A decoupling method is proposed for the elastic stiffness modeling of hybrid robots based on the rigidity principle, screw theory, strain energy, and Castigliano’s second theorem. It enables the decoupling of parallel and serial modules, as well as the individual contributions of each elastic component to the mechanism’s stiffness performance. The method is implemented as follows: (1) formulate limb constraint wrenches and corresponding limb stiffness matrix based on the screw theory and strain energy, (2) formulate the overall stiffness matrix of parallel and serial modules corresponding to end of the hybrid robots based on the rigidity principle, principle of virtual work, the wrench transfer formula, and strain energy methods, and (3) obtain and decouple the overall stiffness matrix and deflection of the robot based on the Castigliano’s second theorem. Finally, A planar hybrid structure and the 4SRRR + 6R hybrid robot are used as illustrative examples to implement the proposed method. The results indicate that selectively enhancing the stiffness performance of the mechanism is the most effective approach.

As a heavy load is applied to the parallel manipulators, it causes inaccuracies while positioning the end-effector or unbalanced dynamic forces in the legs. Various load-balancing techniques overcome this. However, the disadvantage of most load-balancing mechanisms is that they add inertia to the assembly and decrease the speed of motion. This article studies a new load-balancing method (a passive damper mechanism). The passive balancing mechanism is proposed to negate the inertia effects while countering the static inaccuracies in the parallel mechanism. This is verified by the structural analysis of the mechanism. The impact of the damper element on the dynamics of the mechanism is unknown. Hence, a complete mathematical model for the balancing mechanism has been developed to study its impact on the dynamics of the entire structure. Laplace transformations characterize the system response. The inclusion of a passive damper in a 3-prismatic-prismatic-revolute-spherical system was examined and found to be stable and critically damped. Such a passive damper was envisaged to facilitate additional force transmission for the actuators, and the DC gain from the system response validates the torque support for the actuators.

This paper proposes a methodology for architecting microstructures with extremal stiffness, yield, and buckling strength using topology optimisation. The optimised microstructures reveal an interesting transition from simple lattice-like structures for yield-dominated situations to hierarchical lattice structures for buckling-dominated situations. The transition from simple to hierarchical is governed by the relative yield strength of the constituent base material as well as the volume fraction. The overall performances of the optimised microstructures indicate that maximum strength is determined by the buckling strength at low-volume fractions and yield strength at higher-volume fractions, regardless of the base material’s relative yield strength. The non-normalised properties of the optimised microstructures show that higher base material Young’s modulus leads to both higher Young’s modulus and strength of the architected microstructures. Furthermore, the polynomial order of the maximum strength lines with respect to mass density obtained from the optimised microstructures reduces as base material relative yield strength decreases, reducing from 2.3 for buckling-dominated thermoplastic polyurethane to 1 for yield-dominated steel microstructures.

An approach for calculating the effective workspaces of parallel mechanisms has been considered in this paper. The effective workspace is a set of reachable by the end-effector points, where an important parameter (or parameters) from the point of view of operation is not higher than critical. In this article, the speed and torque in the drive and the stiffness of the mechanism are considered as such parameters. An approach to determining the appropriate effective workspace is presented for each parameter. The optimization process, which is based on presented methods, allows one to choose basic technical solutions of the designed robot: the links (lengths and cross-sections), the drives, and types of hinges, which guarantee its operability at the specified operational characteristics. Case studies of a delta robot with four degrees of freedom and a planar five-bar mechanism are presented for testing these approaches. The presented methods are of great practical importance because it uses movement parameters or operational characteristics that are decisive for this mechanism and have clear physical meaning.

We aimed to examine the association between pain, stiffness and fatigue in newly diagnosed polymyalgia rheumatica (PMR) patients using baseline data from a prospective cohort study. Fatigue is a known, but often ignored symptom of PMR. Newly diagnosed PMR patients were recruited from general practice and mailed a baseline questionnaire. This included a numerical rating scale for pain and stiffness severity, manikins identifying locations of pain and stiffness and the FACIT-Fatigue questionnaire. A total of 652 PMR patients responded (88.5%). The mean age of responders was 72.6 years (SD 9.0) and the majority were female (62.0%). Manikin data demonstrated that bilateral shoulder and hip pain and stiffness were common. The mean fatigue score (FACIT) was 33.9 (SD 12.4). Adjusted regression analysis demonstrated that a higher number of pain sites (23–44 sites) and higher pain and stiffness severity were associated with greater levels of fatigue. In newly diagnosed PMR patients, fatigue was associated with PMR symptom severity.

