Tensegrity Ten segrity = tension + integrity Tensegrity Elements: Cables – sustain only tension. Struts – Sustain only compression. The equilibrium between the two types of forces yields static stabilized system – Self-stress.
We are looking for structures that: 1. In generic configuration the self-stress is in all the elements . 2. There are no failing joints. 3. Changing the position of any element can bring to a singular position.
Structures that satisfy the three conditions are Assur structures (graphs) and only them. 1. Recski A. and Shai O., "Tensegrity Frameworks in the One- Dimensional Space", accepted for publication in European Journal of Combinatorics . 2. Servatius B., Shai O. and Whiteley W., “Combinatorial Characterization of the Assur Graphs from Engineering”, accepted for publication in European Journal of Combinatorics . 3. Servatius B., Shai O. and Whiteley W., “Geometric Properties of Assur Graphs”, submitted to the European Journal of Combinatorics
Assur Structure Structure with zero mobility that does not posses a simple sub-structure with the same mobility. In 2D, all the topologies of all the Assur structures are known (Shai, 2008). In 3D, we hope to have them.
Assur structure + Driving links = Mechanism Comment: we are in the direction to have the topologies of all the possible topologies of Mechanisms. Next: singularity property of Assur Structures.
Assur structures are a group of statically determinate structures Special property – while in a certain configuration applying an external force creates a self-stress in all the elements The structure will be rigid Singular point
Dyad- basic Assur structure Structure in a singular position but with a failing joint. Thus, not Assur structure A Triad in singular position always Stiff- no movements Singular point
Deployable Tensegrity Structures (Assur) The device employs all the properties introduced before.
Tensile elements cables Compressed elements -> actuators Controlling cable and actuators length changing structure’s shape while remaining stiff cable cable strut Controlling cable length motor
It is proved that changing the length of one element, a cable, brings the system into a singular position.
2 Plates 3 Cables 3 Actuators Closed loop control system maintains the tension during shape modifications
The proposed control algorithm uses the Assur structures Property – only one cable keeps the tension while all other elements change their length Load Cell Cable Coiling system
ROBOT Applying principles to 3D creates a multi shape robot -Maintain rigidity constantly -Retracts to a compact shape -lightweight -Multiple geometry -Modular