Angular Stiffness Research Articles

Development of an Angular Stiffness Sensor to Measure Dental Implant Stability In Vitro.

This investigation aims to develop an angular stiffness sensor intended for measuring dental implant stability in bone. The sensor hardware included a tiny eccentric motor and an accelerometer to measure a flex constant of an implant with its abutment. The sensor software included a mechanics-based model to convert the flex constant to angular stiffness at the implant/abutment junction to indicate the stability. The sensor's accuracy and effectiveness are demonstrated through use of Sawbones slab models that mimic a mandibular premolar section. The models include a Branemark Mk III implant inserted into Sawbones slabs of 5 different densities with a locator abutment. An incremental insertion torque was first recorded while the implant was placed in the Sawbones models. Then benchtop experiments were conducted to measure resonance frequencies and angular stiffness. Results indicated that angular stiffness increased with Sawbones density, showing high correlation with the measured resonance frequency (R=0.977) and the incremental insertion torque (R=0.959). Finally, accuracy of the angular stiffness sensor is calibrated in light of the resonance frequency. Angular stiffness scores 99% and 95% accuracy for Sawbones models mimicking medium cancellous bones with and without a cortical layer, respectively.

Study on the Effect of Cracks in Diaphragm Couplings on the Dynamic Characteristics of Shaft System

Diaphragm couplings are prone to developing diaphragm cracks under prolonged high-speed operating conditions, which can lead to degradation in the performance of the transmission system and affect the dynamics of the shafting system. To investigate the effects of diaphragm cracks on the dynamics of couplings and the shafting system, a finite element model of a diaphragm coupling with a crack failure is established using ANSYS finite element software to analyze the time-varying characteristics of the diaphragm coupling’s angular and radial stiffness. A shaft dynamics model of the diaphragm coupling with a crack is developed using Timoshenko beam elements to analyze the impact of different crack lengths and locations on the dynamics of the shafting system. The validity of the dynamic model for a diaphragm coupling with a crack is verified through a constant speed experiment conducted on a rotor test bench. The results indicate that diaphragm crack failure causes a change in the periodicity of the time-varying stiffness of the diaphragm coupling, leading to a distinct 2× component appearing in the frequency domain of the transmission shaft system.

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.

Determination of rational parameters of the membrane suspension of the gyroscope rotor

Research is presented to determine the rational design parameters of elastic membrane suspensions of mechanical gyroscope rotors. The results obtained make it possible to significantly reduce the labor intensity and cost of predesign research when developing precision instruments. Keywords:gyroscopes, elastic suspension, gyroscope rotor, membrane elastic suspensions, angular stiffness, rotation angle antonvladim@mail.ru

Dynamic identification method for stiffness of duplex suspension clamp based on system modes

This paper proposes a dynamic identification method based on system modes to identify the stiffness of the duplex suspension clamp in the engine hydraulic pipeline. The hammering method measures the free modes of seven groups of duplex suspension clamp-double pipe (DSC-DP) specimens (including the same diameter and different diameters). The results show that the angular stiffness of duplex suspension clamp (DSC) is related to the first and fifth modes, and the line stiffness is related to the second and sixth modes. The dynamic model of the double pipe system with duplex suspension clamp is established by the dynamic stiffness matrix (DSM) method. The approximation function between the theoretical and the experimental frequency of the duplex suspension clamp is established to reverse the stiffness of the duplex suspension clamp. The frequency response function (FRF) of the system theory and the experiment is predicted according to the results of the reverse stiffness. The coincidence of the frequency results verifies the correctness of the proposed method. Moreover, the validity of the stiffness of the duplex suspension clamp is verified by comparing the frequency results obtained from the theory, experiment, and finite element method (FEM) under the free and fixed boundary conditions. The method of identifying the stiffness of duplex suspension clamp and the obtained stiffness in this paper can provide positive guidance for the vibration analysis and modal test of aero-engine pipelines.