Parallel manipulators, especially those with outputs as one translation and two rotations (1T2R), are being increasingly studied. The kinematic chains of parallel manipulators share the loads and make the stiffness higher than the stiffness of serial manipulators with equivalent limbs. This high stiffness ensures a minimal deformation of the limbs, allowing a high positioning accuracy of the endeffector. Thus, it is very important to be able to measure the stiffness in parallel manipulators. In this work, we present a novel 1T2R multi-axial shaking table (MAST) for automobile pieces testing purposes—the 2PRU–1PRS parallel manipulator—and focus on the analysis of its stiffness all over the useful workspace. Analysis methods based on matrix structural method need to be validated for every parallel manipulator, and we present these steps along with a comparison between experimental and analytical methods.

High-resolution atomic force microscopy (AFM) was used for the in situ evaluation of the anti-inflammatory effects of triptolide on rheumatoid arthritis (RA) fibroblast-like synoviocytes (FLS) to understand the anti-RA effects of triptolide, based on the morphological and biophysical changes observed in RA-FLS. RA-FLS have been reported to play a primary role in inflammatory bone destruction during the development of RA and thus are regarded as an important target for RA treatment. Triptolide pretreatment significantly inhibited tumor necrosis factor-α-induced expression of the interleukin (IL)-1β, IL-6, and IL-8 genes in MH7A cells. Using AFM, we showed that triptolide-induced morphological damage in MH7A cells by inducing significant ultrastructure changes in the membrane, which were closely related to triptolide-induced apoptosis in MH7A cells. Using force measurements determined with AFM, triptolide was shown to increase the stiffness of MH7A cells. These findings not only revealed the strong anti-inflammatory effects of triptolide on RA-FLS, highlighting triptolide as a potential anti-RA agent, but also revealed the possible use of AFM for studying anti-inflammatory responses in RA-FLS, which we expect to be developed into a potential tool for anti-RA drug studies in RA-FLS.

This paper presents a novel reconfigurable parallel mechanism, which can serve as a machine tool. The proposed parallel mechanism can change its structure parameters by driving a bevel gear system fixed in the base platform. First, the forward and inverse kinematics of the proposed mechanism are investigated. Second, the reachable workspace and Jacobian matrix are conducted. Based on the Jacobian matrix, the stiffness model and dexterity of the end effector are developed in detail. Finally, a multi-objective optimization is performed by using the Genetic Algorithm, and the workspace and global performance indexes of stiffness as well as the dexterity are considered as the performance indices to improve the performance of the reconfigurable parallel mechanism. Finally, Pareto frontier figure and several tables are provided to illustrate the results of the optimization. The results showed the proposed method has improved the performance of the reconfigurable machine tool in terms of its stiffness and dexterity.

Incorrect propagation speed of discontinuities may occur by straightforward application of standard dissipative schemes for problems that contain stiff source terms for underresolved grids even for time steps within the CFL condition. By examining the dissipative discretized counterpart of the Euler equations for a detonation problem that consists of a single reaction, detailed analysis on the spurious wave pattern is presented employing the fractional step method, which utilizes the Strang splitting. With the help of physical arguments, a threshold values method (TVM), which can be extended to more complicated stiff problems, is developed to eliminate the wrong shock speed phenomena. Several single reaction detonations as well as multispecies and multi-reaction detonation test cases with strong stiffness are examined to illustrate the performance of the TVM approach.

The neck is an important part of the body that connects the head to the torso, supporting the weight and generating the movement of the head. In this paper, a cable-driven parallel platform with a pneumatic muscle active support (CPPPMS) is presented for imitating human necks, where cable actuators imitate neck muscles and a pneumatic muscle actuator imitates spinal muscles, respectively. Analyzing the stiffness of the mechanism is carried out based on screw theory, and this mechanism is optimized according to the stiffness characteristics. While taking the dynamics of the pneumatic muscle active support into consideration as well as the cable dynamics and the dynamics of the Up-platform, a dynamic modeling approach to the CPPPMS is established. In order to overcome the flexibility and uncertainties amid the dynamic model, a sliding mode controller is investigated for trajectory tracking, and the stability of the control system is verified by a Lyapunov function. Moreover, a PD controller is proposed for a comparative study. The results of the simulation indicate that the sliding mode controller is more effective than the PD controller for the CPPPMS, and the CPPPMS provides feasible performances for operations under the sliding mode control.

