Dynamics analysis of space robot manipulator with joint clearance

Investigation of joint clearance effects on welding robot manipulators

This paper is devoted to a general methodological study on sensitivity analysis and robust optimization for a planar crank-slider mechanism in presence of joint clearances and random parameters and investigate the effects of parameter uncertainty on optimization results when joint clearance sizes are constantly changing due to wear. The first-order sensitivity analysis based on the response surface proxy model is performed. Then, a multiobjective robust optimization algorithm based on sensitivity analysis is carried out to reduce the undesirable effects of joint clearances and random parameters. In the algorithm, a multiobjective robust optimization model derived from the mean and variance of the objective function is constructed. Here, the objective function is defined based on the consideration of reducing the contact force generated at all clearance joints. Additionally, in order to balance computational accuracy and efficiency in the multiobjective robust optimization process, high-precision Kriging agent models are established. The optimum values of design variables are determined by combining Monte Carlo sampling and multiobjective particle swarm optimization method. By combining the Baumgarte approach with Lankarani–Nikravesh contact force model and Coulomb friction model, the dynamic equations of the planar multibody system with clearance joints are established. The uniform probability distribution is applied for characterizing random parameters. Simulation results show that the influence of design variable variations on the objective function changes in relation to the joint clearance size, but their relative influence degree on the objective function will not vary with the size of joint clearances. Moreover, the optimal solution selected on the Pareto front will affect the average levels and peak fluctuations of the dynamic responses in multibody systems.

There are still lots of joint clearances that cannot be eliminated for large-scale flexible spacecraft in post-lock phase. Joint clearance directly affects the attitude maneuver of the flexible spacecraft as well as the pointing accuracy and stability of the payload, which has a great influence on the dynamic characteristics of the spacecraft. Aiming at this issue, a dynamic modelling and control method for the rigid-flexible coupling spacecraft with joint clearance is proposed in this paper. The accurate dynamic model of the joint with clearance is established firstly, thus the dynamic model of flexible structure with joint clearances is built. Then the discrete rigid-flexible coupling nonlinear dynamic model of the spacecraft with clearances is obtained by Hamilton principle and modal discrete method. The Newmark algorithm is used to solve the nonlinear equation. Based on macro fiber composite (MFC) actuator, the rigid-flexible-electrical coupling dynamic equation of the spacecraft is obtained and the control law is designed by the optimum control. The influences of joint parameters, moment of inertia of central rigid body, clearance size and clearance number on the dynamic characteristics of the spacecraft are analyzed. The effects of joint clearance on the attitude maneuver and structural vibration of the spacecraft are emphatically studied. Finally, the active control is applied to the spacecraft using MFC actuator. The results reveal that the joint parameters and moment of inertia of the central rigid body affect the natural frequency of the spacecraft. With the increase of the size of joint clearance and number of clearances, the overall stiffness of the spacecraft decreases gradually, while the attitude angle and vibration displacement response of the spacecraft increase. Through the active control based on MFC, the cooperative control of the attitude maneuver and structural vibration of the spacecraft with clearance can be realized, and the effects of clearance on the dynamic characteristics of the spacecraft can be alleviated.

This paper aims at investigating precisely the dynamic performance of deployable structure constituted by scissor unit mechanisms with clearance joint. Based on the motion law in real joints, the contact model is established using an improved Gonthier nonlinear continuous contact force model, and the friction effect is considered using LuGre model. Moreover, the resulting contact force is suitable to be included into the generalized force of the equations of motion of a multibody system and contributes to replace motion constraints. In the sequel of this process, the effect of joint clearance is successfully introduced into the dynamical model of scissor deployable structure and the dynamic characteristics of deployable structure with joint clearance are obtained using a direct default correction method, which can directly modify the coordinates and speed of the system to avoid the numerical results divergence. Also, the new hybrid contact force model of revolute joint clearance is verified through comparing with the original model. The numerical simulation results show that the improved contact model proposed here has the great merit that predicts the dynamic behavior of scissor deployable structure with joint clearance.