An improved method for calculating the lateral and angular stiffness of spline couplings considering parallel misalignment

Spline couplings are commonly applied in transmission systems for their high torque capability and efficiency. However, misalignment between the splines can lead to clearance, wear, and elastic deformation, affecting spline stiffness non-linearly. An improved method for calculating the lateral and angular stiffness of spline couplings considering parallel misalignment is proposed in this paper. The proposed method takes into account the fillet-foundation stiffness and modifies the tooth stiffness by removing the repeated calculation of energy. The accuracy and efficiency of the proposed method are verified through comparison with finite element (FE) results. The effects of spline torque, length, and misalignment on spline stiffness are also discussed. The analysis results show that both lateral and angular stiffness are affected by the phase angle of the parallel misalignment more than the magnitude. Furthermore, the misalignment has a greater influence on the spline stiffness in stages one and two than in stage three. The proposed method provides a more precise and efficient way to calculate spline stiffness under parallel misalignment, which can improve the design and optimization of spline couplings.

Результаты исследований жесткости стабилизаторов и угла крена кузова грузового автомобиля

Analyzes the change in the body roll angle during curvilinear motion according to the calculation and modeling options in the Matlab&Simulink system. The increase in the values of the required relative to the set angular stiffness of the suspension is investigated. The values of the roll angles of the van body are determined taking into account the required and set angular stiffness of the suspension. Mathematical models of the processes of the electromagnetic system of transverse stabilization have been developed in order to analyze the change in the roll angle of the GAZelle NEXT van with an electromagnetic stabilization system and with a conventional stabilizer during curvilinear motion. As a result of the research, it was found body roll reduction using an electromagnetic stabilization system for curvilinear motion. According to the results, the values of the roll angles obtained in the calculations in the mathematical modeling of the angles for the required stiffness, an assessment was made of the error in the deviation of the roll angles for the options. As a result of the curvilinear motion simulation, the effectiveness of using an electromagnetic stabilization system compared to conventional stabilizers was proven based on a comparison of roll angles.

Dynamic characteristics analysis of a coaxial rotor system with shared bearing bore structure

The nonlinear dynamic model of a shared bearing bore-coaxial rotor system was established with nonlinear forces of the rolling bearings and squeeze film dampers considered, Cross coupling frequency was found in cross coupling vibration simulation. Numerical studies were conducted to reveal the mechanism of the coupling vibration for the shared bearing bore-coaxial rotor system. The coupling vibration characteristics and influencing factors of the shared bearing bore-coaxial rotor system were studied. The results show that the coupling vibration is featured by cross-excitation phenomenon and orbit which shows a “circle in circle” pattern. Besides, the angular stiffness of the shared bearing bore has great influences on the coupling vibration. However, the radial stiffness has almost no effect on the coupling vibration.

A Variable Clutch Mechanism for Adjustable Stiffness Actuators Based on Bending and Torsion of Prismatic Beams

Today, a major obstacle to developing locomotion mechanisms that are as safe and energy efficient as living organisms has been overcome with the development of actuators with adjustable stiffness. This work presents an innovative clutch mechanism whose stiffness can be adjusted based on the combined bending and torsion of the prismatic beams. In this way, the stiffness of any rotary actuator can be adjusted with the help of this clutch mechanism. The adjustable clutch mechanism consists of elastic prismatic beams placed in any position in the power transmission unit. The stiffness of the clutch mechanism is controlled by varying the active clutch length of these prismatic elastic beams using an additional actuator. This work is a new version developed to solve the mechanical problems observed in our previous studies using elastic cylindrical beams. Cylindrical beams subjected to dynamic bending have a higher risk of cracking on the cylindrical surface over time. The cross-section of cylindrical beams subjected to bending is very narrow at the point furthest from the center, which bears the greatest load in bending. For this reason, it has been observed that the beams break due to micro-cracks on the surfaces of the cylindrical beams in long-term use. However, the rectangular beam proposed as a solution to this mechanical problem is subject to combined torsion and bending, complicating the analytical solution. In this study, the stiffness variation of an adjustable elastic coupling mechanism depending on the coupling length was obtained with a simplified discrete analytical approach. Torsional and bending stiffness of the prismatic beams were calculated separately, and their sum gave the angular stiffness of the actuator. The analytical results obtained using this simple approach are compared with the experimental and finite element analysis results. The results show that the current design can adjust the stiffness over a wide range and the simple analytical approach gives more accurate results as the clutch length increases.