A novel n(2-UPS/PS+RPS) spatial hyper-redundant manipulator (SHRM) formed by an optional number of 2-UPS/PS+RPS(2-universal joint-prismatic joint-spherical joint/prismatic joint-spherical joint+revolute joint-prismatic joint-spherical joint) parallel manipulators(PMs) connected in series is proposed and analyzed in this paper. First, the forward kinematics of the 2-UPS/PS+RPS PM is derived in close form. By extending this result to the whole SHRM, the forward kinematics model of the n(2-UPS/PS+RPS) SHRM is established. Second, the compact and elegant expressions for solving the forward velocity of the n(2-UPS/PS+RPS) SHRM are derived. Third, the statics and stiffness of the n(2-UPS/PS+RPS) SHRM are analyzed systematically by considering both active forces and constrained forces existed in each 2-UPS/PS+RPS PM. Finally, an analytically solved example is given for a 4(2-UPS/PS+RPS) SHRM formed by four 2-UPS/PS+RPS PMs. The analytical results are verified by CAD software.

This paper investigates a 6-degree-of-freedom foldable parallel mechanism for the ship-based stabilized platform, which is driven by closed chain linkages. The velocity and acceleration mappings between the moving platform and inputs of the closed chain linkages are deduced in the form of the first- and second-order influence coefficient matrices. The continuous stiffness matrix is deduced; furthermore, the translation and rotational stiffness along any direction are also deduced. With directional stiffness, the singularity of the mechanism is analyzed, and the explanation of the singularity is given from the viewpoint of stiffness. The directions the platform cannot move or lose its constraints are got from directional stiffness.

In this paper, we present the design of two serial spherical mechanisms to substitute for a single spherical joint that is usually used to connect the platform with the base in three degrees of freedom parallel mechanisms. According to the principle derived from the conceptual design, through using the two serial spherical mechanisms as the constraint limb, several redundantly actuated parallel mechanisms are proposed for ankle rehabilitation. The proposed parallel mechanisms all can perform the rotational movements of the ankle in three directions while at the same time the mechanism center of rotations can match the ankle axes of rotations compared with other multi-degree-of-freedom devices, due to the structural characteristics of the special constraint limb and platform. Two special parallel mechanisms are selected to analyze their kinematical performances, such as workspace, dexterity, singularity, and stiffness, based on the computed Jacobian. The results show that the proposed scheme of actuator redundancy can guarantee that the redundantly actuated parallel mechanisms have no singularity, better dexterity, and stiffness within the prescribed workspace in comparison with the corresponding non-redundant parallel mechanisms. In addition, the proposed mechanisms possess certain reconfigurable capacity based on control strategies or rehabilitation modes to obtain sound performance for completing ankle rehabilitation exercise.

This paper concentrates on theoretical and experimental nonlinear stiffness study of milling machine tool spindle angle contact ball bearing. The theoretical study allows us to build an analytical model to define nonlinear stiffness of angle contact ball bearings based on geometrical and physical parameters. Modifications were done on literature's models (e.g. Balls deformations) having positives impacts on conformity of models to experimental results.

FEM model using ANSYS is constructed to analyze the different parameters affecting the nonlinear stiffness of ball bearing. Among those parameters are physical including the geometry, friction coefficient and the boundary conditions of the model and Numerical parameters such as mesh density and penetration.

Experimental tests were done on the spindle ball bearing 7014, to measure the rigidity. Universal tensile testing machine is used to achieve load displacement curves. The developed theoretical model, constructed finite element model and experimental results showed good conformity.

The pulleys of an automotive front engine accessory drive are driven in rotation by a poly-V belt itself driven by the crankshaft pulley. This driving pulley is often used as a torsional vibration damper (TVD) for the crankshaft. Three elements compose the pulley: the hub, a rubber ring and an inertia steel ring with v-ribs on its outer diameter. Although the crankshaft torsional vibrations are dampen, they are transmitted to the belt transmission and therefore to the driven accessories. Hence, recent developments have conducted to add a decoupling function to these pulleys. The decoupling is realized by an other rubber ring. The TVD pulley components are designed in order to dampen crankshaft vibrations over a given frequency range, i.e. stiffness and damping characteristics are determined for the rubber ring. These expected characteristics have to be checked after manufacturing for product certification but also to give some real measured data input for simulation models. An experimental characterization method is presented and discussed for the determination of the stiffness and damping coefficients of the rubber rings used in such pulley. The test rig developed is temperature controlled in order to show the influence of the temperature.