Error modelling and motion reliability analysis of a multi-DOF redundant parallel mechanism with hybrid uncertainties

Error modelling and motion reliability analysis of a planar parallel manipulator with multiple uncertainties

A general methodology for motion error and motion reliability analysis of planar parallel manipulators (PPMs) with random and interval variables is presented. The inherent uncertainties of the manipulator, including tolerances in manufactures, errors in inputs as well as joint clearances are taken into account. The error model of a 3-RRR parallel manipulator is built and the global sensitivity coefficients of motion errors to variations are defined and obtained. The joint clearances are treated as interval variables while the others are treated as random variables. As a result, the motion error of the manipulator could turn out to be the mixture of a random variable and an interval variable. A new motion reliability analysis method based on the First Order Second Moment (FOSM) method and the Monte Carlo simulation (MCS) method is developed for the manipulator with random and interval variables. This paper provides a new idea to better understand the motion reliability affected by the inherent uncertainties of PPMs.

Calibration of a (6 + 3)-DOF kinematically redundant parallel mechanism based on hybrid identification algorithm and two-step compensation strategy

In recent years, parallel robots have become a hot research topic in trauma fracture treatment because of their high precision, high load capacity, and compact structure. However, parallel robots have disadvantages like small workspaces and complex singularity. In this article, a novel redundant parallel mechanism (RPM) for long bone fracture reduction is proposed based on Stewart parallel mechanism (SPM). Six kinematically redundant DOFs (degrees-of-freedom) are added to the RPM. First, the kinematics of the RPM is established, and its workspace is calculated. The analysis results indicate that the position workspace of the RPM is about 19 times larger than that of the SPM. The RPM has a similar range of torsion angles as the SPM, but a more extensive range of tilt angles than the SPM. Second, the singularities of the two parallel mechanisms are compared based on the dimensionally homogeneous Jacobian matrix. The results show that the dexterity of the RPM is much better than the SPM. Third, a multiparameter multi-objective optimization method is proposed to optimize the geometry parameters of the RPM. The statics of the RPM is analyzed by finite element analysis. To further expand the performance of the RPM, the unfixed RPM (URPM) is proposed. The analysis results show that the URPM is superior to the RPM in terms of workspace and dexterity. Finally, experiments are conducted to verify the effectiveness of the proposed methods in this article.

The parallel mechanism exhibits high stiffness and excellent dynamic response, making it ideal for high-precision applications. In our early work, a novel 6-DOF redundant parallel posture mechanism with four limbs for solar wing docking has been proposed; each limb consists of three links and four joints. This paper primarily focuses on optimization design of the mechanism. The calculation of workspace volume reveals that factors influencing the range of posture adjustment include dynamic platform parameters, static platform parameters, the drive trajectory of each kinematic pair, and the angles between each kinematic pair. A sensitivity analysis was conducted to examine the impact of each parameter on the range of posture adjustment. To reduce computational complexity and improve analysis efficiency, a combined approach of single-factor analysis and response surface methodology (RSM) is used in the paper. Single-factor analysis is utilized to evaluate the effect of each parameter on the posture adjustment range. Based on these results, RSM is used to establish a regression model for parameters; thereby, the optimal parameter combination for the mechanism is determined. The regression coefficient R2 = 0.9374 attests to the validity of the proposed model. Finally, a comparison of the posture adjustment range before and after optimization is presented, providing a foundation for the practical application of the redundant parallel mechanism. This paper introduces a novel structural design concept aimed at resolving the conflict between heavy loads and compact sizes in redundant parallel mechanisms while providing valuable insights for miniaturized design.

This paper presents a redundantly actuated six degrees-of-freedom parallel kinematic mechanism with a partially decoupled architecture in its rotational motion. This mechanism is developed to eliminate kinematic complexity of original Eclipse-II known as a redundant parallel mechanism. Since the original Eclipse-II mechanism use kinematic redundancy of parallel mechanism to achieve an advantage in enlarging the workspace of the system, it needs a motion planning algorithm to choose the specific control inputs to determine the desired motion trajectory. This motion planning algorithm causes difficulty in achieving real-time control performance due to its structural complexity. However the redundant parallel mechanism presented in this paper is a redundant parallel mechanism with partially decoupled architecture in its rotational motion. Therefore modified Eclipse-II redundant parallel mechanism can realize effective real-time control performances and continuous 360-degree rotational motion in any direction of the moving platform with six degrees of freedom.

With haptic devices becoming increasingly common in both industrial field and consumer use, parallel mechanisms have been widely introduced for their high rigidity, output, accuracy and high backdrivability due to their multi-legged structure and fixed base actuators. In general parallel mechanism, redundancy enlarges the working area and avoids singularity. The redundant parallel mechanism we present introduces these advantages into haptic applications. Introducing this mechanism into a multiple degrees-of-freedom (DOF) structure realizes a wide range of working areas in rotation. The redundant parallel mechanism implemented in translational force display device, and multi-DOF force display device demonstrate the advantages of the redundant parallel mechanism in haptic applications. Following an overview, we introduce the prototype implementation and evaluation of these devices and discuss the effectiveness of the redundant parallel mechanism in haptic applications.

