Torsional Mechanism Research Articles

Torsional Response of a Two‐Storey Low‐Damage Concrete Wall Test Building

ABSTRACTIn recent earthquakes, poor performance and collapse of buildings attributed to inelastic torsion responses have been reported. The torsional responses of buildings have been extensively studied with analytical models, but large‐scale experiments considering seismic‐induced torsion demands on buildings are rare. A shake‐table test of a two‐storey, low‐damage concrete wall building with strength asymmetry in the plan view was recently conducted, and the response of the building to both unidirectional and bi‐directional loadings at the design‐level earthquake intensity is presented. Analysis of the results includes the global responses of the structural components and the centre of mass for the test building, the strength response of unbonded post‐tensioned walls, the interaction between the translational strengths and torque, the total absorbed energy related to the torsional rotation, and variations in the eccentricities of the centres of rigidity and strength. Furthermore, the seismic response of the test building is explained with a comparison to previously published torsional mechanisms. Key outcomes from the analysis of the test results included: (1) an increase in the strength asymmetry and bi‐directional loading both amplifies the torsional rotations and effects the displacement and strength responses of the structural components along the perimeter of the diaphragm; (2) the comparison to previous torsional mechanisms shows a desirable level of agreement and supports the utilization of these mechanisms to assess the torsional performance of low‐damage wall buildings with irregularities; and (3) despite exhibiting a strong torsional response, the test building with the asymmetric strength configurations still achieved the low‐damage performance targets.

Symmetry breaking and mismatch in the torsional mechanism of ATP synthesis by FOF1-ATP synthase: mathematical number theory proof and its chemical and biological implications.

Can mathematical proofs be employed for the solution of fundamental molecular-level problems in biology? Recently, I mathematically tackled complex mechanistic problems arising during the synthesis of the universal biological currency, adenosine triphosphate (ATP) by the FOF1-ATP synthase, nature's smallest rotary molecular motor, using graph-theoretical and combinatorial approaches for the membrane-bound FO and water-soluble F1 domains of this fascinating molecule (see Nath in Theory Biosci 141:249‒260, 2022 and Theory Biosci 143:217‒227, 2024). In the third part of this trilogy, I investigate another critical aspect of the molecular mechanism-that of coupling between the FO and F1 domains of the ATP synthase mediated by the central γ-subunit of nanometer diameter. According to Nath's torsional mechanism of energy transduction and ATP synthesis the γ-subunit twists during ATP synthesis and the release of stored torsional energy in the central γ-stalk causes conformational changes in the catalytic sites that lead to ATP synthesis, with 1 ATP molecule synthesized per discrete 120° rotation. The twisted γ-subunit breaks the symmetry of the molecule, and its residual torsional strain is shown to readily accommodate any symmetry mismatch existing between FO and F1. A mathematical number theory proof is developed to quantify the extent of symmetry mismatch at any angular position during rotation and derive the conditions for the regaining of symmetry at the end of a 360° rotation. The many chemical and biological implications of the mechanism and the mathematical proof are discussed in detail. Finally, suggestions for further mathematical development of the subject based on ideas from symmetry and group theory have been made. In sum, the answer to the question posed at the beginning of the Abstract is a resounding YES. There exists new, relatively unexplored territory at the interface of mathematics and molecular biology, especially at the level of molecular mechanism. It is hoped that more mathematicians and scientists interested in interdisciplinary work are encouraged to include in their research program approaches of this type-a mathematical proofs-inspired molecular biology-that have the power to lead to new vistas. Such molecular-scale mechanistic problems in biology have proved extraordinarily difficult to solve definitively using conventional experimental, theoretical, and computational approaches.

The Design and Performance Investigation of a Split Four-Track Water-Jet Cleaning Robot for Steel Gate Panels

Steel gates are widely used in river and sea engineering to ensure water retention and flow regulation. Due to the attachment and the alternation of dry and wet environments, water retention easily causes corrosion and destruction, while the attachment is mainly cleaned manually at present. Based on stable adsorption, wall adaptability, and movement ability, a split four-track cleaning robot was developed. The split structure combined with a body swing and torsion mechanism can increase the degree of freedom of attitude adjustment and realize stable crawling of the curved panel. Considering the impact force of the water jet during cleaning, mechanical analysis of robot instability and driving torque on a curved surface was constructed to solve the problem of safe adsorption and flexible movement. A remote control system is constructed to complete the cleaning operation, and the coordination relationship between cleaning and crawling speed is analyzed. The performance test results show that the robot can crawl flexibly and stably on a curved surface, and the crawling speed can be greater than 0.052 m/s when the load is less than 5 kg. A continuous cleaning process has an obvious effect on silt and shellfish attachments, and the robot can meet the actual operational needs. The design process can help in the development of this kind of robot.

