Joint Clearance Research Articles

Examination and comparison of different methods to model closed loop kinematic chains using Lagrangian formulation with cut joint, clearance joint constraint and elastic joint approaches

This work aims at presenting, in a comprehensive manner, several approaches to model and simulate closed loop topologies using the classical Lagrangian formulation. One of the great advantages of the Lagrangian approach is its simplicity and easiness of obtaining the equations of motion. However, a critical aspect arises when the mechanical systems include closed loop topologies, since the process of deriving the equations of motion becomes a complex task. The key point of the present study is to convert the closed loop nature into open systems, which ultimately simplifies the modeling process when the Lagrangian formulation is utilized. For this purpose, three different methods are considered, namely those based on the cut joint approach, the clearance joint constraint model, and the elastic joint formulation are used. In the sequel of this process, a slider-crank mechanism is utilized as a demonstrative application example, and the main results are compared with those obtained with the well-established Newton-Euler method for constrained multibody systems. Moreover, this example allows the comparison of the main characteristics and peculiarities of the described approaches.

Dynamic Parameter Identification of a Pointing Mechanism Considering the Joint Clearance

The clearance of the revolute joint influences the accuracy of dynamic parameter identification. In order to address this problem, a method for dynamic parameter identification of an X–Y pointing mechanism while considering the clearance of the revolute joint is proposed in this paper. Firstly, the nonlinear dynamic model of the pointing mechanism was established based on a modified contact model, which took the effect of the asperity of contact surface on joint clearance into consideration. Secondly, with the aim of achieving the anti-interference incentive trajectory, the trajectory was optimized according to the condition number of the observation matrix and the driving functions of activate joints that could be obtained. Thirdly, dynamic simulation was conducted through Adams software, and clearance was involved in the simulation model. Finally, the dynamic parameter identification of the pointing mechanism was conducted based on an artificial bee colony (ABC) algorithm. The identification result that considered joint clearance was compared with that which did not consider joint clearance. The results showed that the accuracy of the dynamic parameter identification was improved when the clearance was taken into consideration. This study provides a theoretical basis for the improvement of dynamic parameter identification accuracy.

Statistical Tolerance Analysis of 3D-Printed Non-Assembly Mechanisms in Motion Using Empirical Predictive Models

Fused Deposition Modelling (FDM) enables the fabrication of entire non-assembly mechanisms within a single process step, making previously required assembly steps dispensable. Besides the advantages of FDM, the manufacturing of these mechanisms implies some shortcomings such as comparatively large joint clearances and geometric deviations depending on machine-specific process parameters. The current state-of-the-art concerning statistical tolerance analysis lacks in providing suitable methods for the consideration of these shortcomings, especially for 3D-printed mechanisms. Therefore, this contribution presents a novel methodology for ensuring the functionality of fully functional non-assembly mechanisms in motion by means of a statistical tolerance analysis considering geometric deviations and joint clearance. The process parameters and hence the geometric deviations are considered in terms of empirical predictive models using machine learning (ML) algorithms, which are implemented in the tolerance analysis for an early estimation of tolerances and resulting joint clearances. Missing information concerning the motion behaviour of the clearance affected joints are derived by a multi-body-simulation (MBS). The exemplarily application of the methodology to a planar 8-bar mechanism shows its applicability and benefits. The presented methodology allows evaluation of the design and the chosen process parameters of 3D-printed non-assembly mechanisms through a process-oriented tolerance analysis to fully exploit the potential of Additive Manufacturing (AM) in this field along with its ambition: ‘Print first time right’.

A methodology for dynamic behavior analysis of the slider-crank mechanism considering clearance joint

Abstract The slider-crank mechanism is used widely in modern industrial equipment whereby the contact-impact of a revolute clearance joint affects the dynamic behavior of mechanical systems. Combining multibody dynamic theory and nonlinear contact theory, the computational methodology for dynamic analysis of the slider-crank mechanism with a clearance joint is proposed. The differential equations of motion are obtained considering the revolute clearance joint between the connecting rod and slider. In the mechanical system, the contact force is evaluated using the continuous force model proposed by Lankarani and Nikravesh, which can describe the contact-impact phenomenon accurately. Then, the experimental study is performed whereby the numerical results are compared with the test data to validate the proposed model. Moreover, the dynamic response analysis is conducted with various driving velocities and clearance sizes, which also explains that the sensitive dependence of a mechanical system on the revolute clearance joint.