Flexible manipulator is an emerging technique in aerospace engineering, especially in the assembly, testing and maintenance of space stations. Dynamic analysis of a flexible manipulator with multiple clearance joints and hybrid uncertainties is a great challenge as compared to traditional flexible manipulator. To solve the problem, a dynamics model for a simplified flexible manipulator with interval clearance joints and random material properties was established. In this model, the Lankarani–Nikravesh contact force model was used to construct the clearance joint, while a combined feedforward–feedback control strategy based on a PID controller was applied to control the flexible manipulator. In addition, the clearance sizes and the Young’s moduli of the flexible parts were described by interval variables and random fields, respectively. To solve the dynamics model, a general methodology, based on the Karhunen–Loeve expansion and Kriging model, was presented. Finally, numerical examples were employed to demonstrate the validity of the proposed approach. The simulation results indicate that the joint clearance, the flexibility of the components and the uncertainties have great impacts on the kinematic accuracy and dynamic behaviors of the flexible manipulator, while hybrid uncertainties result in worse kinematic accuracy and more complex dynamic behaviors.

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.

This paper compares quasi Monte Carlo methods, in particular so-called (t, m, s)-nets, with classical Monte Carlo approaches for simulating econometric time-series models. Quasi Monte Carlo methods have found successful application in many fields, such as physics, image processing, and the evaluation of finance derivatives. However, they are rarely used in econometrics. Here, we apply both traditional and quasi Monte Carlo simulation methods to time-series models that typically arise in macroeconometrics. The numerical experiments demonstrate that quasi Monte Carlo methods outperform traditional ones for all models we investigate.

Traditional stiffness modeling methods do not consider all factors comprehensively, and the modeling methods are not unified, lacking a global stiffness model. Based on screw theory, strain energy and the virtual work principle, a static stiffness modeling method for redundant over-constrained parallel mechanisms (PMs) with clearance was proposed that considers the driving stiffness, branch deformation, redundant driving, joint clearance and joint contact deformation. First, the driving stiffness and branch deformation were considered. According to the strain energy and Castiliano's second theorem, the global stiffness matrix of the ideal joint mechanism was obtained. The offset of the branch was analyzed according to the restraint force of each branch. The mathematical relationship between the joint clearance and joint contact deformation and the end deformation was established. Based on the probability statistical model, the uncertainty of the offset value of the clearance joint and the contact area of the joint caused by the coupling of the branch constraint force was solved. Finally, taking a 2UPR-RR-2RPU redundant PM as an example, a stiffness simulation of the mechanism was carried out using the finite element method. The research results show that the high-precision stiffness modeling method proposed in this paper is correct, and provides an effective method for evaluating the stiffness performance of the PM.

The clearance joint is one of the important factors which influence system performance and dynamic characteristics. Traditional studies are mainly focused on the planar single degree of freedom (DOF) simple mechanism with one joint clearance, only few researchers investigated mechanisms with more than one DOF considering more than one clearance joint as an object, and few studies systematically analyzed nonlinear characteristics of the clearance joints. This article is devoted to analyzing the effect of multiple clearances and different friction models on the dynamic behavior of a planar multi-DOF mechanism. The 2 DOFs nine bar planar mechanism is selected as the research object. The dynamic model of the planar mechanism with two revolute clearances is built by considering Lagrange equation. The influence of LuGre model and modified Coulomb friction model on the dynamic response of the nine bar mechanism is studied. The effects of the number of clearance joints, clearance values, driving speeds and friction coefficients on the dynamic responses of the mechanism are analyzed. The chaos phenomenon existing in the clearance revolute joints is identified by phase diagram, Poincare map and largest Lyapunov exponent (LLE). Bifurcation diagrams of revolute clearance joints with changing clearance values, driving speeds and friction coefficients are also drawn. A virtual prototype model of 2 DOF nine bar mechanism containing two revolute clearances is built by using ADAMS software to verify the correctness of the numerical results. This research can provide theoretical basis for grasping the dynamic behavior of the planar rigid-body mechanism with clearances and identifying chaos of clearance joints.

Reliability analysis of motion mechanism under three types of hybrid uncertainties

The present study investigates the hybrid reliability modeling of structures in which the inputs contain both random variables and interval variables. Hybrid uncertainty is divided into three categories, including random variables mixed with random variables, interval variables mixed with interval variable, and random variables mixed with interval variables. In order to perform the reliability analysis of structural systems, first, the Bayes method is proposed in the present study to obtain distribution parameters of random variables. Moreover, the self‐sample method is introduced to obtain the interval boundaries based on the least available measuring data. Then, the reliability models are established for three situations and the reliability indices are defined and derived accordingly. The abovementioned three types of reliability indices outline the general situation of structural systems. Finally, the specific calculation process is described in details through different examples. Furthermore, the accuracy and efficiency of the proposed method is discussed by comparing the results obtained from the Monte Carlo simulation and those of other methods. The obtained results indicate that the performance of the proposed model in solving reliability modeling problems is better.

For common parallel mechanisms, outputs are often coupled strongly with inputs. Redundant input parallel mechanism has more inputs than usual and which makes it much more complex. Parallel mechanism is very fit for vibration platform for its high acceleration and rigidity. While acceleration estimation of the moving platform is influenced by many factors, such as mechanism parameters, type structure and performance of servomotor. This paper divides the redundant input parallel mechanism into three parts, including the moving platform, slide-screw-coupling-motor sub-system and the fix-length bar. And then the inverse dynamics is built up by virtual work prince. Finally the acceleration estimation method is introduced by example of this redundant input parallel mechanism.