Statically Balanced Tensegrity Mechanisms By Schenk
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The document summarizes a graduation colloquium on the theory and design of statically balanced tensegrity mechanisms. The objectives of the graduation project were to develop a fundamental understanding of zero stiffness tensegrity structures and generate design guidelines through theoretical research and building a demonstration model. Key findings included that zero stiffness requires the directions of conventional members to lie on a conic, and the number of zero stiffness modes is equal to 6 minus the number of unique bar directions on the conic. A prototype tensegrity structure was designed and built to demonstrate the properties of a statically balanced mechanism.
Statically Balanced Tensegrity Mechanisms By Schenk
- 1. Theory and Design of Statically Balanced Tensegrity Mechanisms Graduation Colloquium Mark Schenk Department of BioMechanical Engineering Faculty of Mechanical, Maritime and Materials Engineering Exam Committee prof. dr. ir. Peter Wieringa dr. ir. Just Herder dr. Simon Guest dr. ir. Arend Schwab
- 2. Contents Introduction tensegrity structures static balancing MSc. thesis objectives Zero Stiffness Tensegrity Structures (zero) stiffness Prototype Conclusions statically balanced tensegrity mechanisms
- 3. Tensegrity Structures – introduction & examples – Special class of bar framework pin-jointed prestressed pure compression, pure tension -> cables and bars pretension required for stiffness -> tens ile int egrity = tensegrity -> delicate balance Needle Tower II , 1969 Kröller-Müller Museum
- 4. Tensegrity Structures – engineering applications – Engineering applications: obvious architectural / design appeal light-weight stowable / deployable biologically inspired
- 5. Static Balancing – introduction & applications – Static Balancing = continuous equilibrium = neutral stability = zero stiffness (Herder 2001) Energy-free / energy-efficient design e.g. rehabilitation, robotics
- 6. Static Balancing – zero-free-length springs – Zero-free-length springs tension is proportional to length normal pretensioned zero-free-length
- 7. Static Balancing – design methodology & limitations – Current design methodology basic designs are extended by means of modification rules complex results possible Limitations ad hoc solutions, no real generic understanding bottom-up vs. top-down “ limited” to 2D
- 8. Statically Balanced Tensegrity Mechanisms – a combination of two fields – tensegrity structures + static balancing = zero stiffness tensegrity structures = statically balanced tensegrity mechanisms Previous examples: (Herder, 2001)
- 9. Statically Balanced Tensegrity Mechanisms – applications & relevance – Totally new class of structures / mechanisms robotics, rehabilitation, deployable structures Academic interest new insights for static balancing -> generic theory? tensegrities <-> 3D pin-jointed structures
- 10. Graduation project – title & objective – Title “ Theory and Design of Statically Balanced Tensegrity Mechanisms.” Objectives fundamental understanding zero stiffness tensegrities -> generic description of static balancing -> develop design guidelines build demonstration model
- 11. Graduation project – research approach – Theoretical research : zero stiffness Stiffness of tensegrity structures engineers structural engineering mathematicians rigidity theory combination
- 12. Stiffness of Structures – tangent stiffness matrix – Stiffness of a structure counting rules (e.g. Maxwell’s rule) tensegrity is prestressed tangent stiffness matrix Tangent stiffness matrix displacements d and forces F formulations -> zero-free-length springs
- 13. Tangent Stiffness Matrix - zero stiffness - Zero stiffness Two components: both components are zero components cancel out
- 14. Zero Stiffness Tensegrity – conventional structures – Conventional interpretation internal mechanisms (undesirable) stabilized by self-stress P δ L/2 L/2
- 15. Zero Stiffness Tensegrity – structures with zero-free-length springs – Zero stiffness tensegrity structures affine transformations (scaling/shear) preserve length of conventional members
- 16. Zero Stiffness Tensegrity - example structure - top side
- 17. Zero Stiffness Tensegrity – length-preserving affine & conic – Length-preserving affine transformation iff all bar directions lie on conic infinitesimal -> finite only zero-stiffness modes Number of zero-stiffness modes no. of unique bar directions k on conic k ≥ 6 : zero-stiffness modes = 1 k < 6 : zero-stiffness modes = 6 - k
- 18. Zero Stiffness Babytoy Babytoy 6 bars 3 bar directions direction lie on conic k ≥ 6 : zero-stiffness modes = 1 k < 6 : zero-stiffness modes = 6 - k 3 zero-stiffness modes
- 19. Prototype Structure - description - Prototype structure demonstrate properties from structure to mechanism Prototype design classic tensegrity structure no zero-free-length springs 3 bars, 9 springs -> 3 springs on each bar
- 20. Prototype Structure - final model - … but, there is a lot of friction
- 21. Conclusions Theory and Design of Statically Balanced Tensegrity Mechanisms theory of statically balanced tensegrity mechanisms length-preserving affine transformations conventional member directions on conic finite mechanisms design of a statically balanced tensegrity mechanism working prototype
- 22. Questions
- 23. Previous examples: (Herder, 2001) 0 @ ® ¯ ° ± ² µ ^ K b l a b l i e b 1 A