Spherical Joint Research Articles

Particle size effect of PTFE on friction and wear properties of glass fiber reinforced epoxy resin composites

Self-lubricating spherical plain joint bearings play a crucial role in aerospace equipment, with their performance primarily depending on the self-lubricating materials positioned between the inner and outer rings. As a typical polymer-based self-lubricating material, glass fiber reinforced epoxy resin composites receive high expectations. Polytetrafluoroethylene (PTFE) as an additive can significantly improve the friction and wear performance of glass fiber reinforced epoxy resin composites. The primary objective of the present study is to reveal the effect law of PTFE particle size on friction and wear properties of glass fiber reinforced epoxy resin composites under dry sliding conditions. Hence, the four particle sizes (P1, average < 1 μm; P2, average 12 μm; P3, average 25 μm; P4, 75–180 μm) of PTFE-filled epoxy composites were prepared. The hardness, compressive strength, and compressive modulus of the epoxy resin composites filled with four particle sizes of PTFE were measured. The coefficient of friction (COF) was evaluated using a reciprocating ball-on-disk tribometer, with a GCr15 ball as the stationary part and the composite disc as the reciprocating component. The wear rate was determined using a Mahr profilometer. The results show that the friction coefficients of four PTFE-filled epoxy resin composites have little difference. However, the wear rate of epoxy composite filled with PTFE particles of the large size (RE/P4) is an order of magnitude lower than that of epoxy composites filled with PTFE particles of the other size. The wear morphology of the composites was analyzed by scanning electron microscopy (SEM), and energy dispersive X-ray spectroscopy (EDS). The higher wear resistance of RE/P4 can be attributed to it exhibiting a stronger role in anchoring glass fibers (GF), compared to other particle-sized PTFE-filled epoxy resin composite materials.

Accuracy Analysis and Experimental Study of a Six-Dimensional Force Sensor with Circular Flexible Spherical Joints.

This paper proposed a circular flexible spherical joint to reduce the processing difficulty and manufacturing cost, and design a six-dimensional force sensor based on it. This paper analyzes the influence of the structural parameters of the flexible spherical joints on the accuracy of the six-dimensional force sensor by comparing the force mapping matrix of flexible spherical and ideal spherical joints. As the force mapping matrix is related to the stiffness matrix, the stiffness matrix of a six-dimensional force sensor based on a circular flexible spherical joint and the force mapping matrix of the generalized external force acting on the sensor was derived. Finally, a set of optimal parameters was selected to create a prototype and was verified through finite elements and experiments. The results show that the six-dimensional force sensor with a circular flexible spherical joint has good accuracy and provides some guidance for the design and analysis of the sensor.

Kinematics and Dynamics Analysis of a 3UPS-UPU-S Parallel Mechanism

In this paper, a two-rotational degrees of freedom parallel mechanism with five kinematic subchains (3UPS-UPU-S) (U, P, and S stand for universal joints, prismatic joints, and spherical joints) for an aerospace product is introduced, and its kinematic and dynamic characteristics are subsequently analyzed. The kinematic and dynamic analyses of this mechanism are carried out in screw coordinates. Firstly, the inverse kinematics is performed through the kinematic equations established by the velocity screws of each joint to obtain the position, posture, and velocity of each joint within the mechanism. Then, a dynamic modeling method with screw theory for multi-body systems is proposed. In this method, the momentum screws are established by the momentum and moment of momentum according to the fundamentals of screws. By using the kinematic parameters of joints, the dynamic analysis can be carried out through the dynamic equations formed by momentum screws and force screws. This method unifies the kinematic and dynamic analyses by expressing all parameters in screw form. The approach can be employed in the development of computational dynamics because of its simplified and straightforward analysis procedure and its high adaptability for different kinds of multi-body systems.