Dynamics of luffing motion of a hydraulically driven shell manipulator with revolute clearance joints

In this study, a modeling method for investigating the dynamic characteristics of a hydraulically driven shell manipulator with revolute clearance joints is presented. This model accounts for the effect of the clearance, the flexibility of the rotating beam, and the coupled dynamic characteristics of the hydraulic cylinder. A modified contact force model was developed to simulate the physical properties of realistic revolute joints with small clearances, heavy loads, and variable contact stiffnesses and damping coefficients with variations of the indentations. Considering the strong coupling relationship between the hydraulic cylinder and the flexible beam, a system equation of motion combining the state variables of the hydraulic cylinder and mechanical system was established. The complex nonlinear friction force of the hydraulic cylinder motion was constructed using a modified LuGre model, and the parameters of the friction model were identified using intelligent identification algorithms. Moreover, a test system for the shell manipulator was established to achieve experimental validation. Finally, the effects of the clearance size and the stiffness of the cylinder support on the dynamic response were investigated.

Novel power hop model for an agricultural tractor with coupling bouncing, stick-slip, and free-play dynamics

Self-excited pitch and bounce oscillation occasionally occurs when a tractor pulls a high-draft load on dry soil. This dynamic instability is referred to as the power hop phenomenon. Power hop drastically degrades tractor performance and ride quality and can result in damage to the tractor, operator injury, and soil compaction. Power hop dynamics are characterised by three typical nonlinear elements; i.e., vertical jumping or bouncing, longitudinal stick-slip dynamics, and free-play in the joint between the tractor and implement. This paper couples these nonlinear elements and develops a novel power hop model for time-domain simulation. The occurrence process of power hop was demonstrated using the developed model using numerical experiments. Parametric investigations were conducted varying the drawbar pull, soil, and tyre conditions. The original draft load, joint clearance, static friction coefficient, ratio of coefficients of dynamic and static friction, front tyre stiffness, and rear tyre stiffness were taken as control parameters. The developed model predicted appropriately the occurrence of power hop for a higher draft load, drier soil, and “front stiff and rear soft” tyre stiffness conditions. The results agree obtained with conventional knowledge concerning power hops accumulated by previous experimental research. Thus, the developed model provides a strong platform adopting measures to control and suppress power hops. • A novel power hop model was developed for time-domain simulation. • Bouncing, stick–slip, and free-play dynamics coupled in a developed model. • Occurrence of power hop was demonstrated in a numerical simulation. • Parametric investigation into various drawbar pull, soil, and tyre conditions. • The developed model predicted power hop appropriately.

Dynamic Performance of Planetary Gear Joint for Satellite Antenna Driving Mechanism Considering Multi-Clearance Coupling

Dynamic pointing and tracking accuracy are the most relevant indicators of dynamic performance for the satellite antenna driving mechanism. Multi-clearance coupling in the joints will incur high-frequency vibration and dynamic errors of the system. Joints of existing analytical models are generally oversimplified as planar revolute hinges, which ignore the coupling effect of multi-clearance. It cannot proficiently predict the dynamic behavior of the driving mechanism with multi-clearance on the orbit. To address this problem, a typical 2K-H planetary gear joint model with multi-clearance coupling has been developed by considering radial clearance, backlash, tooth profile error, time-varying meshing stiffness, and damping. A dynamic model of a typical dual-axis driving mechanism is established to analyze the dynamic characteristics of multibody systems with planetary gear joints. The effects of rotational speed, radial clearance, backlash, and their coupling on the dynamic performance of the dual-axis driving mechanism under different driving modes are explored by numerical simulations. The results show that the coupling of radial clearance and backlash in joints have a significant influence on the dynamic performance of the system. Appropriate clearance design avails the dynamic pointing accuracy and tracking accuracy of the dual-axis driving mechanism.