Torsional Mechanics of Circular DNA.

Circular DNA found in the cell is actively regulated to an underwound state, with their superhelical density close to σ ∼ - 0.06. While this underwound state is essential to life, how it impacts the torsional mechanical properties of DNA is not fully understood. In this work, we performed simulations to understand the torsional mechanics of circular DNA and validated our results with single-molecule measurements and analytical theory. We found that the torque generated at σ ∼ - 0.06 is near but slightly below that required to melt DNA, significantly decreasing the energy barrier for proteins that interact with melted DNA. Furthermore, supercoiled circular DNA experiences force (tension) and torque that are equally distributed through the DNA contour. We have also extended a previous analytical framework to show how the plectonemic twist persistence length depends on the intrinsic bending persistence length and twist persistence length. Our work establishes a framework for understanding DNA supercoiling and torsional dynamics of circular DNA.

Assessment of Left Ventricular Myocardial Torsion Mechanics in Patients with Heart Failure with Reduced versus Preserved Ejection Fraction Receiving Sacubitril/Valsartan

Assessment of Left Ventricular Myocardial Torsion Mechanics in Patients with Heart Failure with Reduced versus Preserved Ejection Fraction Receiving Sacubitril/Valsartan

Photophysics in Biomembranes: Computational Insight into the Interaction between Lipid Bilayers and Chromophores.

ConspectusLight is ubiquitously available to probe the structure and dynamics of biomolecules and biological tissues. Generally, this cannot be done directly with visible light, because of the absence of absorption by those biomolecules. This problem can be overcome by incorporating organic molecules (chromophores) that show an optical response in the vicinity of those biomolecules. Since those optical properties are strongly dependent on the chromophore's environment, time-resolved spectroscopic studies can provide a wealth of information on biosystems at the molecular scale in a nondestructive way. In this work, we give an overview on the multiscale computational strategy developed by us in the last eight years and prove that theoretical studies and simulations are needed to explain, guide, and predict observations in fluorescence experiments. As we challenge the accepted views on existing probes, we discover unexplored abilities that can discriminate surrounding lipid bilayers and their temperature-dependent as well as solvent-dependent properties. We focus on three archetypal chromophores: diphenylhexatriene (DPH), Laurdan, and azobenzene. Our method shows that conformational changes should not be neglected for the prototype rod-shaped molecule DPH. They determine its position and orientation in a liquid-ordered (Lo) sphingomyelin/cholesterol (SM/Chol) bilayer and are responsible for a strong differentiation of its absorption spectra and fluorescence decay times in dioleoylphosphatidylcholine (DOPC) and dipalmitoylphosphatidylcholine (DPPC) membranes, which are at room temperature in liquid-disordered (Ld) and solid-gel (So) phases, respectively. Thanks to its pronounced first excited state dipole moment, Laurdan has long been known as a solvatochromic probe. Since this molecule has however two conformers, we prove that they exhibit different properties in different lipid membrane phases. We see that the two conformers are only blocked in one phase but not in another. Supported by fluorescence anisotropy decay simulations, Laurdan can therefore be regarded as a molecular rotor. Finally, the conformational versatility of azobenzene in saturated Ld lipid bilayers is simulated, along with its photoisomerization pathways. By means of nonadiabatic QM/MM surface hopping analyses (QM/MM-SH), a dual mechanism is found with a torsional mechanism and a slow conversion for trans-to-cis. For cis-to-trans, simulations show a much higher quantum yield and a so-called "pedal-like" mechanism. The differences are related to the different potential energy surfaces as well as the interactions with the surrounding alkyl chains. When tails of increased length are attached to this probe, cis is pushed toward the polar surface, while trans is pulled toward the center of the membrane.