Dynamics and Wear Prediction of Mechanisms Considering Multiple Clearances and Coatings

The increase in joint clearance and system vibration caused by joint wear are important factors that may lead to the failure of the mechanism and a decrease in the motion accuracy of the actuator. In this paper, to investigate the impact of different numbers of spherical joint clearances on the dynamics performance of the mechanism and explore effective measures to reduce the vibration of the mechanism caused by multiple joint clearances, on the basis of the previous research on the mechanism dynamics when there is clearance in a single spherical joint, an improved contact force model is used to study the effects of coating, no coating, and different clearance quantities on the dynamics of a mechanism containing multiple spherical joint clearances. Moreover, the joint reaction forces and contact-impact forces under different working conditions are calculated. In order to reduce the difficulty of calculating the joint wear, an approximate calculation method for contact area is proposed, and an improved Archard wear model is employed to calculate and analyze the changes in wear amount under the influence of both spherical joint clearance and coating.

Analysis of kinematic characteristics of 2-P(RPS + UPS) parallel mechanism with six degrees of freedom

At present, there is an increasing demand for the workspace required for the assembly of components, and a parallel mechanism with a large workspace is urgently needed to make up for it. Therefore, in this paper, a 2-P(RPS + UPS) parallel mechanism (where S, P, R, and U represent spherical, prismatic, revolute, and universal joints) with four branched chains and six degrees of freedom is proposed and its kinematic characteristics are analyzed. First, the speed of the 2-P(RPS + UPS) parallel mechanism is numerically derived and verified by simulation using ADAMS software. Then, the motion decoupling characteristics of the mechanism are analyzed from the expression of the speed and position relationship between the input and output of the mechanism. To minimize the force on each branch in the workspace, scale optimization of the 2-P(RPS + UPS) mechanism and the Stewart mechanism is performed. Further, analysis of the dexterity, singularity, and workspace of the 2-P(RPS + UPS) mechanism is conducted, and the performance of the mechanism is compared with that of the Stewart mechanism. The proposed parallel mechanism has fewer branches, a simple kinematic model, strong motion decoupling, a high bearing capacity, a large workspace, and a low initial position height. Moreover, it can be conveniently transported and stored. Therefore, it has good application prospects in assembly and posture adjustment scenes requiring large workspaces.

Variable-amplitude fatigue behavior of M30 high-strength bolts in end-plate connection joints

High-strength bolts are widely used in connection joints for steel structures. In this paper, the variable-amplitude fatigue behavior of M30 high-strength bolts in end-plate joints is studied. Variable-amplitude fatigue tests were carried out on 19 M30 high-strength bolts using an Amsler pulse fatigue tester. Four cyclic stress amplitude loading modes, including Low to High (L-H), High to Low (H-L), Low to High to Low (L-H-L), and High to Low to High (H-L-H), were applied to the test specimens. In addition, the variable-amplitude fatigue life of M30 high-strength bolts was studied using two forms of cumulative damage models. The stress - fatigue life (S-N) curve was plotted using the equivalent stress amplitude. The obtained S-N curve was compared with the existing bolt fatigue S-N curve and the current specifications. Finally, fatigue fracture was analyzed from macro and micro perspectives. It was found that for most specimens, fatigue fracture occurs at the first joint thread between the bolt and nut, while for a few bolts, fatigue fracture occurs at the joint between the bolt head and bolt. With a fatigue life of 2 million cycles as the threshold, the fatigue limit is 107.5 MPa, which is 2.67 times higher than that specified by ANSI/AISC 360 – 16. Additionally, the fatigue properties of high-strength bolts in end-plate connections are better than those in bolted sphere joints at higher stress levels. At low stress levels, the contact pressure formed by the extrusion of the end-plate reduces the fatigue life of the bolts. Furthermore, unlike the constant-amplitude fatigue fracture, the variable-amplitude fatigue fracture has an obvious load change boundary line.