Analysis and control of state jump in space deployable structures under alternating temperature loads

Abstract. State jump has been experimentally observed in space deployable structures working in alternating temperature environments. State jump is a phenomenon in which the geometric shape of the structure changes after the temperature loading and unloading process, which makes the working accuracy of the space deployable structure intrinsically unpredictable. This paper aims to investigate the causes of this state jump phenomenon and seek measures to reduce its effect. Firstly, the static multiple-stable-state phenomenon resulting in state jump is analyzed for clearance joints in deployable structures. Then, an equivalent model consisting of a variable stiffness spring and a contact element for state jump analysis is proposed, which is verified by a finite element simulation. Influence factors and control methods of state jump are further explored. Finally, numerical results of a space deployable structure of an umbrella-shaped antenna show the effectiveness of the developed analytical method.

Correlation dimension and bifurcation analysis for the planar slider-crank mechanism with multiple clearance joints

Joint clearance serves as a crucial element of nonlinearity in multibody systems. The quantization of the system chaos is conducive to not only the understanding of the nonlinear nature but the rationalization of system controlled parameters. In the present work, the system dynamics for the planar slider-crank mechanism with multiple clearance joints is depicted by the correlation dimension and bifurcation actions. Considering the obliqueness of the slider, the general configuration of the planar joint is proposed. Generalized coordinates and the Lagrangian approach are adopted to derive the dynamic motion equations. The effects of clearance size and driving speed on the bifurcations of the dynamic response are investigated. Furthermore, the fractal dimension of the strange attractor is identified by the correlation dimension from time series. Based on the Cao method, the Mutual Information (MI) function, and the Grassberger-Procaccia (G-P) algorithm, the controlled factors in the evaluation of correlation dimension are cautiously determined. Ultimately, the compound effect of translational and revolute clearance joints on the mechanism dynamics is featured. The numerical results testify that the correlation dimension of the slider displacement approximately saturates beyond a specific translational clearance value. Moreover, with the parameters used in this work, the complexity of system response seems to be more sensitive to the variation of translational clearance size than with the revolute joint.

Experimental and numerical study on viscously-damped outriggers with amplifying devices

A novel concept, labeled as amplified viscously-damped outrigger (AVDO) is proposed in this paper. It combines the viscously-damped outrigger (VDO) and steel amplifying devices to make the damper achieve higher energy dissipation capacity. Two newly-proposed configurations of AVDO were fabricated and compared with the conventional VDO by the dynamic cyclic loading test. The test results showed that AVDO can effectively amplify the deformation and energy dissipation of the damper. The change rule of the amplification factor and the difference between the experimental value and the theoretical value was analyzed, which highlighted that the deformation of components and the clearance in the pin joint had a great influence on the amplification of AVDO. Furthermore, a newly-developed model of joint clearance was used in the FE analysis of AVDO and validated with the experimental results. The stiffness of amplifying devices and outriggers and the joint clearance size effect on displacement amplification factor of AVDO were investigated. The amplifying device and the outrigger need to have sufficient stiffness to ensure the amplification effectiveness of AVDO, and it is suggested to reduce the clearance in the pin joint wherever applicable.

Temperature rise by viscous dissipation effect on synovial fluid induced by oscillating motion in artificial hip joint

A distinctive case study on the temperature rise, induced exclusively by viscous dissipation effect, due to the oscillating motion on a specific composition of synovial fluid within a clearance alike to an artificial hip joint, is investigated numerically for the first time, using the Ansys Fluent software. The joint clearance is modelled as concentric quarter hemispheres filled with a specific synovial fluid. The oscillating frequency considers the normal human walking speed and insulated thermal boundary conditions applied to surfaces that signifies the maximum viscous dissipation effect. Second order implicit time scheme is selected to achieve better result accuracy and ensure the unconditionally stable condition. The result shows that the viscous dissipation effect contributes to a maximum rise of 2.8° Celsius in temperature at the 1-h time mark, which is seen to lie within the in-vivo and in-vitro experiments reported in the literature. It is advocated that the viscous dissipation effect in the synovial fluid should be included in artificial hip joint model studies.