Dynamics modeling and quantitative analysis of multibody systems including revolute clearance joint

In practical operation of mechanisms, joint clearances and compliance influence the overall performance drastically. Excessive clearances induce extra degrees of freedom at the joint, while compliance provides an additional torque. This paper presents the dynamic analysis of partially compliant planar slider–crank mechanism with joint clearance. When joint clearance is considered, an additional intermittent impact force acts on the system and velocity and acceleration as well as forces at the joints change drastically. Therefore, mechanisms are often made compliant with limited number of joints. In order to model compliant linkage, equivalent torque is introduced at the joint using pseudo-rigid-body modeling. Initially, the turning moment and force equations of crank, coupler, and slider are obtained in terms of contact forces at the clearance joint. Effect of clearance at the crank pin on the kinematic and dynamic characteristics is studied in detail.

This article numerically investigates the effects of revolute joint clearance and structural flexibility on the overall dynamic characteristics of a deployable solar array system. Considering torque spring, close cable loop configuration, and lock mechanism, a typical mechanism composed of a main body with a yoke and two panels is used as a demonstration case to study the effects of clearance and flexibility on the dynamic response of the deployable solar array system in the deployment and lock process. The normal contact force model and tangential friction model in clearance joint are established using Lankarani Nikravesh model and modified Coulomb friction model, respectively. The numerical simulation results reveal that the coupling of clearance and flexibility makes different effects on the dynamic characteristics of the deployable space solar arrays for different operation stages. Besides, the clearance and flexibility of a mechanical system play crucial roles in predicting accurately the dynamic response of the system, which is the foundation of mechanism design, precision analysis, and control system design.

Uncertainties caused by measuring errors or incomplete knowledge affect the dynamic response and functional reliability of the mechanical system, particularly for the mechanisms with clearance joints. Considering that dependency between the interval parameters in the uncertain quantification of mechanical systems with clearance joints is prone to be ignored, in this article, a dynamic analysis procedure considering the correlation between interval parameters is presented. Firstly, the continuous contact force model and modified friction force model are embedded into the deterministic dynamic governing equations of the mechanical system with clearance joints derived by the Lagrangian method. To characterize the correlation between interval uncertainties, the convex ellipsoid model is employed, and a Chebyshev-based convex scanning method is developed to obtain the bounds of dynamic response. Finally, a robot manipulator with clearance joint considering dependent uncertainties is illustrated as an example to investigate the clearance effect and correlations between uncertainties on the dynamic behavior. In the numerical simulation, the geometrical parameters of the manipulator arm are regarded as dependent interval parameters. The results show that the dependence between interval uncertainties induces relatively conservative bounds and should be considered carefully in the case of a large clearance size existing in the mechanical system.

Effects of balancing and link flexibility on dynamics of a planar mechanism having joint clearance

Clearance imposes some uncontrollable degrees of freedom to a manipulator. Therefore, poor dynamic performance, low accuracy, reduction in components lifetime and generation of undesirable vibrations result in the impacts of mating parts in a clearance joint. In this study, the effects of clearance on the dynamics of a planar 3-RRR parallel manipulator are investigated. Then, an optimization algorithm for simultaneously kinematic and dynamic synthesis has been carried out to reduce these effects and improve the performance and the accuracy of the manipulator. The algorithm is based on changing the lengths and the mass distribution of the links. By combining the Lagrange equations with Lankarani–Nikravesh contact force model, a series of dynamic equations are established. Then, the highly nonlinear optimization problem is tackled via a PSO method. The last but not the least, the efficiency of the algorithm and its superiority have been demonstrated by a numerical example. We claim that the linear and angular accelerations of the links and the contact forces in the joints are bounded and evolve very smoothly in the optimal design. Finally, to verify the validity of the optimization algorithm, the planar 3-RRR parallel manipulator is modeled in MSC.ADAMS software and the simulation results are compared for the original and the optimal manipulators.

Clearances are essential for the assemblage of mechanisms to allow the relative motion between the joined bodies. This clearance exists due to machining tolerances, wear, material deformations, and imperfections, and it can worsen the mechanism performance when the precision and smoothly-working are intended. Energy is a subject which is less paid attention in the area of clearance. The effect of the clearance on the energy of a flexible slider-crank mechanism is investigated in this paper. A clearance exists in the joint between the slider and the coupler. The contact force model is based on the Lankarani and Nikravesh model and the friction force is calculated using the modified Coulomb\'s friction law. The hysteresis damping which has been included in the contact force model dissipates energy in clearance joints. The other source for the energy loss is the friction between the journal and the bearing. Initial configuration and crank angular velocity are changed to see their effects on the energy of the system. Energy diagrams are plotted for different coefficients of friction to see its influence. Finally, considering the coupler as a flexible body, the effect of flexibility on the energy of the system is investigated.