Numerical study on dynamic analysis of a nine-module floating aquaculture platform under irregular waves

A numerical study of the dynamics of a nine-module floating aquaculture platform in irregular waves is proposed, to examine the effect of the connector type between net cages and incident wave direction on the hydrodynamic response. A numerical model based on the coupled boundary element method and lumped-mass model was used to simulate the dynamic behavior of the aquaculture platform. Time-domain statistical analysis, and time-frequency analysis based on Hilbert-Huang transform on the motion responses of net cages and the mooring force responses of the platform were then carried out. The results indicate that the mooring system has a decisive influence on the frequency-domain characteristics of surge motion, while the influence of connector can be ignored. The surge motion under flexible hawser connector is less sensitive to wave incident direction, while the wave direction has a greater impact on surge motion under spherical joint connector. The amplitudes of pitch motion under two different connectors decrease significantly under oblique incident waves, compared with perpendicular incident wave condition. The wave incident direction has little effect on the overall mooring force response of the platform. The mooring force responses at different positions show completely different frequency characteristics when the cages are connected by spherical joints. The larger the pitch response of the cage, the smaller the mooring force response of the mooring chain connected to the net cage. There is a positive correlation between the gravity frequency of the mooring force response and the gravity frequency of the pitch response of the net cage.

Optimization of Swivel Spherical Hinge Structure Design Based on the Response Surface Method

The accurate analysis of key components of a spherical hinge structure directly affects bridge quality and safety during construction. Considering the key components of a spherical joint structure as the research object, a refined calculation model for the spherical joint is established to examine its stress using finite element analysis. The influence of design parameters on the mechanical characteristics of the spherical hinge structure is systematically analyzed. The response surface method (RSM), devised using a Box–Behnken design, is used to optimize the design of the spherical hinge structure parameters. A response surface model is established to derive the scheme of the optimized spherical hinge structure design. Moreover, by comparing the structural contact stress and rotational traction force before and after optimization, the effectiveness and necessity of the spherical hinge structure optimization are verified. The result comparison shows that the maximum contact stress and rotational traction force in the spherical hinge structure after optimization are reduced by 13.86% and 8.42%, respectively, compared with those before optimization. The relative error between the calculated and predicted values is approximately 3%, indicating that the RSM is feasible for optimizing key components of the spherical hinge structure. Its optimization effect is evident. Based on the identified optimal parameters of the spherical hinge structure, a range of recommended design parameters for the key structure of the rotating spherical hinge at different load carrying capacities is established using the interpolation method, which provides a valuable reference for engineering practice.

Workspace analysis of axial offset joint based on parameterization

AbstractThe axial offset joint has two rotating axes that do not intersect but have a specific offset in space. It is used widely in parallel manipulators (PMs). The offset-joint workspace can directly affect the PM workspace. This study performed a theoretical derivation and workspace analysis of a class of axial offset joints. First, a theoretical parametric model describing the rotation range of the offset joint is established that considers the interference of the offset joint because of the contact between the upper- and lower-joint brackets during movement. Second, the analytical expressions of the offset-joint workspace are formulated based on the coordinate system transformation. The offset-joint workspace is theoretically calculated in this study using formulations. Then, through a comparative analysis, the superiority of the offset joint compared with the universal joint is verified. The theoretical formulations in this paper can be used to calculate the workspace of a class of axial offset joints. Finally, based on a workspace analysis of three types of PMs using offset, universal, and spherical joints, the offset-joint PM workspace is much larger than those of the other two types.

Kinematics of the Hybrid 6-Axis (H6A) manipulator

AbstractThis paper presents a comprehensive study of the forward and inverse kinematics of a six-degrees-of-freedom (DoF) spatial manipulator with a novel architecture. Developed by Systemantics India Pvt. Ltd., Bangalore, and designated as the H6A (i.e., Hybrid 6-Axis), this manipulator consists of two arm-like branches, which are attached to a rigid waist at the proximal end and are coupled together via a wrist assembly at the other. Kinematics of the manipulator is challenging due to the presence of two multi-DoF passive joints: a spherical joint in the right arm and a universal in the left. The forward kinematic problem has eight solutions, which are derived analytically in the closed form. The inverse kinematic problem leads to $160$ solutions and involves the derivation of a $40$ -degree polynomial equation, whose coefficients are obtained as closed-form symbolic expressions of the pose parameters of the end-effector, thus ensuring the generality of the results over all possible inputs. Furthermore, the analyses performed lead naturally to the conditions for various singularities involved, including certain non-trivial architecture singularities. The results are illustrated via numerical examples which are validated extensively.