Mechanisms of flexible four-bar linkages: A brief review

The usages of linkage mechanisms in diverse applications, including manufacturing, are extensively appreciated. The synthesis of mechanisms for given motion and path generation has becomemore significant. The data of the kinematics of machines, thus, is a very important aspect of modern-day manufacturing. From conventional perception, kinematics' knowledge prevents many realistic mechanisms like pin deformation, joint clearances, and manufacturing inexactitudes, which cannot be overlooked. This study aims to explain the different design optimization processes and the analysis of flexible four-bar linkages for achieving a better solution. This study could be an essential step for setting the appropriate resources and optimizing the four-bar mechanism design to reduce the deviation from the desired output. The high-speed rotation of the mechanism may cause vibration and deformation in the system. So, different methods may be applied for improved four-bar mechanisms. This study provides us withprobable to resolve such conditions as precise load values regarding other vibrating elements. Like MATLAB, ADAMS, and ANSYS, the soft-computing method has been formulated to strengthen the researcher's analysis ability. These software packages may provide the improved design data in the form of displacement, deformation, and vibration frequency of the four-bar Mechanisms.

Improving Robot Precision Positioning Using a Neural Network Based on Levenberg Marquardt–APSO Algorithm

This paper proposes a robot calibration method that uses an extended Kalman filter (EKF) and a neural network based on Levenberg-Marquardt combined accelerated particle swarm optimization (LMAPSO) to improve the accuracy of the robot's absolute position. After the EKF optimizes all geometric parameters, the robot position still contains non-geometric errors due to joint clearance, gear backlash, and link deflection that are impossible to model. Therefore, an artificial neural network model (ANN) is designed to compensate for these un-modeled errors. The Levenberg-Marquardt combined accelerated particle swarm optimization (LMAPSO) provides a robust optimization search algorithm to optimize the weight and bias of the neural network based on the training set. An experiment on a five-bar parallel robot shows that geometric and non-geometric calibration reduced the maximum absolute position error from (1.548 to 0.045) mm. The experimental results demonstrate the proposed calibration method's effectiveness with the robot's absolute position accuracy improving by 98%.

Nonlinear dynamic characteristics and control of planar linear array deployable structures consisting of scissor-like elements with revolute clearance joint

This paper comprehensively deals with the parametric effects of the joint clearance and friction coefficient on the dynamics of planar deployable structures consisting of scissor-like elements (SLEs). The dynamic model for scissor deployable structure is based on a comprehensive consideration of the symmetry and array characteristics of this mechanism and on a Lagrange method, which represents the motion equations. A modified nonlinear contact-force model is employed to evaluate the intrajoint contact force, and the incorporation of the friction effect between the inter-connecting bodies is included in this study. The total impact forces produced in the real mechanical joint are embedded into the dynamics and the differential equations of motion are solved numerically based on a set of initial conditions. The clearance size, angle velocity, and friction coefficient are analyzed and discussed separately. Using Poincaré map, the regular and irregular responses of the deployable mulitibody systems are observed. Next, a control scheme is evaluated to maintain a more stable behavior and continuous contact between the clearance joints. The controlled results are compared with those without control, concluding that some undesired effects caused by the clearance joints can be prevented or reduced, resulting in continuous contact at the clearance joint.

Reliability analysis of radially retractable roofs with revolute joint clearances

Rectractable roofs commonly encounter a motion deviation due to the implementation of revolute joints clearances. This paper presents the reliability analysis of a Hoberman radial linkage mechanism with multi-loops. The effective length model is employed, and the effect of revolute joint clearance is reflected in the link length deviation. The loop incremental method is introduced and modified to analyze the position deviation of the multi-loops linkage mechanism. And reliability evaluation models are established based on the probability density functions. A case study is performed on the simple radially retractable mechanism. Position sensitivity, deviation and reliability of target nodes of the retractable roof are obtained for the development process. Moreover, a parametric analysis is carried out to investigate the effect of the calculation path, the link length, the number of circular links, and the folding number of links. The principle in this work can be used to guide the reliability evaluation and optimal design of radially retractable roof systems.

Wave Motion Dynamic Analysis of Planar Frame Structures With Clearance Joints

Abstract Due to kinematic function requirements, deployable structures inevitably have many clearance joints. The existence of clearance joints not only reduces the structural stiffness but also leads to complex nonlinear dynamic characteristics. This paper proposed a general numerical method based on the wave motion theory, which is able to analyze these complex nonlinear dynamic characteristics of frame structures with clearance joints. The dynamic model of frame structures with clearance joints is derived on the basis of continuous wave equations. The clearance joint is modeling by combining Lankarani and Nikravesh contact model with the Ambrósio friction model. The established dynamic model of frame structures is solved by the finite difference time domain (FDTD) method. A triangular frame structure with two clearance joints is taken as the numerical example for the verification of the proposed numerical method. Numerical results show that the longitudinal wave affects the distribution direction of contact positions and the transverse wave mainly affects the distribution range of contact positions. It has been also found that the introduction of torsional springs with reasonable pretension torque is able to significantly improve the distribution of contact positions and reduce state uncertainties of clearance joints in structural vibrations.

