Joint Clearance Research Articles

Dynamic modeling of spatial parallel mechanism with multi-spherical joint clearances

The parallel mechanism has advantages of the high speed, high precision, strong carrying capacity, and high structural rigidity. Most of the previous studies concerning the dynamic modeling focused on planar mechanisms with revolute clearance joints or spatial mechanisms with one spherical joint clearance, while few studies focused on spatial parallel mechanisms with multi-spherical joint clearances. In this article, a general dynamic modeling method for spatial parallel mechanism with multi-spherical joint clearances based on Lagrange multiplier method is proposed. Taking 4universal joint-prismatic joint-spherical joint/universal joint-prismatic joint- universal joint (4UPS-UPU) spatial parallel mechanism as an example, the constraint equations of common kinematic pairs in spatial parallel mechanism, such as universal joint, spherical joint, and prismatic joint, are derived in detail. The dynamic model of the parallel mechanism with two spherical joint clearances combining the Flores contact force model and the LuGre friction model is established. The correctness of model has also been verified by comparing the analysis results of MATLAB with those of ADAMS. It can be seen that dynamic model of spatial parallel mechanism with multi-spherical joint clearances could be easily established by this method, which provides a theoretical reference to establish the dynamic model of other parallel mechanism with multi-clearance in the future.

A methodology for modeling and simulating frictional translational clearance joint in multibody systems including a flexible slider part

The objective of this paper is to present a simple and effective methodology for modeling and simulating frictional translational clearance joint in planar multibody systems including a flexible slider part. By using the finite element method (FEM), the slider is divided into finite elements, and the distributed body forces and boundary stresses (contact forces) on the slider are equivalent to the nodal forces. The normal contact forces are described by a nonlinear viscoelastic contact force model, while the frictional forces are evaluated by the Coulomb dry friction model. By lumping the mass matrix and presenting it in diagonal form, the equations of motion are then inertially decoupled, and the frictional forces are solved independently via trial-and-error algorithm. A penalty method for the revolute joint connecting the slider and other bodies is applied, and equations of motion are integrated numerically. Finally, two numerical examples are given to test the feasibility and effectiveness of the methodology in this paper.

Mechanically robust and abrasion-resistant polymer nanocomposites for potential applications as advanced clearance joints

Despite exceptional dimensional stability, polyamide 6 (PA6) still suffers relatively low mechanical strength and stiffness as compared with metallic and ceramic materials, which thus significantly limits its engineering applications. Herein, we have demonstrated the fabrication of high-performance PA6 composites with excellent mechanical and wear resistance by introducing nanoscale silicon carbide (SiC) as the reinforcer and anti-wear agents. The results show that the addition of 5 wt% nanoscale SiC (NS) increases the tensile strength of PA6 by 54% (reaching 64.8 MPa) while the elongation at break is over 6 times (around 304%) of that of the PA6 matrix, which giving rise to a 9.6 times increase in the fracture toughness. Moreover, the addition of 30 wt% of NS reduces the friction coefficient from 0.31 for the PA6 to 0.12, indicating improved anti-wear performances. Such significant improvements in both mechanical and anti-wear properties are primarily due to the high stiffness of NS and the strong interfacial interactions with the PA6 matrix. In addition, the effects of friction coefficient on dynamic characteristics of mechanism with clearance are also investigated to gain an insightful understanding on the improved anti-wear properties. This work provides a facile approach to the design of advanced polymer composites combining excellent mechanical and anti-wear performances.

An improved model of contact collision investigation on multi-body systems with revolute clearance joints

An improved contact collision model for the impact analysis of a slider–crank mechanism with revolute clearance joints is presented and discussed in this paper. Clearances in revolute joints are inevitable due to wear, machining tolerance, and local deformations. In view of the energy loss and the stiffness changes during collision, which modifies the coulomb friction force, an improved contact collision force model is established. The influence of clearance size, speed, and friction on the acceleration of slider is analyzed, and the simulation results are compared with the experimental data. The results demonstrate that the parameters of clearance joints have obvious effects on dynamic characteristics, and the improved model can accurately describe the dynamic characteristics of joints with clearance.