Design and Analysis of a Reconfigurable Hybrid Robot for Machining of Large Workpieces

Abstract Large workpieces are important components of core equipment in aerospace and other fields, where the machining mainly focuses on the surfaces and inner cavities. However, it may be unsuitable for existing machining robots to directly achieve integrated machining, that is, not only the high-precision surface machining but also the machining of different inner cavities in a limited space. To satisfy these machining requirements, a new reconfigurable hybrid robot (RHR) is proposed, called the 3PRR-3PSS-UPU RHR, for machining the surface and inner cavity of large workpieces (where P, P, R, S, and U stand for the actuated prismatic joint, passive prismatic joint, revolute joint, spherical joint, and universal joint, respectively). The proposed RHR consists of two parallel manipulators (PMs), in which one is a spatial 3PRR PM with one translational degree-of-freedom (DOF) and the other is a 3PSS-UPU reconfigurable PM (RPM) with different configurations of two rotational and one translational (2R1T) DOFs using locking equipment, which is the main advantage of the designed robot. The inverse kinematics and singularities of two PMs are analyzed. The stiffness performance of the spatial 3PRR PM is compared with that of a moving slider with one translational DOF. By evaluating the workspace and motion/force transmissibility, the kinematic performance of two PMs is presented using several local and global indices, followed by the dimensional optimization of link parameters. Based on the structural characteristics and excellent performance, it can be inferred that the 3PRR-3PSS-UPU RHR has great potential for machining large workpieces.

Spherical Joint Actuator with Backstepping Sliding Mode Control for Robotic Manipulator Rigid-Flexible Coupling System

At present, the output shaft of a permanent magnet spherical actuator (PMSA) is a rigid structure, which has the problems of small load weight ratio and high energy consumption. It is difficult to meet the application requirements of lightweight, high speed, and low energy consumption. In this paper, a PMSA is proposed as the driving motor for the rigid-flexible coupling system (R-FCS) of the robotic manipulator, and a flexible mechanical arm is used to replace the rigid output shaft of the PMSA to connect the hand claw to form a spherical joint. Firstly, the partial differential dynamics model of the robotic manipulator in the coordinate system is established based on the Hamilton method, and the R-FCS is constructed according to the momentum conservation equation combined with the rigid axis dynamics model of the PMSA. Then, a backstepping sliding mode controller (BSMC) is designed to form a closed-loop control system by selecting an appropriate nonlinear gain function to estimate the unknown disturbances of the system, and the stability of the controller is guaranteed by the Lyapunov theory. Finally, the simulation and experimental results verify that the R-FCS can achieve better trajectory tracking and provide an effective driving method for robotic manipulator spherical joint.

Dynamic Analysis of a Delta Parallel Robot with Flexible Links and Joint Clearances

Delta robot is a lightweight parallel manipulator capable of accurately moving heavy loads at high speed and acceleration along a spatial trajectory. This intensive dynamic process may have a significant impact on the end-effector trajectory precision and motor behavior. The paper highlights the influence on the dynamic behavior of a Delta robot by considering individual and combined effects of clearances and friction in the spherical joints, as well as the flexibility of the rod elements. The CAD modeling of the Delta robot and its motion simulation on a representative spatial trajectory where the maximum allowed values of speed and acceleration are reached were performed using the Catia and Adams software packages. The obtained results show that the methods used were successfully applied and the effects are mutually interconnected, but not cumulative.

Effect of neglecting passive spinal structures: a quantitative investigation using the forward-dynamics and inverse-dynamics musculoskeletal approach.