Tuning mechanical behavior of polymer materials via multi-arm crosslinked network architectures

Crosslinked polymer materials provide tremendous opportunities for delivering unique material properties for a wide variety of applications such as shape-memory and self-healing materials, aerospace materials, and biomedical systems. Most crosslinked polymer networks investigated to date are designed based on covalent or noncovalent crosslinkers that include two-ended connections to the backbone polymer base. In this paper, we investigate the topic of multi-arm crosslinking of polymer materials using a computational platform. We take advantage of molecular dynamics simulations and graph theory to define computational models that describe potential architectures for multi-arm crosslinked polymer networks. We also discuss feasible experimental routes for implementation of these approaches. We investigate how the polymer network architecture affects the mechanical and self-healing behavior of the material. Our results show that the angular stiffness of multi-arm crosslinkers can be adjusted to control the mechanical strength of the overall polymer network. Additionally, using graph theory, we find that the complex connections that exist between the crosslinkers and the backbone polymer chains define the overall connectivity of the polymer network, which in turn dictates the mechanical behavior of the material. Furthermore, we find that increasing the number of crosslinking arms may improve the self-healing behavior, but it can reduce the overall mechanical strength of the polymer network. The findings of this paper can motivate future experimental and data-driven studies to realize more sophisticated crosslinked polymer materials with a large number of degrees of freedom to deliver a variety of tunable properties.

Mechanical Evaluation of Knee Ligament Allografts for Thumb Metacarpophalangeal and Finger Proximal Interphalangeal Reconstruction

Purpose This study evaluated knee collateral ligaments for use as allografts in small joint reconstruction in the hand, specifically the thumb metacarpophalangeal (MCP) joint ulnar collateral ligament (UCL) and the index finger proximal interphalangeal (PIP) joint radial collateral ligament (RCL), and compared them to the current gold standard, tendon autograft. Methods Uniaxial tensile testing was performed on native thumb MCP UCLs and index finger PIP RCLs and 2.5-mm–diameter grafts prepared from hemi-flexor carpi radialis (hemi-FCR) tendons and knee medial collateral ligaments (MCLs) cadaveric allografts. In situ angular testing was performed in thumb MCP and index finger PIP joints. Each MCP/PIP joint was secured to a mechanical testing system and cyclically loaded. The UCL/RCL was resected and reconstructed with either an MCL or hemi-FCR. Cyclic loading was repeated, followed by angular load to failure. Results Uniaxial testing of MCL allografts demonstrated greater ultimate stress, ultimate load, and elastic modulus than hemi-FCR grafts and native UCLs/RCLs. The maximum angular deviation of the reconstructed MCP and PIP joints was not significantly different compared with the intact joint with either an MCL or hemi-FCR graft. In situ load to failure demonstrated no differences in failure torque or angular stiffness between MCPs reconstructed with a hemi-FCR and MCL allograft, whereas reconstructed PIP joints demonstrated improved angular stiffness with an MCL allograft compared with a hemi-FCR. Conclusions Medial collateral ligament allografts demonstrated improved mechanical properties compared with hemi-FCR tendon grafts during uniaxial testing, and grafts performed equivalently in in situ testing of reconstructed thumb/finger joints. Clinical relevance Prepared knee ligament allografts may provide a viable graft material for use in reconstruction of small hand ligaments. This new allograft material avoids the need to harvest a tendon autograft and has a biologic structure similar to native hand ligaments. This study evaluated knee collateral ligaments for use as allografts in small joint reconstruction in the hand, specifically the thumb metacarpophalangeal (MCP) joint ulnar collateral ligament (UCL) and the index finger proximal interphalangeal (PIP) joint radial collateral ligament (RCL), and compared them to the current gold standard, tendon autograft. Uniaxial tensile testing was performed on native thumb MCP UCLs and index finger PIP RCLs and 2.5-mm–diameter grafts prepared from hemi-flexor carpi radialis (hemi-FCR) tendons and knee medial collateral ligaments (MCLs) cadaveric allografts. In situ angular testing was performed in thumb MCP and index finger PIP joints. Each MCP/PIP joint was secured to a mechanical testing system and cyclically loaded. The UCL/RCL was resected and reconstructed with either an MCL or hemi-FCR. Cyclic loading was repeated, followed by angular load to failure. Uniaxial testing of MCL allografts demonstrated greater ultimate stress, ultimate load, and elastic modulus than hemi-FCR grafts and native UCLs/RCLs. The maximum angular deviation of the reconstructed MCP and PIP joints was not significantly different compared with the intact joint with either an MCL or hemi-FCR graft. In situ load to failure demonstrated no differences in failure torque or angular stiffness between MCPs reconstructed with a hemi-FCR and MCL allograft, whereas reconstructed PIP joints demonstrated improved angular stiffness with an MCL allograft compared with a hemi-FCR. Medial collateral ligament allografts demonstrated improved mechanical properties compared with hemi-FCR tendon grafts during uniaxial testing, and grafts performed equivalently in in situ testing of reconstructed thumb/finger joints.