Wear Analysis of Spatial Parallel Mechanisms With Multiple Three-Dimensional Spherical Clearance Joints

The goal of this work is to investigate the dynamic responses of the parallel mechanism with irregular clearances caused by wear and to further reveal the influences of multiple clearance interaction on wear. The motion model and the force model of spherical clearance joint based on a continuous contact force model and a static friction model are established. The dynamic equation of the spatial parallel mechanism considering two spherical clearance joints is derived. A general wear analysis strategy to establish spherical clearance joint with sustainable updation of the surface profile is presented, and the dynamic responses of parallel mechanism after wear are studied. The interaction between two wear joints with different initial clearance values is further investigated. The results show that it is necessary to consider the factor of irregular clearances caused by wear in the analysis of dynamics behavior for precision mechanisms. Proper distribution of clearance values can reduce wear of clearance joint and improve the useful life of mechanism to a certain extent. This work provides a foundation for life prediction and reliability analysis of parallel mechanisms.

A novel parallel recursive dynamics modeling method for robot with flexible bar-groups

Based on Hamilton equation of motion and Lagrange principle, this paper proposes a novel parallel recursive dynamics modeling method for robot with flexible bar-groups that comprise flexible link, flexible joint and joint clearance. Using the virtual joint velocity, constraint force impulse and derivative of canonical momentum, the dynamics model of flexible link is established, and the dynamics model of flexible joint is built by the generalized force and energy of flexible joint. Then, based on kinematics constraints and dynamics constraints, the general comprehensive dynamics model of robot with flexible bar-groups is obtained. Finally, the proposed dynamics modeling method is applied to Delta parallel robot and KUKA serial robot, compared with the existing dynamics modeling methods by experiments, our approach is not only closer to the actual situation, but also has higher algorithm efficiency and better universality, which can lay foundation for the prediction of dynamic characteristics, and achieve the accurate and efficient control for different types of robots.

A Moment Approach to Positioning Accuracy Reliability Analysis for Industrial Robots

The uncertain variables of the link dimensions and joint clearances, whose deviation is caused by manufacturing and assembling errors, have a considerable influence on the positioning accuracy of industrial robots. Understanding how these uncertain variables affect the positioning accuracy of industrial robots is very important to select appropriate parameters during design process. In this paper, the positioning accuracy reliability of industrial robots is analyzed considering the influence of uncertain variables. First, the kinematic models of industrial robots are established based on the Denavit–Hartenberg method, in which the link lengths and joint rotation angles are treated as uncertain variables. Second, the Sobol’ method is used to analyze the sensitivity of uncertain variables for the positioning accuracy of industrial robots, by which the sensitive variables are determined to perform the reliability analysis. Finally, in view of the sensitive variables, the first-four order moments and probability density function of the manipulator's positioning point are assessed by the point estimation method (PEM) in three examples. The Monte Carlo simulation method, the maximum entropy problem with fractional order moments (maximum entropy problem with fractional order moments method (ME-FM) method), and the experimental method are also performed as comparative methods. All the results demonstrate that the proposed PEM has a higher accuracy and efficiency to assess the positioning accuracy reliability of industrial robots.

Retrieval Analysis And Principal Variable Analysis Of 127 M2a-38 Mm™ Metal On Metal Hip Replacements

BackgroundThe objective of this study was to investigate the factors which affected the material loss from 127 M2a-38 mm™ hip replacements. MethodsThe alignment and patient data was obtained for 127 patients. The explants bearings and tapers were measured to determine the level of material loss and their geometry. Results87 joints were edge wearing (EW), 28 normally wearing (NW) and 12 had edge interaction (EI). The NW joints were wearing at a mean bearing combined rate of 0.34 mm3/yr. For the NW joints, bearing clearance was linked to the bearing combined volumetric loss rate (r = 0.446). The rates of loss from the head's taper was 0.21 mm3/yr. Lower wearing and lower clearance joints had higher values of loss from the tapers. The taper loss from joints with a positive clearance were significantly higher (p = .026) than those with a negative clearance. ConclusionsThe results demonstrate that bearing loss rates for NW joints was as expected. The high number of joints showing signs of edge wearing resulted from low clearances and a low cup articular arc angle. The taper loss was lower than other similar joint designs with positive clearances resulting in greater loss.

