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To achieve variable stiffness, this paper aims to design a flexible actuator with variable stiffness by using the magnetorheological effect of magnetorheological fluid. The variable stiffness actuator can well meet the safety requirements of human–robot interaction and be more adaptable to unknown or complex environments. The variable stiffness actuator designed in this study can realize the continuous and controllable change of stiffness compared with the existing actuator.

The principle of variable stiffness actuator is illustrated in detail; the three-dimensional model and mechanical model of the flexible actuator are provided. The magnetic field distribution of the actuator coil is analyzed, and the dynamic model of the actuator is provided.

Output torque test suggests that the magnetorheological fluid variable stiffness actuator (VSAMF) can output a stable torque which meets the designing requirements of the test; sinusoidal follow-up test shows that VSAMF can implement sinusoidal follow-up; variable stiffness test shows that VSAMF can achieve real-time variable stiffness adjustment; the crash test suggests that VSAMF can well protect machines when meeting obstacles.

In this paper, a new variable stiffness joint is proposed through changing the current to change the performance of the stiffness, and it can realize the continuous and controllable change of stiffness.

The purpose of this paper is to propose an simple and efficient stiffness model for line contact under elastohydrodynamic lubrication (EHL) and to investigate the gear meshing stiffness by the proposed model.

The method combines the surface contact stiffness and film stiffness as EHL contact stiffness. The EHL contact stiffness can be calculated by the external load and displacement of the load action point. The displacement is the sum of deformation of the film and contact surface and is equal to the distance of the mutual approach of two contact bodies.

The conclusion is drawn that the contact stiffness calculated by the proposed model is smaller than that by the minimum film model and larger than that by the mean film model. It is also concluded that the gear meshing stiffness under EHL is slightly smaller than that under dry contact.

The EHL contact stiffness can be obtained by the increment of external load and mutual approach directly. The calculation of oil film stiffness and surface contact stiffness separately is avoided.

The peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-11-2019-0465

The purpose of this paper is to study the behavior of negative stiffness beams when arranged in a honeycomb configuration and to compare the energy absorption capacity of these negative stiffness honeycombs with regular honeycombs of equivalent relative densities.

A negative stiffness honeycomb is fabricated in nylon 11 using selective laser sintering. Its force-displacement behavior is simulated with finite element analysis and experimentally evaluated under quasi-static displacement loading. Similarly, a hexagonal honeycomb of equivalent relative density is also fabricated and tested. The energy absorbed for both specimens is computed from the resulting force-displacement curves. The beam geometry of the negative stiffness honeycomb is optimized for maximum energy absorption per unit mass of material.

Negative stiffness honeycombs exhibit relatively large positive stiffness, followed by a region of plateau stress as the cell walls buckle, similar to regular hexagonal honeycombs, but unlike regular honeycombs, they demonstrate full recovery after compression. Representative specimens are found to absorb about 65 per cent of the energy incident on them. Optimizing the negative stiffness beam geometry can result in energy-absorbing capacities comparable to regular honeycombs of similar relative densities.

The honeycombs were subject to quasi-static displacement loading. To study shock isolation under impact loads, force-controlled loading is desirable. However, the energy absorption performance of the negative stiffness honeycombs is expected to improve under force-controlled conditions. Additional experimentation is needed to investigate the rate sensitivity of the force-displacement behavior of the negative stiffness honeycombs, and specimens with various geometries should be investigated.

The findings of this study indicate that recoverable energy absorption is possible using negative stiffness honeycombs without sacrificing the high energy-absorbing capacity of regular honeycombs. The honeycombs can find usefulness in a number of unique applications requiring recoverable shock isolation, such as bumpers, helmets and other personal protection devices. A patent application has been filed for the negative stiffness honeycomb design.

This study aims to propose a new variable stiffness robot joint (VSR-joint) for operating safely. More and more variable stiffness actuators are being designed and implemented because of their ability to minimize large forces due to shocks, to safely interact with the user and their ability to store and release energy in passive elastic elements.