Stiffness evaluation of a novel ankle rehabilitation exoskeleton with a type-variable constraint

This paper presents a novel ankle rehabilitation exoskeleton with two rotational degrees of freedom, which is suitable for dynamical rehabilitation for patients with neurological impairments. Its stiffness performance is assessed in consideration that the interaction between the footplate and the ground may deflect the mechanism away from the desired/predefined motion patterns. The novel design employs a universal-prismatic-universal (U-P-U) joint link, whose constraint type changes between a couple and a line vector during manipulation of the exoskeleton. To conduct a stiffness analysis of such a mechanism with a type-variable constraint – for the first time – a modified screw-based method (SBM) is proposed. Comparisons with the results obtained from finite element analysis verified that, the modified SBM provides reliable estimates of the exoskeleton's stiffness within the complete workspace (covering the constraint-type transition configurations). The stiffness of the exoskeleton is further evaluated by acquiring the minimum/maximum stiffness values, after computing the distribution of the most crucial linear and angular stiffness parameters within the workspace. Moreover, the influence of the architectural parameters on the stiffness properties is considered for further design optimization.

Gravity-Compensation Design Approaches for Flexure-Pivot Time Bases

While flexure time bases have gained significant traction in the watchmaking industry thanks to their high quality factor and monolithic design, maintaining a stable frequency in varying orientations of wrist watches with respect to gravity remains a significant challenge. This results from the fact that the flexures play two roles simultaneously: guiding the oscillating mass along a one-degree-of-freedom pivotal motion, and providing the oscillator’s elastic restoring force. Indeed, varying stress-stiffening effects induced by the varying direction of the weight of the oscillating mass affect the pivot angular stiffness, which impacts its oscillating frequency. In order to address this issue, two design approaches are presented which, when combined, allow to reach the strict chronometric standards of mechanical watches. Firstly, the frequency differences for all vertical positions (i.e., gravity orthogonal to the rotation axis) are mitigated by designing architectures with reduced parasitic center shift, or by offsetting the center of mass (COM) along their axis of symmetry, or both. Secondly, the frequency differences between vertical and horizontal positions (i.e., gravity parallel to the rotation axis) are reduced by offsetting the COM along the rotation axis. The implementation and effectiveness of these approaches are demonstrated by numeric simulations, as well as by experimental measurements performed on watch-scale silicon etched prototypes.