A new approach to enhance the stiffness of heavy-load parallel robots by means of the component selection

Abstract Stiffness enhancement is one of the most crucial issues for the parallel robots as machine tools. Different from the previous methods including the structural comparison and dimensional synthesis, a new approach to enhance the stiffness of heavy-load parallel robots from the direction of component selection is proposed in this paper. To contain the main parameters of components, an overall stiffness matrix is proposed, where the effects of link deformations and joint clearances are considered. In order to meet the stiffness requirements of the machine tool in practical machining directions, a new stiffness index and an objective function are also derived on the basis of the overall stiffness model. In addition, since the number of component parameters is huge, particle swarm optimization technology is utilized to obtain the appropriate results. Finally, two examples of the A3 head and the Tricept based are presented to demonstrate the practicability of the proposed enhancement approach. According to the results of numerical examples, it shows that the proposed approach is feasible, and it can further enhance the stiffness of parallel robots after the structural comparison and dimensional synthesis.

End-effector positioning due to joint clearances: A comparison among three planar 2-DOF parallel manipulators

This paper develops a model for studying the effect of joint clearances on the end-effector’s loci for planar parallel manipulators with 2 degree-of-freedom (DOF). The condition for developing end-effector loci equations with respect to the joint clearance relies on the fact that at least one point of contact is always presented in each joints. The motivation of this work lies in the fact that the proposed procedure allows the study of parallel manipulators that can be considered as design concepts for developing an x-y cutting table for a textile industry. Numerical simulations enable to compare three 2-DOF planar parallel manipulators architectures: i) 2-RRR, ii) 2-RPR, and iii) 2-RPR. A Monte Carlo simulation allows us to find the area of possible end-effector locations for a specific value of clearance. Also, the equations allow us to find the largest distance from the desired location to the one obtained considering clearance. Findings shed some lights on establishing which parallel manipulator is less affected to joint clearance.

Research on Influence of Joint Clearance on Precision of 3-TPT Parallel Robot

Abstract. The error model of the working accuracy of parallel mechanism was established in this paper. The D-H matrix method and error independent method were used to analyze the clearance error of mechanism joint based on the inverse position kinematics solution. The theoretical model describing the position error of the moving platform position error affected by its joint clearance was developed when the moving platform was parallel to fixed platform in the ideal state; the clearance error model of 3-TPT Parallel mechanism was established based on D-H matrix method and error independent method while the joint clearance error source was given. The effect of joint clearance error on the working accuracy of 3-TPT parallel mechanism was analyzed by Monte Carlo method. The effect of posture error due to revolution of the moving platform about coordinate axis on the error of parallel mechanism was simulated and analyzed based on D-H matrix method in the non-ideal state.

Non-probabilistic kinematic reliability analysis of planar mechanisms with non-uniform revolute clearance joints

Owing to the inevitable phenomena in which the wear of a revolute joint is non-uniform and severely affects the output motion accuracy, a conservative and efficient motion accuracy evaluation of mechanisms considering non-uniform wear is required by designers. Hence, this paper presents an integrated non-probabilistic kinematic analysis of precision mechanisms with non-uniform wear in joint by combining multi-body dynamic analysis, wear prediction and kinematic reliability analysis. The presented accuracy measurement and corresponding solution strategy can be used as the objective or constraint in dimensional synthesis to realise a longer service life. The non-uniform clearance is quantified by unknown but bounded variables, the boundary of which is expressed by the B-spline function. Furthermore, the kinematic reliability is calculated based on the non-probabilistic interval interference model. Two numerical examples consisting of wear prediction, motion error quantification, and reliability evaluation are presented to demonstrate the validity and applicability of the developed methodology.

