Equilibrium conditions of a tensegrity structure

Williamson, D.; Skelton, Robert E.; Han, Jeongheon

doi:10.1016/s0020-7683(03)00400-1

Cited by 44 publications

(23 citation statements)

References 11 publications

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“…The traditional formulation based on director cosines (Sultan and Skelton, 2003) produces concise representations, but introduces trigonometric expressions that complicate the resulting constraints. On the other hand, vector-based representations enlarge the space, but produce simple constraints, which leads to a simpler mathematical treatment (Williamson et al, 2003). This paper follows the second approach since it is in agreement with the philosophy of the CuikSuite , the software package in which we integrated the tools described herein.…”

Section: Problem Formalizationmentioning

confidence: 80%

Path planning for active tensegrity structures

Porta

Hernández-Juan

2016

International Journal of Solids and Structures

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This paper presents a path planning method for actuated tensegrity structures with quasi-static motion. The valid configurations for such structures lay on an equilibrium manifold, which is implicitly defined by a set of kinematic and static constraints. The exploration of this manifold is difficult with standard methods due to the lack of a global parametrization. Thus, this paper proposes the use of techniques with roots in differential geometry to define an atlas, i.e., a set of coordinated local parameterizations of the equilibrium manifold. This atlas is exploited to define a rapidly-exploring random tree, which efficiently finds valid paths between configurations. However, these paths are typically long and jerky and, therefore, this paper also introduces a procedure to reduce their control effort. A variety of test cases are presented to empirically evaluate the proposed method.

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Section: Problem Formalizationmentioning

confidence: 80%

Path planning for active tensegrity structures

Porta

Hernández-Juan

2016

International Journal of Solids and Structures

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“…where ⊗ is the Kronecker product symbol (Williamson et al 2003) and I 3 is the third-rank identity matrix. The linear stiffness matrix K M is positive semi-definite for all tensegrities consisting of conventional elements with positive axial stiffness, or in other words,…”

Section: (C) Super-stability Conditionsmentioning

confidence: 99%

Self-equilibrium and super-stability of truncated regular polyhedral tensegrity structures: a unified analytical solution

Zhang

Cao

et al. 2012

Proc. R. Soc. A.

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In spite of their great importance and numerous applications in many civil, aerospace and biological systems, our understanding of tensegrity structures is still quite preliminary, fragmented and incomplete. Here we establish a unified closed-form analytical solution for the necessary and sufficient condition that ensures the existence of self-equilibrated and super-stable states for truncated regular polyhedral tensegrity structures, including truncated tetrahedral, cubic, octahedral, dodecahedral and icosahedral tensegrities.

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“…In addition to guaranteeing asymptotic satisfaction of the constraints, the resulting modes of the constraint dynamics (20) should not be so fast as to cause numerical problems as a result of the differential equations becoming too "stiff". Now, from (17), we havë…”

Section: Theorem 22 the Constraint Forcesf K Which Act On The Unit mentioning

confidence: 99%

“…A more fundamental problem is to be able to establish conditions under which the steady state nonlinear input-output function H is invertible. Some recent results [20] may provide further insights into this problem. A related problem is to be able to analyse 'smoothness' properties of H in order to provide a better understand as to why the neural network provided such an accurate approximation of H −1 .…”

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confidence: 90%