Accuracy analysis and optimization of an extendible support structure with joint clearances

An extendible support structure (ESS) used for unfolding and supporting the antenna array of the Synthetic Aperture Radar (SAR) satellite is reviewed and modeled in this paper. The structure is parameterized by calibrating 12 independent parameters, and following which, angular accuracy of the ESS with joint clearances is modeled. The maximum angular error is obtained by the particle swarm optimization (PSO) and validated by the Monte Carlo simulation. A novel error reduction method is then proposed to improve the accuracy of the structure. In the proposed method, the uncertainty of the joint clearance is eliminated using force constraints by adding small torsional springs. Various joint clearance models with force constraints are proposed to obtain the optimal spring allocation, and based on which, the angular error is further reduced by optimizing the structure of the ESS. The Quasi-Monte-Carlo-based Sobol method for global sensitivity analysis is used to select the design parameters for optimization. Finally, the angular error is greatly reduced.

Nonlinear dynamics analysis of shift manipulator for robot driver considering multiple revolute clearance joints and variable load

Clearance joints and variable load have a great influence on the dynamic performance of shift manipulator for robot driver. In this article, a dynamics model of clearance joint and a simulation method of variable load are proposed to analyze the influence of clearance joint and variable load on the dynamic performance of shift manipulator. Firstly, a hybrid nonlinear contact force model is established to describe the normal contact force of revolute clearance joint, and a modified Coulomb friction model is used to describe the tangential contact force of revolute clearance joint. On this basis, a virtual prototype dynamics model of shift manipulator with multiple revolute clearance joints is established. Then a power transmission model of shift manipulator including the variable load model at the end of shift manipulator is established. The time-varying and nonlinear characteristics of the load in gear engaging direction are simulated by neural network. Finally, the influences of different clearance dimension and variable load on the dynamic performance of shift manipulator are analyzed. Experiment and simulation results show the validity of the presented analysis, which provides a basis for further structure optimization of shift manipulator.

Global performance criterion of robotic manipulator with clearances based on reliability

This paper presents a novel performance criterion applied to robotic manipulators based on kinematic reliability. The kinetostatic performance criteria have been used to quantify the effect of errors in the manipulators. Nevertheless, design criteria based on the kinematic errors produced by joint clearances have not been established. This contribution proposes a novel performance index based on kinematic reliability concepts that evaluates the effect of the kinematic error produced by clearances over a required workspace. The application of the proposed global kinematic reliability criterion is evaluated for serial and parallel manipulators.

Nonlinear dynamic modeling and fluid–mechanism interaction analysis of reciprocating pump–pipeline system

The dynamic characteristics of reciprocating pump–pipeline system are directly affected by the fluid–mechanism dynamic interaction related to the slider-crank mechanism, valves and pipes conveying fluid. In this article, the fluid–mechanism interaction and nonlinearities involved in the kinetic of slider-crank mechanism, the motions of pump valves and the dynamic transmission in pipeline are explored for the nonlinear dynamic modeling of reciprocating pump–pipeline interaction systems. The nonlinear fluid–mechanism coupling model and corresponding analysis procedure are presented for investigating the system dynamic characteristics at all operating conditions. An experiment platform consisting of a simplex plunger reciprocating pump and suction and discharge pipes with a flow control valve is established to validate the proposed model. By the comparisons of pressure pulsations under multi-working conditions, the results obtained from the proposed model show good agreement with the test data. The dynamic characteristic of pump, as well as the effects of interaction and nonlinearity on the flow pulsation, are studied with the proposed model. It is found that nonlinear factors such as joint clearance and nonlinear spring stiffness are of great importance to the lag characteristics of pump valves and the pressure pulsation of pump–pipe system. The amplitudes of pressure pulsation increase with the decrease of control valve opening nonlinearly, and the effect of flow control valve becomes significant when the opening is less than 40%.