Research on dynamic characteristic of connecting rod with joint clearance

In order to study the dynamic characteristics of revolving joint with clearance, the theoretical model of the revolving joint with clearance is established by using Newton Euler method and “contact-separation” state model. The kinetic equations are solved by using the Gear algorithm in MATLAB software. The change curves of the contact force and the center trajectory of the revolving joint shaft with clearance are obtained considering different clearance, contact stiffness, and rotational speed together. The research results have laid a theoretical foundation for improving the joint forces and the accuracy by using controller.

Thermal characteristics analysis and error prediction for lubricated multi-link high-speed precision presses

Thermal models are important in the process of predicting the thermal characteristics and corresponding thermal error of multi-link high-speed precision presses (MLHSPPs) with an oil-lubrication system. Previous models only involved the effects of bearing stiffness, temperature change of bearings, flexibility of crank shaft on the heat generation power, while the influences of revolute clearance joint and flexibility of linkage are seldom considered, which inevitably reduces the accuracy of thermal analysis. To overcome this problem, dynamic models of flexible multi-link mechanisms (MLM) with clearance, lubrication, crankshaft-bearing system are constructed, the interaction forces between pin and bushing are obtained to calculate its heat generation power. Then, an improved model of MLHSPP with lubrication is proposed to analyze the temperature evolution and the thermal error between slider and work table at the position of LDP, by considering bearing stiffness, temperature change of bearings, flexibility of crank shaft, linkage, clearance, lubrication and thermal contact resistance all together. Compared with results from traditional models, the simulation data from this improved thermal model agree well with experiment, which proves the validity of the proposed model. Furthermore, the temperature rise and the thermal error of MLHSPP between slider and work table at the position of LDP under different input speeds, lubricating oil flux and contact angles of ball bearing were also studied.

Determining power consumption using neural model in multibody systems with clearance and flexible joints

Even if today’s manufacturing technology has great advances, clearance between joint parts in a multibody system is inevitable due to the assemblage and relative motion of neighbour links. If a joint has excessive clearance size, it leads to negative effects on the system performance and unforeseeable power consumption occurs during the life-cycle of a mechanical system. Instant change at the electric current makes the actuator lifetime shorter. In this study, actuator current fluctuation and power consumption in the spatial multibody system are investigated. Classic and compliant slider-crank mechanisms with clearance and flexible joints are studied together. Hertz contact theory comprising the model of Lankarani and Nikravesh is considered to comment on the joint forces on the power consumption. Coulomb’s friction law is preferred to evaluate the friction behaviours. A dynamic neural predictor is also designed to determine the current fluctuation for the different working parameters. Experimental data is used for the prediction stability of the neural model. The results outline that the clearance joint has a dominant effect on the power consumption and the current fluctuation of the actuator. The designed neural predictor has stable and superior performances to predict and estimate the current fluctuation. In the design stage of the system, therefore, researchers can judge the power consumption of similar mechanical systems having imperfect joints and may select the suitable actuator for real working conditions.

Effects of passive vibration absorbers on the mechanisms having clearance joints

In the current study, the dynamic behavior of two planar mechanisms with revolute joints, in the presence of clearances is investigated. Subsequently, a control scheme with the aim of restraining the clearance and maintaining a more stable behavior is proposed. This approach is based on using tuned mass damper (TMD) in order to reduce the effects of clearances in mechanisms for passive control purpose. The applied absorber’s mass is insignificant and they are little in size. By attaching two perpendicular absorbers in order to control the clearance, the oscillations are notably reduced. The proposed methodology is applied to planar multibody mechanical systems with revolute clearance joints with a view to demonstrating its features. The absorber performance is evaluated for changes around the designed state and the results show that the designed absorbers have a good robustness with variations to changes in different parameters.