The design of VSR-joint is compact and integrated highly and the operating is simply. The mechanics, the principle of operation and the model of the VSR-joint are proposed. The principle of operation of VSR-joint is based on a lever arm mechanism with a continuously regulated pivot point. The VSR-joint features a highly dynamic stiffness adjustment along with a mechanically programmable system behavior. This allows an easy adaption to a big variety of tasks.

Preliminary results are presented to demonstrate the fast stiffness regulation response and the wide range of stiffness achieved by the proposed VSR-joint design.

In this paper, a new variable stiffness joint is proposed through changing the cantilever arm to change the performance of the elastic element, which is compact, small size and simple adjustment.

An ideal method for predicting the fatigue life of spherical thrust elastomeric bearings has not been reported, thus far. This paper aims to present a method for predicting the fatigue life of laminated rubber spherical thrust elastomeric bearings.

First, the mechanical properties of standard rubber samples were tested; the axial stiffness, cocking stiffness, torsional stiffness and fatigue life of several full-size spherical thrust elastomeric bearings were tested. Then, the stiffness results were calculated using the neo-Hookean, Mooney–Rivlin and Yoeh models. Using a modified Mooney–Rivlin constitutive model, this paper proposes an improved method for fatigue life prediction, which considers the laminated characteristics of a spherical thrust elastomeric bearing and loads of multiple multi-axle conditions.

The Mooney–Rivlin model could accurately describe the stiffness characteristics of the spherical thrust elastomeric bearings. A comparative analysis of experimental results shows that the model can effectively predict the life of a spherical thrust elastomeric bearing within its range of use and the prediction error is within 20%.

The fatigue parameters of elastomeric bearings under multiaxial loads were fitted and corrected using experimental data and an accurate and effective multiaxial fatigue-life prediction expression was obtained. Finally, the software was redeveloped to improve the flexibility and efficiency of modeling and calculation.

There is an increasing popularity for the continuum robot in minimally invasive surgery owing to its compliance and dexterity. However, the dexterity takes the challenges in loading and precise control because of the absence of the shape tracking for the continuum robot. The purpose of this paper is to propose a new type of continuum manipulator with variable stiffness that can track the bending shape timely.

The low-melting-point alloy (LMPA) is used to implement the stiffness variation and shape detection for the continuum manipulator. A conceptual design for a single module is presented, and the principle of stiffness control based on the established static model is formulated. Afterward, a shape detection method is introduced in which the shape of the continuum manipulator can be detected by measuring the resistance of every LMPA. Finally, the effect of the proposed variable stiffness method is verified by simulation; the variable stiffness and shape detection methods are evaluated by experiments.

The results from the simulations and experiments indicate that the designed continuum manipulator has the ability of stiffness variation over 42.3% and the shape detection method has high precision.

Compared with conventional structures, the novel manipulator has a simpler structure and integrates the stiffness variation and shape detection capabilities with the LMPA. The proposed method is promising, and it can be conveniently extended to other continuum manipulators.

The purpose of this paper is to obtain the single-tooth stiffness, single-tooth time-varying meshing stiffness and comprehensive meshing stiffness of the internal and external face gears and to analyze the influence of the modulus, pressure angle and tooth width of each face gear on the single-tooth stiffness of the gear in nutation face gear transmission.

From the point of view of material mechanics, the gear teeth of nutation face gear are simplified as spacial variable cross-section beams. The shear deformation of gear teeth, the bending deformation of tooth root and the additional elastic deformation caused by the base deformation are gotten by simplified trapezoidal section method, thus the stiffness of nutation face gear teeth can be obtained. The comparison with finite element method results verifies the rationality of simplified trapezoidal section method for calculating the tooth stiffness of nutation face gear.

The variation of stiffness of internal and external face gears along the meshing line and tooth height in nutation face gear transmission is studied, and the variation laws of single tooth stiffness, single-tooth-pair mesh stiffness and single tooth time-varying meshing stiffness of nutation face gear teeth are obtained.