Over the last two decades, extensive work has been conducted on dynamic effect of joint clearances in multibody mechanical systems. In contrast, little work has been devoted to optimizing the performance of these systems. In this study, analysis of revolute joint clearance is formulated in term of a Hertzian-based contact force model. For illustration, the classical slider-crank mechanism with a revolute clearance joint at the piston pin is presented, and a simulation model is developed using the analysis/design code MSC.ADAMS. The clearance is modeled as a pin-in-a-hole surface-to-surface dry contact, with appropriate contact force model between the joint and bearing surfaces. Different simulations are performed to demonstrate the influence of the joint clearance size and the input crank speed on the dynamic behavior of the system with the clearance joint. An innovative design-of-experiment (DOE)-based method for optimizing the performance of a mechanical system with the revolute joint clearance for different ranges of design parameters is then proposed. Based on the simulation model results from sample points, which are selected by a Latin hypercube sampling (LHS) method, a polynomial function Kriging meta-model is established instead of the actual simulation model. The reason for development and use of the meta-model is to bypass computationally intensive simulations of a computer model for different design parameter values in place of a more efficient and cost-effective mathematical model. Finally, numerical results obtained from two application examples, considering the different design parameters, including the joint clearance size, crank speed, and contact stiffness, are presented for further analyzing the dynamics of the revolute clearance joint in a mechanical system. This allows for predicting the influence of design parameter changes, in order to minimize contact forces, accelerations, and power requirements due to the existence of joint clearance.

In mechanical systems, the effect of friction on the dynamic response of the mechanism is unavoidable. In order to describe the friction behavior at the revolute joint of mechanical systems more accurately, the friction coefficient is modeled as a nonlinear function with respect to pressure and rotational speed based on material-level friction tests. Combined with the Ambrósio friction model, we propose a friction model with nonlinear friction coefficient, and the dynamics of a crank-slider mechanism containing a revolute clearance joint is analyzed based on the proposed model. The results show that the friction model with nonlinear friction coefficient can improve the accuracy of numerical simulation of the system and promote the capability of prediction of dynamic response of complex mechanical systems with joint clearance.

Clearance is inevitable for manufacture and assembly in the revolute joints of multibody systems. Excessive value of joint clearance will lead to the poor dynamic performance of mechanism, namely noise, vibration and fatigue failure. This paper presents the development of a dynamic model for planar multibody systems with clearance joints. Based on the continuous contact law, the contact force model proposed by Lankarani and Nikravesh is employed to describe the contact–impact phenomenon between pin and hole. And, the incorporation of the friction influence on revolute joint clearance is conducted by a modified friction force model. According to the geometric relationship between contact elements, the kinematics of the multibody systems is mapped into the global coordinate systems. Additionally, an experimental test platform is set up whereby a slider–crank mechanism with two clearance joints is used as an example to demonstrate the correctness and effectiveness of the proposed approach. Finally, the effects of joint clearance on the dynamic characteristics of planar multibody systems are investigated.

In general, joints are assumed without clearance in the dynamic analysis of multi-body echanical systems. When joint clearance is considered, the mechanism obtains two uncontrollable degrees of freedom and hence the dynamic response considerably changes. The joints’ clearances are the main sources of vibrations and noise due to the impact of the coupling parts in the joints. Therefore, the system responses lead to chaotic and unpredictable behaviors instead of being periodic and regular. In this paper, nonlinear dynamic behavior of a four-bar linkage with clearance at the joint between the coupler and the rocker is studied. The system response is performed by using a nonlinear continuous contact force model proposed by Lankarani and Nikravesh [1] and the friction effect is considered by a modified Coulomb friction law [2]. By using the Poincare portrait, it is proven that either strange attractors or chaos exist in the system response. Numerical simulations display both periodic and chaotic motions in the system behavior. Therefore, bifurcation analysis is carried out with a change in the size of the clearance corresponding to different values of crank rotational velocities. Fast Fourier Transformation is applied to analyze the frequency spectrum of the system response.