TEL AVIV UNIVERSITYTEL AVIV UNIVERSITYFACULTY OF ENGINEERINGFACULTY OF ENGINEERING

SCHOOL OF MECHANICAL ENGINEERINGSCHOOL OF MECHANICAL ENGINEERING

Deployable Tensegrity RobotsDeployable Tensegrity RobotsOffer ShaiOffer Shai

Uri Ben HananUri Ben HananYefim MorYefim Mor

Michael SlovotinMichael SlovotinLeon GinzburgLeon GinzburgAvner Bronfeld Avner Bronfeld

Itay TehoriItay Tehori

TENSEGRITYTENSEGRITYSYSTEMSSYSTEMS

TensegrityTensegrity TenTensegritysegrity = = tensiontension + + integrityintegrity

Tensegrity ElementsTensegrity Elements : :

Cables – sustain only tensionCables – sustain only tension . .

Struts – Sustain only compressionStruts – Sustain only compression . .

The equilibrium between the two The equilibrium between the two types of forces yields static types of forces yields static stabilized system – Self-stressstabilized system – Self-stress..

We are looking for structures thatWe are looking for structures that::

1.1. In generic configuration the self-stress is in In generic configuration the self-stress is in all all the elementsthe elements. .

22 . .There are no There are no failing jointsfailing joints..

33 . .Changing the position of any element canChanging the position of any element can bring to a bring to a singular positionsingular position..

Structures that satisfy the Structures that satisfy the three conditions are three conditions are AssurAssur

structures (graphs) and only structures (graphs) and only themthem..

11 . .Recski A. and Shai O., "Tensegrity Frameworks in the One-Recski A. and Shai O., "Tensegrity Frameworks in the One- Dimensional Space", accepted for publication in Dimensional Space", accepted for publication in European European Journal of Combinatorics Journal of Combinatorics..

2. Servatius B., Shai O. and Whiteley W., “Combinatorial2. Servatius B., Shai O. and Whiteley W., “Combinatorial Characterization of the Assur Graphs from Engineering”, Characterization of the Assur Graphs from Engineering”, accepted for publication in accepted for publication in European Journal of CombinatoricsEuropean Journal of Combinatorics..

33 . .Servatius B., Shai O. and Whiteley W., “Geometric Properties of Servatius B., Shai O. and Whiteley W., “Geometric Properties of Assur Graphs”, submitted to the Assur Graphs”, submitted to the European Journal of European Journal of Combinatorics Combinatorics

Assur StructureAssur Structure

Structure with zero mobility that does not posses a Structure with zero mobility that does not posses a simple sub-structure with the same mobilitysimple sub-structure with the same mobility..

In 2D, all the topologies of all the Assur structures In 2D, all the topologies of all the Assur structures are known (Shai, 2008). In 3D, we hope to have are known (Shai, 2008). In 3D, we hope to have them.them.

Hierarchic Order of Assur Groups in 2DHierarchic Order of Assur Groups in 2D

Assur structureAssur structure + + Driving linksDriving links = Mechanism = Mechanism

Comment: we are in the direction to have the topologies of all Comment: we are in the direction to have the topologies of all the possible topologies of Mechanismsthe possible topologies of Mechanisms..

Next: singularity property of Assur StructuresNext: singularity property of Assur Structures..

Assur structures are a group of statically Assur structures are a group of statically determinate structuresdeterminate structures

Special property – while in a certain configuration Special property – while in a certain configuration applying an external forceapplying an external force

creates a self-stress in all the elementscreates a self-stress in all the elements

The structure will be rigidThe structure will be rigid

Singular point

Dyad- basic Assur Dyad- basic Assur structurestructure Structure in a singular position butStructure in a singular position but

with a failing joint. Thus, not Assur structurewith a failing joint. Thus, not Assur structure

A

Singular point

Triad in singular position alwaysTriad in singular position alwaysStiff- no movementsStiff- no movements

Deployable Tensegrity Structures (Assur)Deployable Tensegrity Structures (Assur)

The device employs all the properties The device employs all the properties introduced beforeintroduced before..

Tensile elements Tensile elements cablescablesCompressed elements -> actuatorsCompressed elements -> actuators

cablecable

strut

Controlling cable and Controlling cable and actuators length actuators length changing structure’s shapechanging structure’s shapewhile remaining stiffwhile remaining stiff

Controlling cable length

motor

It is proved that changing the length of It is proved that changing the length of one elementone element,,a cable, brings the system into a singular positiona cable, brings the system into a singular position . .

2 Plates

3 Cables

3 Actuators

Closed loop control system maintains the tension Closed loop control system maintains the tension during shape modificationsduring shape modifications

The proposed control algorithm uses the Assur structuresThe proposed control algorithm uses the Assur structures

Property – Property – only one cable keeps the tension while allonly one cable keeps the tension while all other elements change their lengthother elements change their length

Load Cell

CableCoilingsystem

ROBOTROBOT

Applying principles to 3D creates a multi Applying principles to 3D creates a multi shape robotshape robot

--Maintain rigidity constantlyMaintain rigidity constantly--Retracts to a compact shapeRetracts to a compact shape

--lightweightlightweight--Multiple geometryMultiple geometry

--ModularModular