Semi-Analytical Finite Element Approach for 6-DOF Characterizations of PMB Load

A typically new semi-analytical finite element approach has been used to calculate the force and moment of permanent magnet bearing (PMB) in this article. PMB stator and rotor consist of ring-type cylindrical magnets having an axial magnetization. This article focuses on the characterization of magnetic moment, stiffness matrix, model validation, and comparisons of the moment with other simulating software. This article also explains how angular stiffness or resisting magnetic moment of PMB improves with the change of rotor magnet length and positional shift of the rotor.

Joint stiffness of a musculoskeletal bionic leg based on the foot stiffness ellipse model

For the bionic jumping robot, there is contact force between the foot and the environment inevitably. Bionic jumping robots need to interact with the environment for force/position information in a compliant manner. Therefore, it is necessary to analyze the joint stiffness and foot stiffness of a bionic jumping robot. Based on analyzing the muscle arrangement and flexible jumping movement principle of a dog leg, a kind of musculoskeletal leg driven by pneumatic artificial muscles (PAMs) is presented. The centroid trajectory of the bionic leg is planned for jumping. Each joint stiffness is derived by the joint torque, which is changing with PAM inner pressure and joint angular displacement. On the other hand, joint stiffness can be planned by the foot stiffness. A kind of ellipse stiffness model of foot is proposed by analyzing the foot elastic potential energy caused by the contact force, and each joint stiffness of the bionic leg is calculated by the foot stiffness, which is mapping by the Jacobian matrix. The joint angular stiffness is analyzed by changing the foot stiffness ellipse parameters, and the expected joint stiffness of the bionic leg for jumping is planned based on the foot stiffness model. This study will pay a foundation for controlling the joint stiffness to achieve stable jumping of the bionic leg.

Research on the Mechanism of the Stiffness Performance of Rolling Bearings under Wrong Assembly State

In this paper, a quasi-static angular contact ball bearing model, considering assembly accuracy is constructed, while a numerical solution method for bearing stiffness under bad assembly state is established. A 7014C angular contact ball bearing is used as the research object and five groups of different spacer inclinations are designed to imitate the installation error of the spindle bearing. The bearing stiffness performance was comparatively analyzed, according to the five spacers. The effect of preload and rotation speed on bearing stiffness are systematically investigated, considering different parallelism errors, as induced by the spacers. The influence mechanism of the badly assembled bearing on the respective stiffness anisotropy is studied based on the proposed model. The results show that the variations of the inclination between the inner and outer rings of the bearing exhibit a very weak effect on the axial stiffness, while the influence on the radial and angular stiffness is more significant.

Neuromuscular, kinetic and kinematic differences in drop jumping between male adolescents with and without intellectual disability

BackgroundIndividuals with intellectual disability (ID) have lower performance in vertical jumps compared to individuals without ID. Training programmes including drop jump (DJ) exercises to gap this deficit are required. However, there is a lack of knowledge on biomechanical variables may influence DJ performance in young people with ID. Research questionAre there differences in the neuromuscular, kinetic and kinematic parameters in DJ between male adolescents with and without ID (WID and NID, respectively). MethodsThirteen male adolescents WID (Wisk III intelligence quotient: 55.6 ± 11.2) and thirteen age-matched boys NID executed DJ from 30 cm on a force-plate. The vastus lateralis (VL) and biceps femoris (BF) electromyogram (EMG) as well as the knee kinematics and kinetics were obtained. ResultsWID had significantly (p < .05) lower DJ height, knee power, peak angular velocity and stiffness compared to NID. VL activity was higher and BF/VL co-activation was lower in WID than NID. SignificanceThe deficit in DJ performance shown in WID was accompanied with lower power and stiffness, as well as lack of coordination in the lower limb muscles. Improving these variables, with specific and targeted training interventions, may diminish the performance gap with their age-matched counterparts.

