a script file for AutoCAD."

Push Me Pull Me is an interactive app that enables users to manipulate structural forms, helping to understand how structures respond to being loaded. The mouse is used to simulate a load pressing on the structure and the software simulates how the structure reacts. Push Me Pull Me runs on Java.

Example: gennaroSenatore uploaded a movie showing how to find equilibrium for class-1 tensegrity structures and for a new tensegrity sculpture that is being built at the University of Kent designed by Expedition Engineering. The simulation was done in Push-Me-Pull-Me. (Oct 2014)

Bob Connelly and Bob Terrell enable access to a catalog of several hundred tensegrity structures that are held rigidly together with incompressible struts and inextendable cables connecting point nodes.

According to the site, "These structures are highly symmetric in the sense that there is a symmetry of the structure that takes any node to any other, there is a symmetry of the structure that takes any strut to any other, and there are two classes of cables, where there is a symmetry of the structure that takes any cable to any other in the same class."

Burkhardt hosts a series of Java dynamic viewer applications on his website. Burkhardt is a significant early researcher into tensegrity, and these simulators were advanced for their time. However, newer simulators include physics and shading. Burkhardt provides accurate vertex data sheets that might be useful to other programmers today.

Interactive Application Tensegrity Modeling by Xozzox

From the website: "xozzox design and consulting Services support you in constructing, optimizing, and building tensegrity structures. This includes structure definition, form finding (taking into account the influence of gravity and realistic modelling of strut-cord joints), custom interactive visualizations, etc. We create virtual models and physical Tensegrity Objects using a diverse range of materials for struts and cords. "

Tyler's Springie is a Java 1.1 tensegrity simulator using Java, VRML and POV Ray. It allows simulation of four basic elements:

Struts: Solid members which exert force when compressed

Cables: These are tensile-only members - capable of resisting extension, but not compression

Nodes: Joints, hubs and connectors

Skins: These are membranes, capable of joining the gaps between struts

The simulation is performed in a virtual world with either two or three spatial dimensions. Forces simulated in Springie's universe include compressive and tensile forces, electrostatic attraction and repulsion, elastic collisions, gravity and friction. Models of physical objects can be dynamically edited and manipulated in this environment. Persistence of Springie's models is performed using XML.

Tyler also offers a low-bandwidth version of Springie - known as SprView. It runs as an applet and loads compressed model files from archives over the internet. SprView is intended for embedding tensegrity models in web pages.

Tyler's Tensegrity Simulator simulates the physics of mass-compression-tension structures and allows them to be manipulated interactively in real time from within a browser window. A number of structures are available to view - including some "hexagonal" domes - and some conventional geodesic structures. The physics simulation allows the shapes to be distorted and even smashed up "a process which gives some idea of the stability of the structures."

The simulator is written in Java, requiring version 1.1 or better.

SpringDance by Alan Ferguson was a simple model builder based on Struck, the original EIG app by Gerald de Jong. It was written in Delphi for Windows only. It is no longer supported.

## Online Applications

## Table of Contents

## Generic Tools Useful In Tensegrity Research

## Form-Finding and Static Analysis of Tensegrity Structures

Researchers at Case Western Reserve University (Cleveland, USA) developed a unified approach through Finite Element Analysis (FEA) and unconstrained non-linear programming for form-finding and static analysis of tensegrity structures. The group distributes an NLP package enabling the unconstrained minimization of a smooth nonlinear real-valued function F(X) as per parameters specified in a configuration file. In their words:

"This text describes a mathematical model for both form finding and static analysis of tensegrity structures. The static analysis can be formulated as an unconstrained nonlinear programming problem, where the objective function is the total potential energy and the displacements of the nodal points are the unknowns. A special line element that can show a constant tension for any displacement of its nodes is used to define a prestressed equilibrium configuration. A quasi-Newton method is used, which avoids the evaluation of the tangent stiffness matrix. Download the complete text as MS-Word and PDF documents, computer source codes written in Ada95 and executable codes for Windows. The computer codes generate a script file for AutoCAD."