Purpose: Inverse-dynamics (ID) analysis is an approach widely used for studying spine biomechanics and the estimation of muscle forces. Despite the increasing structural complexity of spine models, ID analysis results substantially rely on accurate kinematic data that most of the current technologies are not capable to provide. For this reason, the model complexity is drastically reduced by assuming three degrees of freedom spherical joints and generic kinematic coupling constraints. Moreover, the majority of current ID spine models neglect the contribution of passive structures. The aim of this ID analysis study was to determine the impact of modelled passive structures (i.e., ligaments and intervertebral discs) on remaining joint forces and torques that muscles must balance in the functional spinal unit. Methods: For this purpose, an existing generic spine model developed for the use in the demoa software environment was transferred into the musculoskeletal modelling platform OpenSim. The thoracolumbar spine model previously used in forward-dynamics (FD) simulations provided a full kinematic description of a flexion-extension movement. By using the obtained in silico kinematics, ID analysis was performed. The individual contribution of passive elements to the generalised net joint forces and torques was evaluated in a step-wise approach increasing the model complexity by adding individual biological structures of the spine. Results: The implementation of intervertebral discs and ligaments has significantly reduced compressive loading and anterior torque that is attributed to the acting net muscle forces by -200% and -75%, respectively. The ID model kinematics and kinetics were cross-validated against the FD simulation results. Conclusion: This study clearly shows the importance of incorporating passive spinal structures on the accurate computation of remaining joint loads. Furthermore, for the first time, a generic spine model was used and cross-validated in two different musculoskeletal modelling platforms, i.e., demoa and OpenSim, respectively. In future, a comparison of neuromuscular control strategies for spinal movement can be investigated using both approaches.

Magnetic Ball Chain Robots for Endoluminal Interventions.

This paper introduces a novel class of hyperredundant robots comprised of chains of permanently magnetized spheres enclosed in a cylindrical polymer skin. With their shape controlled using an externally-applied magnetic field, the spherical joints of these robots enable them to bend to very small radii of curvature. These robots can be used as steerable tips for endoluminal instruments. A kinematic model is derived based on minimizing magnetic and elastic potential energy. Simulation is used to demonstrate the enhanced steerability of these robots in comparison to magnetic soft continuum robots designed using either distributed or lumped magnetic material. Experiments are included to validate the model and to demonstrate the steering capability of ball chain robots in bifurcating channels.

Influence of welding residual stress on bending resistance of hollow spherical joints

Welded hollow spherical joints are widely used in large-span spatial structures because of their simple organization and convenient construction. However, in the sphere-pipe connection welds of the joints, welding residual stress is generated, which will adversely affect the mechanical properties of the joints and the overall structure. In this paper, the parametric model of welded hollow spherical joints was established by employing the geometric configuration dimensions of those joints frequently used in engineering. Through the combination of experimental research and numerical simulation, the welding residual stress of welded hollow spherical joints and its impact on joints' bending resistance were studied. First of all, based on the distribution pattern of the stress, bending test of the joints was carried out and revealed the influence of welding residual stress on the bending stiffness and ultimate bending capacity of the joints; Then, through the results of experimental analysis and finite element calculation, and with parametric analysis, the impact of welding residual stress on joints' bending resistance was clarified with the variation of parameters such as the hollow sphere diameter D, wall thickness t and the connecting steel pipe diameter d. It is shown that welding residual stress has a great impact on joints' bending stiffness, with a reduction more than 10%, while it doesn't affect their ultimate bending capacity much, with an influence no more than 5%. In addition, as D increases, t, and d decrease, its impact on the bending resistance rises.

Investigation on Flexural Fracture Behaviour of Bolted Spherical Joints with Crack Propagation in Screw Threads.

