The equilibrium and form-finding of general tensegrity systems with rigid bodies

Ma, Shuo; Chen, Muhao Texas A&m University; Peng, Zhangli; Yuan, Xiying; Skelton, Robert E.

doi:10.1016/j.engstruct.2022.114618

Cited by 14 publications

(7 citation statements)

References 43 publications

(52 reference statements)

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“…where γ = [γ 1 , • • • , γ nc ] T collects the force densities and ⊕ means the direct sum of matrices. Expression (29) shows the system's generalized tension force is linear in the cables' force densities. This notable property is also found in the dynamics framework for "bars-only" tensegrities by Skelton et al [25,26].…”

Section: Tensile Cablesmentioning

confidence: 99%

“…Expression (29) allows any constitutive laws of the cables. In the following, we adopt a common practice by assuming linear stiffness, linear damping, and a slacking behavior.…”

Section: Tensile Cablesmentioning

confidence: 99%

“…Therefore, in the "bodies-and-bars" setting of tensegrity structures, it would be beneficial to retain the non-minimal formulations of rigid bars. In line with this thought, a recent work [29] combines the nodal coordinates of rigid bars and minimal coordinates of rigid bodies to formulate static equilibrium equations for form-finding problems. However, it has not developed dynamic equations, and the introduction of minimal coordinates can have "contaminating" effects on the formulations.…”

Section: Introductionmentioning

confidence: 99%

“…However, it has not developed dynamic equations, and the introduction of minimal coordinates can have "contaminating" effects on the formulations. For example, Euler angles are used as a minimal description of orientations [29], so trigonometric functions are unavoidable.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

A Unified Framework for Dynamic Analysis of Tensegrity Structures with Arbitrary Rigid Bodies and Rigid Bars

Luo¹,

Wu²,

Xu³

2022

Preprint

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This paper develops a unified framework to study the dynamics of tensegrity systems with any arbitrary rigid bodies and rigid bars. The natural coordinates are adopted as a completely non-minimal modeling approach to describe both rigid bodies and rigid bars in terms of different combinations of basic points and base vectors. Various coordinate combinations are then unified into polymorphic expressions that succinctly encompass Class-1-to-k tensegrities. Then, the Lagranged'Alembert principle is employed to derive the dynamic equation, which has a constant mass matrix and is free from trigonometric functions as well as centrifugal and Coriolis terms. For numerical analysis of nonlinear dynamics, a modified symplectic integration scheme is derived, accommodating non-conservative forces and boundary conditions. Additionally, formulations for statics and linearized dynamics around static equilibrium states are derived to help determine cable actuation values and calculate natural frequencies and mode shapes, which are commonly needed for structural analyses. Numerical examples are given to demonstrate the proposed approach's abilities in modeling tensegrity structures composed of Class-1-to-k modules and conducting dynamic simulations with complex conditions, including slack cables, gravity loads, seismic grounds, and cable-based deployments. Finally, two novel designs of tensegrity structures exemplify new ways to create multi-functional composite structures.

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Section: Tensile Cablesmentioning

confidence: 99%

“…Expression (29) allows any constitutive laws of the cables. In the following, we adopt a common practice by assuming linear stiffness, linear damping, and a slacking behavior.…”

Section: Tensile Cablesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A Unified Framework for Dynamic Analysis of Tensegrity Structures with Arbitrary Rigid Bodies and Rigid Bars

Luo¹,

Wu²,

Xu³

2022

Preprint

View full text Add to dashboard Cite

show abstract

“…According to the numerical examples, the form-finding calculating process can be improved the convergence speed and optimisation precision through the dynamic relaxation (DR) method. Besides, the algorithms which transformed the form-finding problems into non-linear and linear optimisation problems have become a significant constituent part of form-finding methods [6][7][8][9][10][11][12]. But most of the formfinding approaches have not involved the noise-suppressing during the form-finding process.…”

Section: Introductionmentioning

confidence: 99%

The dynamic relaxation form finding method aided with advanced recurrent neural network

Zhao

Sun

Liu

et al. 2023

CAAI Trans on Intel Tech

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How to establish a self-equilibrium configuration is vital for further kinematics and dynamics analyses of tensegrity mechanism. In this study, for investigating tensegrity formfinding problems, a concise and efficient dynamic relaxation-noise tolerant zeroing neural network (DR-NTZNN) form-finding algorithm is established through analysing the physical properties of tensegrity structures. In addition, the non-linear constrained optimisation problem which transformed from the form-finding problem is solved by a sequential quadratic programming algorithm. Moreover, the noise may produce in the form-finding process that includes the round-off errors which are brought by the approximate matrix and restart point calculating course, disturbance caused by external force and manufacturing error when constructing a tensegrity structure. Hence, for the purpose of suppressing the noise, a noise tolerant zeroing neural network is presented to solve the search direction, which can endow the anti-noise capability to the form-finding model and enhance the calculation capability. Besides, the dynamic relaxation method is contributed to seek the nodal coordinates rapidly when the search direction is acquired. The numerical results show the form-finding model has a huge capability for high-dimensional free form cable-strut mechanisms with complicated topology. Eventually, comparing with other existing form-finding methods, the contrast simulations reveal the excellent antinoise performance and calculation capacity of DR-NTZNN form-finding algorithm.

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A Tensegrity Joint for Low‐Inertia, Compact, and Compliant Soft Manipulators

Hao

Wang

Song

et al. 2023

Advanced Intelligent Systems

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Compact, low‐inertia, and soft compliant robotic joint mechanisms are in great demand for ensuring safe interactions in human–robot collaborative tasks. Tensegrity, of which the structural integrity is constrained by tension, does not involve static/sliding friction among the rigid components. However, this mechanical stability is very susceptible to actuation errors. It requires complex kinematics modeling and sophisticated control model with sensing feedback. Herein, a low‐inertia tensegrity joint that is covered/protected by a fiber Bragg grating (FBG)‐embedded silicone sheath is proposed, with the aim to reinforce the joint motion stability and enable self‐contained sensing feedback. A learning‐based closed‐loop controller is also designed and trained with the proper joint configurations selected by a two‐step sampling method. Both the kinematics and static equilibriums of such configurations can be well satisfied. The experiments demonstrate that the joint can follow paths accurately in 2D by compensating manipulation error shortly under the closed‐loop control. The joint stiffness can also be varied against the external/impulsive disturbances. It can be foreseen that this primitive robot joint component with 2 degrees of freedom (DoFs) can provide safe, compliant interaction with human, for which a simple test of maneuvering a portable ultrasound probe (≈210 g) for abdominal imaging is demonstrated.

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The equilibrium and form-finding of general tensegrity systems with rigid bodies

Cited by 14 publications

References 43 publications

A Unified Framework for Dynamic Analysis of Tensegrity Structures with Arbitrary Rigid Bodies and Rigid Bars

A Unified Framework for Dynamic Analysis of Tensegrity Structures with Arbitrary Rigid Bodies and Rigid Bars

The dynamic relaxation form finding method aided with advanced recurrent neural network

A Tensegrity Joint for Low‐Inertia, Compact, and Compliant Soft Manipulators

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