Link: arcaro.org/tension/

Link: www.arcaro.org/tension/tensegrity/tensegrity.zip

## Finite Element Method Software

Rhinoceros and Ansys Workbench are two software packages mentioned in the article on finite element method analysis.## Tensegrity Models posted To Google Sketchup

Google Sketchup hosts many tensegrity models, a selection below.Links:

Tensegrity Block Parabolic Dome by Spencer Hunter, http://sketchup.google.com/3dwarehouse/details?mid=48af374092827ef97303c1d25b01e311&ct=mdrm

Other Google Sketchup models, http://sketchup.google.com/3dwarehouse/search?q=tensegrity&styp=m&btnG=Search

## Push Me Pull Me Load Simulator

Push Me Pull Me is an interactive app that enables users to manipulate structural forms, helping to understand how structures respond to being loaded. The mouse is used to simulate a load pressing on the structure and the software simulates how the structure reacts. Push Me Pull Me runs on Java.

Example: gennaroSenatore uploaded a movie showing how to find equilibrium for class-1 tensegrity structures and for a new tensegrity sculpture that is being built at the University of Kent designed by Expedition Engineering. The simulation was done in Push-Me-Pull-Me. (Oct 2014)

Links:

Push-Me-Pull-Me Website: http://expeditionworkshed.org/workshed/push-me-pull-me/

## Tensegrity-Specific Tools

## Catalog of Highly Symmetric Tensegrity Structures

Bob Connelly and Bob Terrell enable access to a catalog of several hundred tensegrity structures that are held rigidly together with incompressible struts and inextendable cables connecting point nodes.

According to the site, "These structures are highly symmetric in the sense that there is a symmetry of the structure that takes any node to any other, there is a symmetry of the structure that takes any strut to any other, and there are two classes of cables, where there is a symmetry of the structure that takes any cable to any other in the same class."

Link: Highly Symmetric Tensegrity Structures Introduction

Link: www.math.cornell.edu/~tens/pro.html

## Dynamic Tensegrity Viewers by Burkhardt

Burkhardt hosts a series of Java dynamic viewer applications on his website. Burkhardt is a significant early researcher into tensegrity, and these simulators were advanced for their time. However, newer simulators include physics and shading. Burkhardt provides accurate vertex data sheets that might be useful to other programmers today.

List of Burkhardt's tensegrity viewers: http://www.trip.net/~bobwb/ts/tenseg/tview/index.html

Link: Java1-Based Tensegrity Viewer

Link: Java2D-Based Tensegrity Viewer

## Interactive Application Tensegrity Modeling by Xozzox

From the website: "xozzox design and consulting Services support you in constructing, optimizing, and building tensegrity structures. This includes structure definition, form finding (taking into account the influence of gravity and realistic modelling of strut-cord joints), custom interactive visualizations, etc. We create virtual models and physical Tensegrity Objects using a diverse range of materials for struts and cords. "Link: xozzox.com/objects.html

## Springie Tensegrity Simulator by Tyler

Tyler's Springie is a Java 1.1 tensegrity simulator using Java, VRML and POV Ray. It allows simulation of four basic elements:

Struts: Solid members which exert force when compressedCables: These are tensile-only members - capable of resisting extension, but not compressionNodes: Joints, hubs and connectorsSkins: These are membranes, capable of joining the gaps between strutsThe simulation is performed in a virtual world with either two or three spatial dimensions. Forces simulated in Springie's universe include compressive and tensile forces, electrostatic attraction and repulsion, elastic collisions, gravity and friction. Models of physical objects can be dynamically edited and manipulated in this environment. Persistence of Springie's models is performed using XML.

Tyler also offers a low-bandwidth version of Springie - known as SprView. It runs as an applet and loads compressed model files from archives over the internet. SprView is intended for embedding tensegrity models in web pages.

Link: springie.com

## Tensegrity Simulator by Tyler

Tyler's Tensegrity Simulator simulates the physics of mass-compression-tension structures and allows them to be manipulated interactively in real time from within a browser window. A number of structures are available to view - including some "hexagonal" domes - and some conventional geodesic structures. The physics simulation allows the shapes to be distorted and even smashed up "a process which gives some idea of the stability of the structures."

The simulator is written in Java, requiring version 1.1 or better.

Link: hexdome.com/simulator/

## SpringDance Tensegrity Simulator by Ferguson

SpringDance by Alan Ferguson was a simple model builder based on Struck, the original EIG app by Gerald de Jong. It was written in Delphi for Windows only. It is no longer supported.

## Links and References

Portal To SoftwareOnline SW

Offline SW:Code Aster, Finite Element Method, NASA robotics