Effect of friction on the dynamic analysis of slider-crank mechanism with clearance joint

In this paper, we are interested in the effect of friction on dynamic behavior of a crank-slider mechanism with clearance joint. Due to the clearance existence in the revolute joint, it is important to choose an appropriate contact force model to analyze the dynamic response, the dynamic equations are established by combining Lagrange’s equation of the first kind with modified contact force model and LuGre friction model, the Baumgarte stabilization approach was used to improve the numerical stability. Simulation and experimental tests were carried out to verify this model. The system dynamic response hysteresis, and the more energy consumption when friction is considered in the mechanism. The influence of friction coefficient on the nonlinear dynamic characteristics of the mechanism with clearance joint is analyzed. The dynamic performance of the mechanism considering friction presents significant differences at the accelerations level. Friction plays a positive role in the stability of the system.

Research on the Motion Error Analysis and Compensation Strategy of the Delta Robot

The Delta robots are widely used in packaging, sorting, precision positioning, and other fields. Motion accuracy is an important indicator for evaluating robot performance. However, due to the existence of mechanism errors, the motion accuracy of the robot will be reduced. Therefore, how to reduce motion errors and improve accuracy are important issues for robots. The purpose of the present study is to analyze the motion error and propose an error compensation scheme to improve the motion accuracy of the robot. Firstly, the kinematic model of the robot is established by the D-H matrix transformation method. An error model considering dimension error, the error of revolute joint clearance, driving error, and the error of spherical joint clearance is established. Additionally, the influence of different errors on the motion accuracy is analyzed. Secondly, an error compensation strategy of controlling the driving angle is proposed. The analysis of error compensation is carried out by a numerical example. Comparing the results before and after compensation, it is known that the robot can move along the desired position, so the notion error of the robot is compensated, which proves that this method is effective for improving the motion accuracy of the robot.

Motion Reliability Analysis of the Delta Parallel Robot considering Mechanism Errors

Delta parallel robots are widely used in assembly detection, packaging sorting, precision positioning, and other fields. With the widespread use of robots, people have increasing requirements for motion accuracy and reliability. This paper considers the influence of various mechanism errors on the motion accuracy and analyzes the motion reliability of the mechanism. Firstly, we establish a kinematic model of the robot and obtain the relationship between the position of the end effector and the structural parameters based on the improved D–H transform rule. Secondly, an error model considering the dimension error, the error of revolute joint clearance, driving error, and the error of spherical joint clearance is established. Finally, taking an actual robot as an example, the comprehensive influence of mechanism errors on motion accuracy and reliability in different directions is quantitatively analyzed. It is shown that the driving error is a key factor determining the motion accuracy and reliability. The influence of mechanism errors on motion reliability is different in different directions. The influence of mechanism errors on reliability is small in the vertical direction, while it is great in the horizontal direction. Therefore, we should strictly control the mechanism errors, especially the driving angle, to ensure the motion accuracy and reliability. This research has significance for error compensation, motion reliability analysis, and reliability prediction in robots, and the conclusions can be extended to similar mechanisms.

Rigid-flexible-thermal analysis of planar composite solar array with clearance joint considering torsional spring, latch mechanism and attitude controller

This paper establishes a thermal-structural coupling model of planar spacecraft system with large flexible composite solar array under nodal coordinate formulation and absolute nodal coordinate formulation framework. Perfect revolute joint is adopted as connection type to give the different influences from fixed constraint used in previous researches, and consequently, torsional spring, latch mechanism, and attitude controller are involved into the spacecraft system. Imperfect revolute joint is further introduced to investigate the coupling effects of thermal load, adjustment motion, and joint clearance on dynamics of the system, including spacecraft attitude, solar panel responses, and wear prediction. Results of six comparison models (with or without clearance joint, considering thermal environment, or adjustment motion, and considering both these two conditions) show that the coupling effect of thermal environment and overall motion brings dramatic and unmanageable shock to the system with clearance joint, that is no longer can be seen as a simple superposition of each single condition effect like the system with ideal joint, although the suspension damper property of clearance joint can weaken thermal-induced vibration or motion induced vibration separately. For a period after attitude adjustment, wear depth of the system subjected to solar radiation is two orders of magnitude lager than that of the system without considering thermal environment. Joint clearance and thermal environment should be considered both; for on-orbit spacecraft system, the coupling effects of them are significant and non-ignorable for relevant mechanism design and performance analysis.