Interval Analysis Method for Determining Maximum Taskspace of Cable-driven Parallel Mechanisms

This article develops a geometric method to estimate the error space of 3-DoF planar mechanisms with the Minimum Volume Ellipsoid Enclosing (MVEE) approach. Both the joint clearance and input uncertainty are considered in this method. Three typical planar parallel mechanisms are used to demonstrate. Error spaces of their serial limbs are analyzed, respectively. Thereafter, limb-error-space-constrained mobility of manipulator, namely, the manipulator error space is analyzed. MVEE method has been applied to simplify the constraint modeling. A closed-form expression for the manipulator error space is derived. The volume of the manipulator error space is numerically estimated. The study approached in this paper develops a geometric error analysis method of parallel mechanisms with clear algebraic expressions. Moreover, far fewer forward kinematics computations have been performed in the proposed method than in the widely used interval analysis method. Although the estimated error space is larger than that in practice, due to the enclosing ellipses enlarge the regions of limb error space, the method has attractive advantage of high computational efficiency.

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Comparison between non-probabilistic interval analysis method and probabilistic approach in static response problem of structures with uncertain-but-bounded parameters

Communications in Numerical Methods in Engineering ◽

10.1002/cnm.668 ◽

2004 ◽

Vol 20 (4) ◽

pp. 279-290 ◽

Cited By ~ 23

Author(s):

Zhiping Qiu ◽

Yi Ma ◽

Xiaojun Wang

Keyword(s):

Interval Analysis ◽

Probabilistic Approach ◽

Analysis Method ◽

Static Response ◽

Interval Analysis Method

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INTERVAL AND SUBINTERVAL ANALYSIS METHODS OF THE STRUCTURAL ANALYSIS AND THEIR ERROR ESTIMATIONS

International Journal of Computational Methods ◽

10.1142/s0219876206000771 ◽

2006 ◽

Vol 03 (02) ◽

pp. 229-244 ◽

Cited By ~ 65

Author(s):

Y. T. ZHOU ◽

C. JIANG ◽

X. HAN

Keyword(s):

Interval Analysis ◽

Taylor Expansion ◽

Truncation Error ◽

Estimation Methods ◽

Uncertain Parameters ◽

Analysis Method ◽

Interval Analysis Method ◽

Analysis Methods ◽

Second Derivatives ◽

Error Estimations

In this paper, the interval analysis method is introduced to calculate the bounds of the structural displacement responses with small uncertain levels' parameters. This method is based on the first-order Taylor expansion and finite element method. The uncertain parameters are treated as the intervals, not necessary to know their probabilistic distributions. Through dividing the intervals of the uncertain parameters into several subintervals and applying the interval analysis to each subinterval combination, a subinterval analysis method is then suggested to deal with the structures with large uncertain levels' parameters. However, the second-order truncation error of the Taylor expansion and the linear approximation of the second derivatives with respect to the uncertain parameters, two error estimation methods are given to calculate the maximum errors of the interval analysis and subinterval analysis methods, respectively. A plane truss structure is investigated to demonstrate the efficiency of the presented method.

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An Interval Analysis for the Mesco Ductile Fracture

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.324-325.971 ◽

2006 ◽

Vol 324-325 ◽

pp. 971-974 ◽

Cited By ~ 2

Author(s):

Chang Hong Liu ◽

Hu Huang

Keyword(s):

Confidence Interval ◽

Ductile Fracture ◽

Interval Analysis ◽

Random Parameter ◽

Interval Number ◽

Experimental Results ◽

Analysis Method ◽

Fracture Characteristics ◽

Interval Analysis Method

With the concepts of the confidence interval, a random parameter can be transformed into an interval number in the mesco ductile fracture. Hence analyses of the random isolated void model can be used in the interval analysis method. Based on the macro- and mesco-experimental results of four steels, 30CrMnSiA, 40CrNiMoA, No.45 and No.20, the probabilistic fracture characteristics of the four steels are given. Finally the interval isolated void models in the four steels are discussed.

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