Influence of Fit Clearance and Tightening Torque on Contact Characteristics of Spindle–Grinding Wheel Flange Interface

The spindle and grinding wheel flange (GWF) adopt double positioning of a tapered surface and end face. Due to the processing quality, the contact state of the spindle–GWF interface cannot be determined accurately. Based on the theory of finite element and the Yoshimura integral method, an analysis method for the contact stiffness of the spindle–GWF interface was established. In addition, the effects of the spindle–GWF interface’s original clearance and tightening torque on the contact pressure, final contact state and contact stiffness of the spindle–GWF interface were investigated and experimentally verified. It was found that the final contact state of the spindle–GWF changed when the tightening torque increased, especially when the original contact state was tapered contact, and the final contact state changed significantly after assembly. The contact pressure and contact stiffness of the spindle–GWF interface are increased by increasing the tightening torque. The radial stiffness is more affected by the end clearance variation compared to the axial and angular stiffness. When the original contact state is tapered contact, the radial stiffness of the interface is at maximum in three contact states. This research provides theoretical guidance for GWF assembly on gear-grinding machines.

Characterizing the Mechanical Stiffness of Passive-Dynamic Ankle-Foot Orthosis Struts.

People with lower limb impairment can participate in activities such as running with the use of a passive-dynamic ankle-foot orthosis (PD-AFO). Specifically, the Intrepid Dynamic Exoskeletal Orthosis (IDEO) is a PD-AFO design that includes a carbon-fiber strut, which attaches posteriorly to a custom-fabricated tibial cuff and foot plate and acts in parallel with the impaired biological ankle joint to control sagittal and mediolateral motion, while allowing elastic energy storage and return during the stance phase of running. The strut stiffness affects the extent to which the orthosis keeps the impaired biological ankle in a neutral position by controling sagittal and mediolateral motion. The struts are currently manufactured to a thickness that corresponds with one of five stiffness categories (1 = least stiff, 5 = most stiff) and are prescribed to patients based on their body mass and activity level. However, the stiffness values of IDEO carbon-fiber struts have not been systematically determined, and these values can inform dynamic function and biomimetic PD-AFO prescription and design. The PD-AFO strut primarily deflects in the anterior direction (ankle dorsiflexion), and resists deflection in the posterior direction (ankle plantarflexion) during the stance phase of running. Thus, we constructed a custom apparatus and measured strut stiffness for 0.18 radians (10°) of anterior deflection and 0.09 radians (5°) of posterior deflection. We measured the applied moment and strut deflection to compute angular stiffness, the quotient of moment and angle. The strut moment-angle curves for anterior and posterior deflection were well characterized by a linear relationship. The strut stiffness values for categories 1–5 at 0.18 radians (10°) of anterior deflection were 0.73–1.74 kN·m/rad and at 0.09 radians (5°) of posterior deflection were 0.86–2.73 kN·m/rad. Since a PD-AFO strut acts in parallel with the impaired biological ankle, the strut and impaired biological ankle angular stiffness sum to equal total stiffness. Thus, strut stiffness directly affects total ankle joint stiffness, which in turn affects ankle motion and energy storage and return during running. Future research is planned to better understand how use of a running-specific PD-AFO with different strut stiffness affects the biomechanics and metabolic costs of running in people with lower limb impairment.

Optimization of Dual-Mass Flywheel Parameters Based on a Multicondition Simulation Test

A dual-mass flywheel is an important part of an automobile transmission system whose function is to ensure the smooth transmission of engine power to a gearbox. Vehicle vibration and noise are major indicators of vehicle comfort, while dual-mass flywheel technology can preferably solve the comfort problem. Based on the created torsional vibration model, this paper describes the testing of the torsional characteristics under various conditions with an LMS AMESim simulation. The results show that the noise in the cab is fundamentally below 60 dB. The computational formula for the angular stiffness of an arc coil spring is derived, and then the spring angular stiffness is optimized with arithmetic averaging, which reveals an adjusted angular stiffness of 12.8 Nm/°. Additionally, the requirement for the angular acceleration of the WOT input shaft (i.e., being less than 500 rad/s2) is satisfied for various gears. The test results show that the double-mass flywheel can attain a vibration isolation efficiency of around 85%, which more effectively reduces the transmission vibration and noise and improves the vehicle comfort.