2-Site versus 3-site models of ATP hydrolysis by F1-ATPase: definitive mathematical proof using combinatorics and conservation equations.

The F1-ATPase enzyme is the smallest-known molecular motor that rotates in 120° steps, driven by the hydrolysis of ATP. It is a multi-subunit enzyme that contains three catalytic sites. A central question is how the elementary chemical reactions that occur in the three sites are coupled to mechanical rotation. Various models and coupling schemes have been formulated in an attempt to answer this question. They can be classified as 2-site (bi-site) models, exemplified by Boyer's binding change mechanism first proposed 50years ago, and 3-site (tri-site) models such as Nath's torsional mechanism, first postulated 25years ago and embellished 1year back. Experimental data collated using diverse approaches have conclusively shown that steady-state ATP hydrolysis by F1-ATPase occurs in tri-site mode. Hence older models have been continually modified to make them conform to the new facts. Here, we have developed a pure mathematical approach based on combinatorics and conservation laws to test if proposed models are 2-site or 3-site. Based on this novel combinatorial approach, we have proved that older and modified models are effectively bi‒site models in that catalysis and rotation in F1-ATPase occurs in these models with only two catalytic sites occupied by bound nucleotide. Hence these models contradict consensus experimental data. The recent 2023 model of ATP hydrolysis by F1-ATPase has been proved to be a true tri-site model based on our novel mathematical approach. Such pure mathematical proofs constitute an important step forward for ATP mechanism. However, in what must be considered an aspect with great scientific potential, the power of such mathematical proofs has not been fully exploited to solve molecular biological problems, in our opinion. We believe that the creative application of pure mathematical proofs (for another example see Nath in Theory Biosci 141:249-260, 2022) can help resolve with finality various longstanding molecular-level issues that arise as a matter of course in the analysis of fundamental biological problems. Such issues have proved extraordinarily difficult to resolve by standard experimental, theoretical, or computational approaches.

Clinical and functional outcome of traumatic osteochondral fracture in adolescent patella.

The objective of this descriptive cross-sectional study was to assess the functional outcomes of adolescents who had undergone internal fixation for patellar post-traumatic OCD fracture from 2019-2021. The injury mechanism was divided into two categories: a) torsional mechanism and b) direct contact injury. All candidates underwent X-ray and MRI/CT scan prior to the surgery to confirm the diagnosis. Operative treatment was open reduction and internal fixation (ORIF) of osteochondral fragment using headless screws. All patients were assessed pre-operatively with knee-ROM/IKDC (International Knee Documentation committee) score and satisfaction score, and postoperatively at one year follow-up. Fourteen patients were selected, with the mean age of 16.1±3.2 years. On one-year follow-up, no difference was noted in ROM when compared to the unaffected limb. The mean satisfaction score was 86±6.3 %. The mean pre-operative-IKDC score was 47.6±5.8 out of 100, whereas on one-year follow-up it was 88.6±2.2 which was statistically significant (p<0.05). Excellent outcomes can be achieved with headless screws for urgent ORIF (next elective list) of the osteochondral fragment.

Nucleosomes play a dual role in regulating transcription dynamics

Transcription has a mechanical component, as the translocation of the transcription machinery or RNA polymerase (RNAP) on DNA or chromatin is dynamically coupled to the chromatin torsion. This posits chromatin mechanics as a possible regulator of eukaryotic transcription, however, the modes and mechanisms of this regulation are elusive. Here, we first take a statistical mechanics approach to model the torsional response of topology-constrained chromatin. Our model recapitulates the experimentally observed weaker torsional stiffness of chromatin compared to bare DNA and proposes structural transitions of nucleosomes into chirally distinct states as the driver of the contrasting torsional mechanics. Coupling chromatin mechanics with RNAP translocation in stochastic simulations, we reveal a complex interplay of DNA supercoiling and nucleosome dynamics in governing RNAP velocity. Nucleosomes play a dual role in controlling the transcription dynamics. The steric barrier aspect of nucleosomes in the gene body counteracts transcription via hindering RNAP motion, whereas the chiral transitions facilitate RNAP motion via driving a low restoring torque upon twisting the DNA. While nucleosomes with low dissociation rates are typically transcriptionally repressive, highly dynamic nucleosomes offer less of a steric barrier and enhance the transcription elongation dynamics of weakly transcribed genes via buffering DNA twist. We use the model to predict transcription-dependent levels of DNA supercoiling in segments of the budding yeast genome that are in accord with available experimental data. The model unveils a paradigm of DNA supercoiling-mediated interaction between genes and makes testable predictions that will guide experimental design.