Nutation face gear transmission is a new type of transmission. The stiffness of face gear teeth is analyzed, and the variation rules of single tooth stiffness, single-tooth-pair mesh stiffness and single tooth time-varying meshing stiffness of nutation face gear teeth are obtained, which not only enriches the research of nutation face gear transmission but also has important guiding significance for the application of nutation face gear in engineering practice.

Bellows-type fluid viscous damper can be used to isolate micro vibration in high-precision satellites. The conventional model cannot describe hydraulic stiffness in the medium- and high-frequency domain of this damper. A simplified analytical model needs to be established to analyze hydraulic stiffness of the damping element in this damper.

In this paper, a bellows-type fluid viscous damper is researched, and a simplified model of the damping element in this damper is proposed. Based on this model, the hydraulic stiffness and damping of this damper in the medium- and high-frequency domains are studied, and a comparison is made between the analytical model and a finite element model to verify the analytical model.

The results show that when silicone oil has low viscosity, a model that considers the influence of the initial segment of the damping orifice is more reasonable. In the low-frequency domain, hydraulic stiffness increases quickly with frequency and remains stable when the frequency increases to a certain value; the stable stiffness can reach 106 N/m, which is much higher than the main stiffness. Excessive dynamic stiffness in the high-frequency domain will cause poor vibration isolation performance. Adding compensation bellows to the end of the original isolator may be an effective solution.

A model of the isolator containing the compensation bellows can be derived based on this analytical model. This research can also be used for dynamic modeling and vibration isolation performance analysis of a vibration isolation platform based on this bellows-type fluid viscous damper.

This paper proposed a simplified model of damping element in bellows-type fluid viscous damper, which can be used to analyze hydraulic stiffness in this damper and it was found that this damper showed stable hydraulic stiffness in the medium- and high-frequency domains.

This paper aims to study the relationship between normal contact stiffness and contact load. It purpose a new calculation model of the normal contact stiffness of joint surfaces by considering the elastic–plastic critical deformation change of asperities contact.

The paper described the surface topography of joint surfaces based on fractal geometry, and fractal parameters and of fractal function derived from measurement data. According to the plastic–elastic contact theory, the contact deformation characteristic of asperities was analyzed; the critical deformation estimation model was presented, which expressed critical deformation as the function of fractal parameters and contact deformation; the contact stiffness calculation model of single asperity was brought forward by considering critical deformation change.

The paper combined the surface topography description function, analyzed the asperity contact states by considering the critical deformation change, and calculated normal contact stiffness based on fractal theory and contact deformation analysis. The comparison between theoretical contact stiffness and experimental data indicated that the theoretical normal contact stiffness agreed with the experimental data, and the estimation model for normal contact stiffness was appropriate.

Owing to the possibility of plastic deformation during the loading process, the experimental curve between the contact stiffness and the contact load is nonlinear, resulting in an error between the experimental results and the theoretical calculation results.

The paper established the relationship between critical deformation and fractal surface topography by constructing asperity distribution function. The paper proposed a new normal contact stiffness calculation model of joint surfaces by considering the variation of critical deformation in contact process.

This paper aims to propose a normal and tangential contact stiffness model to investigate the contact characteristics between rough surfaces of machined joints based on fractal geometry and contact mechanics theory considering surface asperities interaction.

The fractal geometry theory describes surface topography and Hertz contact theory derives the asperities elastic, elastic-plastic and plastic contact deformation. The joint normal and tangential contact stiffness are obtained. The experiment method for normal and tangential contact stiffness are introduced.

The relationship between dimensionless normal contact load and dimensionless normal and tangential contact stiffness are analyzed in different plasticity index. The results show that they are nonlinear relationships. The normal and tangential contact stiffness are obtained based on theoretical and experimental methods for milling and grinding machined specimens. The results indicate that the present model for the normal and tangential contact stiffness are consistent with experimental data, respectively.

The normal and tangential contact stiffness models are constructed by using the fractal geometry and the contact mechanics theory considering surface asperities interaction, which includes fully elastic, elastic-plastic and fully plastic contacts deformation. The present method can generate a more reliable calculation result as compared with the contact model no-considering asperities interaction.