Motion Reliability Analysis of a 3-RRR Parallel Manipulator With Random and Interval Variables

2016 ◽  
Author(s):  
Zhenhui Zhan ◽  
Xianmin Zhang
Keyword(s):  
Reliability Analysis ◽  
Parallel Manipulator ◽  
Random Variable ◽  
Parallel Manipulators ◽  
Analysis Method ◽  
Motion Error ◽  
Interval Variables ◽  
First Order Second Moment ◽  
Joint Clearances ◽  
Mcs Method

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.

scholarly journals An Efficient Time-Variant Reliability Analysis Method with Mixed Uncertainties

Algorithms ◽  
2021 ◽  
Vol 14 (8) ◽  
pp. 229
Author(s):  
Fangyi Li ◽  
Yufei Yan ◽  
Jianhua Rong ◽  
Houyao Zhu
Keyword(s):  
Reliability Analysis ◽  
Limit State ◽  
Random Variables ◽  
Equivalent Model ◽  
Independent Random Variables ◽  
Problem Analysis ◽  
Analysis Method ◽  
Calculation Algorithm ◽  
Reliability Problem ◽  
Interval Variables

In practical engineering, due to the lack of information, it is impossible to accurately determine the distribution of all variables. Therefore, time-variant reliability problems with both random and interval variables may be encountered. However, this kind of problem usually involves a complex multilevel nested optimization problem, which leads to a substantial computational burden, and it is difficult to meet the requirements of complex engineering problem analysis. This study proposes a decoupling strategy to efficiently analyze the time-variant reliability based on the mixed uncertainty model. The interval variables are treated with independent random variables that are uniformly distributed in their respective intervals. Then the time-variant reliability-equivalent model, containing only random variables, is established, to avoid multi-layer nesting optimization. The stochastic process is first discretized to obtain several static limit state functions at different times. The time-variant reliability problem is changed into the conventional time-invariant system reliability problem. First order reliability analysis method (FORM) is used to analyze the reliability of each time. Thus, an efficient and robust convergence hybrid time-variant reliability calculation algorithm is proposed based on the equivalent model. Finally, numerical examples shows the effectiveness of the proposed method.

Kinematic Reliability Analysis of Robotic Manipulator

2019 ◽  
Vol 142 (4) ◽  
Author(s):  
Dequan Zhang ◽  
Xu Han
Keyword(s):  
Saddle Point ◽  
Reliability Analysis ◽  
Target Position ◽  
Robotic Manipulators ◽  
Analysis Method ◽  
Saddle Point Approximation ◽  
Motion Error ◽  
End Effector ◽  
Standard Normal ◽  
Dependent Coordinates

Abstract Kinematic reliability of robotic manipulators is the linchpin for restraining the positional errors within acceptable limits. This work develops an efficient reliability analysis method to account for random dimensions and joint angles of robotic mechanisms. It aims to proficiently predict the kinematic reliability of robotic manipulators. The kinematic reliability is defined by the probability that the actual position of an end-effector falls into a specified tolerance sphere, which is centered at the target position. The motion error is indicated by a compound function of independent standard normal variables constructed by three co-dependent coordinates of the end-effector. The saddle point approximation is then applied to compute the kinematic reliability. Exemplification demonstrates satisfactory accuracy and efficiency of the proposed method due to the construction and the saddle point since random simulation is spared.

A Time-Variant Reliability Analysis Method Based on Stochastic Process Discretization

2014 ◽  
Vol 136 (9) ◽  
Author(s):  
C. Jiang ◽  
X. P. Huang ◽  
X. Han ◽  
D. Q. Zhang
Keyword(s):  
Stochastic Process ◽  
Reliability Analysis ◽  
System Reliability ◽  
Limit State ◽  
Complex Structure ◽  
Random Variable ◽  
State Function ◽  
Analysis Method ◽  
Reliability Problem ◽  
Reliability Method

Time-variant reliability problems caused by deterioration in material properties, dynamic load uncertainty, and other causes are widespread among practical engineering applications. This study proposes a novel time-variant reliability analysis method based on stochastic process discretization (TRPD), which provides an effective analytical tool for assessing design reliability over the whole lifecycle of a complex structure. Using time discretization, a stochastic process can be converted into random variables, thereby transforming a time-variant reliability problem into a conventional time-invariant system reliability problem. By linearizing the limit-state function with the first-order reliability method (FORM) and furthermore, introducing a new random variable, the converted system reliability problem can be efficiently solved. The TRPD avoids the calculation of outcrossing rates, which simplifies the process of solving time-variant reliability problems and produces high computational efficiency. Finally, three numerical examples are used to verify the effectiveness of this approach.

Jacobian-based stiffness analysis method for parallel manipulators with non-redundant legs

2015 ◽  
Vol 230 (3) ◽  
pp. 341-352 ◽  
Author(s):  
Antonius GL Hoevenaars ◽  
Patrice Lambert ◽  
Just L Herder
Keyword(s):  
Parallel Manipulator ◽  
Screw Theory ◽  
Parallel Manipulators ◽  
Structural Elements ◽  
Analysis Method ◽  
End Effector ◽  
Stiffness Analysis ◽  
Compliant Joints ◽  
Lower Mobility ◽  
Actuated Joints

Stiffness is an important element in the model of a parallel manipulator. A complete stiffness analysis includes the contributions of joints as well as structural elements. Parallel manipulators potentially include both actuated joints, passive compliant joints, and zero stiffness joints, while a leg may impose constraints on the end-effector in the case of lower mobility parallel manipulators. Additionally, parallel manipulators are often designed to interact with an environment, which means that an external wrench may be applied to the end-effector. This paper presents a Jacobian-based stiffness analysis method, based on screw theory, that effectively considers all above aspects and which also applies to parallel manipulators with non-redundant legs.

Discussion of Reliability Analysis for Aircraft Wing Box Structural System

2010 ◽  
Vol 118-120 ◽  
pp. 236-240
Author(s):  
Wei Tao Zhao ◽  
Da Qian Zhang
Keyword(s):  
Reliability Analysis ◽  
Failure Probability ◽  
Structural Reliability ◽  
Random Variable ◽  
Complex Problem ◽  
Structural System ◽  
Aircraft Wing ◽  
Failure Path ◽  
First Order Second Moment ◽  
Wing Box

It is very complex problem that the reliability of aircraft wing box structural system with many random variables (such as area, thickness, material modulus, load etc.) is analyzed. In the paper, the reliability analysis method of aircraft wing box structural system is proposed based on the theory of structural reliability and stochastic finite element. The explicit expression of safe margin and the sensitivity of safe margin to each random variable are given, which improves the accuracy and efficiency of reliability calculation. The relationship of the level of failure path with structural system failure probability is discussion. The failure probability of element is calculated by using first order second moment method, and the main failure path of structural system is identified by using the advanced branch and bound method, and the failure probability of structural system is evaluated by using probabilistic network evaluation technique method. Numerical examples show that the method is of efficient and accurate, and the 3 or 4 level of failure path is acceptable for wing box structural system considering efficiency and accuracy.

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