Optical torque calculations and measurements for DNA torsional studies

The angular optical trap (AOT) is a powerful instrument for measuring the torsional and rotational properties of a biological molecule. Thus far, AOT studies of DNA torsional mechanics have been carried out using a high numerical aperture oil-immersion objective, which permits strong trapping but inevitably introduces spherical aberrations due to the glass-aqueous interface. However, the impact of these aberrations on torque measurements is not fully understood experimentally, partly due to a lack of theoretical guidance. Here, we present a numerical platform based on the finite element method to calculate forces and torques on a trapped quartz cylinder. We have also developed a new experimental method to accurately determine the shift in the trapping position due to the spherical aberrations by using a DNA molecule as a distance ruler. We found that the calculated and measured focal shift ratios are in good agreement. We further determined how the angular trap stiffness depends on the trap height and the cylinder displacement from the trap center and found full agreement between predictions and measurements. As a further verification of the methodology, we showed that DNA torsional properties, which are intrinsic to DNA, could be determined robustly under different trap heights and cylinder displacements. Thus, this work has laid both a theoretical and experimental framework that can be readily extended to investigate the trapping forces and torques exerted on particles with arbitrary shapes and optical properties.

A study on robust design of cruciform torsional beam/cantilever beam

The electro-thermal actuator of a micro-electromechanical system (MEMS) has high power consumption and low response speed. To overcome this shortcoming, a steady state mechanism of cross torsion beam/cantilever beam is proposed in conjunction with the micro-electro-thermal actuator. Through the analysis of the structure and working principle of the cross torsion beam/cantilever beam, as well as the randomness analysis of its design variables and noise factors, the robust design is carried out, and the algorithm program of the stochastic model is written to solve the robust design model. The results show that the robust design method can not only ensure that the cantilever beam will not collapse excessively after the whole mechanism is released from the air but also ensure the robustness of the design solution when the design variables and noise factors change.

Experimental investigation on seismic behaviour of concrete-filled corrugated steel tubes under cyclic torsional loads

Concrete-filled thin-walled galvanized corrugated steel tube (CFCST) is a novel composite member with competitive mechanical behaviour, durability and construction convenience. Several preliminary experimental and numerical works have been conducted on the compressive, flexural, shear, and monotonic torsional performances. However, the unique geometric characteristics of the helical corrugated steel tube (CST) may lead to significant torsional direction-dependent behaviour and complex cyclic torsional working mechanisms, which have not been investigated. This paper therefore presents an experimental investigation of the CFCST under cyclic torsional loads, encompassing the main test variables of member types, diameter-to-thickness ratios, axial compression ratios, and core concrete strengths. The failure modes, hysteretic curves, ductility, energy dissipation capacity, and stiffness degradation are carefully addressed. The cyclic torsional working mechanism of CFCST is discussed through the cyclic test results and strain analysis. The cumulative damage caused by the cyclic torsional loading case is also analysed via the comparisons between the monotonic and cyclic experimental results. The applicability of the existing design methods for the torsional bearing capacity is examined, with specific design suggestions proposed.

Torsional progressive damage mechanisms in 3-D braided carbon fiber/epoxy resin composite tubes

3-D braided composites are a promising material for manufacturing tubular structures. However, a thorough understanding of their damage mechanisms under torsion is required to maximize their potential applications. The present work constructed a multiscale equivalent model, integrating mesoscopic and homogeneous structures to reveal torsional behavior of 3-D braided carbon fiber/epoxy resin composite tubes. The cumulative failure process, spatial stress distribution and interface damage were calculated to illustrate stress transfer and damage initiation and propagation. It is found that stress varies on the surface and internally within the representative unit cell (RUC). The yarns experience both axial tension parallel to the direction of torsion and axial compression perpendicular to the direction of torsion. The stress difference between them leads to damage initiation and propagation. Interfacial cracking as main damage mode hinders the stress transfer between resin and fiber bundles. The results show that the braided yarn path, axial stress dispersion in two directions and localization of damage effectively impede the torsional damage propagation.