Bolted spherical joints, due to their prominent merits in installation, have been widely used in modern spatial structures. Despite significant research, there is a lack of understanding of their flexural fracture behaviour, which is important for the catastrophe prevention of the whole structure. Given the recent development to fill this knowledge gap, it is the objective of this paper to experimentally investigate the flexural bending capacity of the overall fracture section featured by a heightened neutral axis and fracture behaviour related to variable crack depth in screw threads. Accordingly, two full-scale bolted spherical joints with different bolt diameters were evaluated under three-point bending. The fracture behaviour of bolted spherical joints is first revealed with respect to typical stress distribution and fracture mode. A new theoretical flexural bending capacity expression for the fracture section with a heightened neutral axis is proposed and validated. A numerical model is then developed to estimate the stress amplification and stress intensity factors related to the crack opening (mode-I) fracture for the screw threads of these joints. The model is validated against the theoretical solutions of the thread-tooth-root model. The maximum stress of the screw thread is shown to take place at the same location as the test bolted sphere, while its magnitude can be greatly reduced with an increased thread root radius and flank angle. Finally, different design variants related to threads that have influences on the SIFs are compared, and the moderate steepness of the flank thread has been found to be efficient in reducing the joint fracture. The research findings could thus be beneficial for further improving the fracture resistance of bolted spherical joints.

Residual performance of compression stiffened welded hollow spherical joints after exposure to elevated temperatures

The post-fire residual behavior of the joints and their accurate identification are critical issues for the assessment of the fire damage in the commonly used grid structures. Accordingly, it will be determined, whether the structure is directly used, disassembled, or used after repair. In this paper, the residual performance of compression stiffened welded hollow spherical joints after a fire is studied using the methods of air cooling and water cooling. The failure mode, load-displacement curves, and residual mechanical properties of the joints are analyzed. The results show that the residual performance of the joints after a fire is mainly related to the exposure temperature and the cooling mode. In air-cooled joints, the initial axial stiffness and bearing capacity decrease with the increase of exposure temperature, while the ductility increases significantly. In water-cooled joints, the initial axial stiffness and ductility decrease with the increase of exposure temperature, and the bearing capacity shows a decreasing trend before 500 °C and gradually increases after 500 °C. When conducting the FEM simulation of the experimental specimens, three-dimensional hexahedral elements were adopted with the relationship of the steel material after elevated temperature consisting of a combination of straight lines. The validity of the FEM model was verified by comparison with the experimental results. Based on the results of the parametric analyses, a calculation formula is proposed for predicting the residual bearing capacity and initial axial stiffness of compression stiffened welded hollow spherical joints after a fire.

Failure Analysis of High-Strength Bolts in Spherical Joint Assembly under In-Plane Quasi-Static Loading

Failure Analysis of High-Strength Bolts in Spherical Joint Assembly under In-Plane Quasi-Static Loading

Buckling capacity of steel circular hollow section considering the restraint of welded hollow spherical joints

An integral finite element model of steel circular hollow section and welded hollow spherical joints is established to consider the restraint of welded hollow spherical joints on steel circular hollow section in this paper. The buckling modes are used as the initial geometrical imperfection forms of the steel circular hollow section. Based on the statistics method, a method for calculating the buckling capacity design value of the steel circular hollow section with uniform reliability considering the restraint of welded hollow spherical joints is established, and the formula for calculating error of this value at certain confidence is deduced. The relationships between the buckling capacity design value of steel circular hollow section and the structural parameters of the member and joint are determined quantitatively by linear regression method. A practical formula for the buckling capacity design value of steel circular hollow section considering the restraint of welded hollow spherical joints is derived. Compared to the results calculated by the design code indicates that if the difference of restraint effect which is caused by different welded hollow spherical joint is ignored, the buckling capacity value of steel circular hollow section calculated based on the unified effective length coefficient may be bigger or smaller than that of the actual case. Therefore, refined consideration should be placed on the different restraint of welded hollow spherical joints of different sizes on steel circular hollow section, and the restraint of the end joints should be accurately considered when determining the buckling capacity of steel circular hollow sections.