Interactive mechanism of bending and torsion and springback prediction method for spatial tubes

Spatial tubes, known for their attributes of lightweight, large section modulus, and high strength, find extensive applications across various industries. Nevertheless, in the course of forming spatial tubes, springback poses a significant challenge in enhancing the forming quality. In this paper, the bound approximations for the combined bending and twisting of circular tubes employing the power-hardening material model are deduced innovatively. Drawing upon the boundary approximation theory, the interactive mechanism of bending and twisting is meticulously examined. The forming principles of the four-axis free-bending (FFB) are expounded. Concurrently, an innovative method for predicting springback, based on the established bound approximations within the framework of total plasticity theory, is introduced, which holds significant importance for addressing combined bending and torsion issues in engineering applications. Noteworthy findings reveal that the interaction between bending and twisting exhibits a predominant sensitivity to the hardening exponent n and the higher n the material has, the less pronounced the interaction will be. The augmentation of torsion contributes to mitigating the springback resulting from bending, and conversely, a similar effect is observed with the influence of bending on torsion. These findings contribute significantly to the understanding of combined bending and twisting problems. The proportionality coefficients of bending and twisting, denoted as λM and λT, are defined and investigated via comprehensive finite element (FE) simulations. Furthermore, this method of springback prediction is corroborated by FE simulations as well as the FFB experiments.

The vibration isolation proprieties of an X-shaped structure with enhanced high-static and low-dynamic stiffness via torsional magnetic negative stiffness mechanism

The vibration isolation proprieties of an X-shaped structure with enhanced high-static and low-dynamic stiffness via torsional magnetic negative stiffness mechanism

Constrained Origami Artificial Muscle-Driven Robotic Manipulator Capable of Coordinating Twisting and Grasping Motions for Object Manipulation.

Grasping and twisting motions are vital when manipulating objects due to their fundamental role in enabling precision, adaptability, and effective interaction. However, few studies in soft robotics exploiting artificial muscles have achieved object manipulation in situ through the coordination of twisting and grasping motions akin to our forearm and hand's capabilities. Especially, when using the same artificial muscle module to achieve these two motions will greatly simplify the manufacturing and control complexity. Here, we introduce identical origami artificial muscle modules (OAMMs) subjected to distinct end constraints into the design of the robotic manipulator, allowing it to achieve independent grasping and twisting motions to achieve effective, precise object manipulation. Applying different end constraints to the identical OAMMs yields distinct motions at their ends, where utilizing a fixed end and a sliding end realizes pure translation, while opting for a fixed end and a rotating end enables pure rotation. The differentially constrained OAMMs then serve as soft actuators for the manipulator's torsional mechanism and grasping mechanism to accomplish independent, controllable twisting and grasping motions. The coordination of twisting and grasping motions finally enables the manipulator to complete various tasks, including installing a light bubble, pouring the water from a lidded bottle into a cup, and sorting and stacking puzzle blocks. Our study pioneers the utilization of OAMMs for precise and versatile object manipulation through the coordination of independent twisting and grasping motions.

Coupling and biological free-energy transduction processes as a bridge between physics and life: Molecular-level instantiation of Ervin Bauer’s pioneering concepts in biological thermodynamics

The nonequilibrium coupled processes of oxidation and ATP synthesis in the biological process of oxidative phosphorylation (OXPHOS) are fundamental to all life on our planet. These steady-state energy transduction processes ‒ coupled by proton and anion/counter-cation concentration gradients in the OXPHOS pathway ‒ generate ∼95 % of the ATP requirement of aerobic systems for cellular function. The rapid energy cycling and homeostasis of metabolites involved in this coupling are shown to be responsible for maintenance and regulation of stable nonequilibrium states, the latter first postulated in pioneering biothermodynamics work by Ervin Bauer between 1920 and 1935. How exactly does this occur? This is shown to be answered by molecular considerations arising from Nath’s torsional mechanism of ATP synthesis and two-ion theory of energy coupling developed in 25 years of research work on the subject. A fresh analysis of the biological thermodynamics of coupling that goes beyond the previous work of Stucki and others and shows how the system functions at the molecular level has been carried out. Thermodynamic parameters, such as the overall degree of coupling, q of the coupled system are evaluated for the state 4 to state 3 transition in animal mitochondria with succinate as substrate. The actual or operative P to O ratio, the efficiency of the coupled reactions, η, and the Gibbs energy dissipation, Φ have been calculated and shown to be in good agreement with experimental data. Novel mechanistic insights arising from the above have been discussed. A fourth law/principle of thermodynamics is formulated for a sub-class of physical and biological systems. The critical importance of constraints and time-varying boundary conditions for function and regulation is discussed in detail. Dynamic internal structural changes essential for torsional energy storage within the γ-subunit in a single molecule of the FOF1-ATP synthase and its transduction have been highlighted. These results provide a molecular-level instantiation of Ervin Bauer’s pioneering concepts in biological thermodynamics.

Cardiac MRI feature-tracking-derived torsion mechanics in systolic and diastolic dysfunction in systemic light-chain cardiac amyloidosis

To describe the myocardial torsion mechanics in cardiac amyloidosis (CA), and evaluate the correlations between left ventricle (LV) torsion mechanics and conventional parameters using cardiac magnetic resonance imaging feature tracking (CMR-FT). One hundred and thirty-nine patients with light-chain CA (AL-CA) were divided into three groups: group 1 with preserved systolic function (LV ejection fraction [LVEF] ≥50%, n=55), group 2 with mildly reduced systolic function (40%≤LVEF <50%, n=51), and group 3 with reduced systolic function (LVEF <40%, n=33), and compared with age- and gender-matched healthy controls (n=26). All patients underwent cine imaging and late gadolinium-enhancement (LGE). Cine images were analysed offline using CMR-FT to estimate torsion parameters. Global torsion, base-mid torsion, and peak diastolic torsion rate (diasTR) were significantly impaired in patients with preserved systolic function (p<0.05 for all), whereas mid-apex torsion and peak systolic torsion rate (sysTR) were preserved (p>0.05 for both) compared with healthy controls. In patients with mildly reduced systolic function, global torsion and base-mid torsion were lower compared to those with preserved systolic function (p<0.05 for both), while mid-apex torsion, sysTR, and diasTR were preserved (p>0.05 for all). In patients with reduced systolic function, only sysTR was significantly worse compared with mildly reduced systolic function (p<0.05). At multivariable analysis, right ventricle (RV) end-systolic volume RVESV index and NYHA class were independently related to global torsion, whereas LVEF was independently related to sysTR. RV ejection fraction (RVEF) was independently related to diasTR. LV global torsion performed well (AUC 0.71; 95% confidence interval [CI]: 0.61, 0.77) in discriminating transmural from non-transmural LGE in AL-CA patients. LV torsion mechanics derived by CMR-FT could help to monitor LV systolic and diastolic function in AL-CA patients and function as a new imaging marker for LV dysfunction and LGE transmurality.

Walking Motion of Articulated Mobile Robot with Torsion Mechanism

Walking Motion of Articulated Mobile Robot with Torsion Mechanism

Study on torsional response and ultimate loading of unbonded flexible risers under corrosion defects

During the process of deep-sea oil and gas exploitation, unbonded flexible risers (UFRs) are corroded by CO2 and other media over long periods of time, which causes serious damage to the tensile armor layers and threatens the safety of the UFRs in service. To study the effects of torsional response, ultimate loading, and failure mode on UFRs after corrosion, and to reveal the torsional failure mechanism of the UFR while considering corrosion defects, an 8-layer UFR torsional response model is established in this paper. Local bending of the UFR and lateral buckling failure of the inner tensile armor layer occur under counterclockwise ultimate torsion, whereas strength failure of the inner tensile armor layer occurs under clockwise torsion. When the degree of corrosion is 0.4 mm, the counterclockwise torsional stiffness of thickness corrosion, width corrosion, and combined corrosion decreases by 27.6%, 10.8%, and 28.4%, and the ultimate loading of counterclockwise torsion for thickness corrosion, width corrosion, and combined corrosion decreases by 37%, 13.4%, and 39.3%, respectively. Therefore, the influence of thickness corrosion and combined corrosion on the torsional response of UFRs is worthy of further attention.