Uncertainty analysis and allocation of joint tolerances in robot manipulators based on interval analysis

Wu, Weidong; Rao, Singiresu S.

doi:10.1016/j.ress.2005.11.009

Cited by 96 publications

(40 citation statements)

References 20 publications

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“…Parkinson provided an application in which tolerances of a system is selected using optimization technique [9]. In Weidong Wu, S. S. Rao's research, they focus on the optimal allocation of joint tolerances with consideration of the positional and directional errors of the robot end effector and the manufacturing cost Tolerance Design of Robot Parameters Using Generalized Reduced Gradient Algorithm [3]. Similar Rao R. S et al [10], the interval analysis is used for predicting errors in the performance of robot.…”

Section: Literature Reviewmentioning

confidence: 99%

“…The right hand side matrices illustrate the position and direction of the end effector and they are determined based on the control trajectory of robot in space. The expansion the equation (1, 2) can be rewritten as: n s a p a a a a n s a p a a a a n s a p a a a a  (3) where: n, s, a are direction vectors; P is location vector; a ij with i, j =1÷3 is the direction cosine; a 14 , a 24 , a 34 are elements projected onto the global coordinate system Oxyz as P's components, respectively.…”

Section: The Formation Of the Optimal Problemmentioning

confidence: 99%

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Tolerance Design of Robot Parameters Using Generalized Reduced Gradient Algorithm

Trung¹,

Li²,

Long³

2017

IJMMM

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Abstract-In robot design, how to allocate tolerances for parts in manufacturing and assembling of robot is very important because this directly affects product quality and manufacturing cost. This paper introduces a technique using the Generalized Reduced Gradient algorithm optimization to allocate tolerances into robot parts. This method consists of three steps. First, based on the particular structure of robot, various methods are considered before the best method suitable for modeling the associated equation is chosen. Then, a mathematical model for tolerance allocation is formulated and transferred into the non-linear multi-variable optimization problem. Finally, this optimization problem is solved by using the Generalized Reduced Gradient algorithm. Two examples are used to verify the feasibility of the proposed method; the accuracy and effectiveness of the proposed method in producing the tolerance allocations is also illustrated via calculation and simulation results.

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Section: Literature Reviewmentioning

confidence: 99%

Section: The Formation Of the Optimal Problemmentioning

confidence: 99%

Tolerance Design of Robot Parameters Using Generalized Reduced Gradient Algorithm

Trung¹,

Li²,

Long³

2017

IJMMM

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“…[15,Lemma 3.4] and [14,Lemma 4.4]). Moreover, our approach can apply to other nonlinear evolution equations with complex boundaries, for instance, the damped semilinear wave equation with critical growth exponent and dissipative boundary condition [16]; semilinear parabolic equation with dynamical boundary condition [11]; Cahn -Hilliard equation with the Wentzell boundary condition [12].…”

Section: Remark 23mentioning

confidence: 99%

“…Under the basic assumption that the nonlinearity is analytic with respect to the dependent variable, we develop several new Łojasiewicz-Simon type inequalities (with boundary term) which vary from problem to problem (Ref. [11,12,[14][15][16]) and obtain the convergence result as well as the estimates for convergence rate.…”

Section: Introductionmentioning

confidence: 99%

Convergence to equilibrium for some nonlinear evolution equations with dynamical boundary condition

2007

Proc Appl Math and Mech

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“…Interval analysis represents the uncertainty by the distribution intervals of parameters, and is very suitable to the situation that the boundaries of parameters are the only valuable information [7][8]. The solutions of interval equations include direct method, combined method, and interval-truncation method.…”

Section: Introductionmentioning

confidence: 99%

Calculation of Failure Probability of Series and Parallel Systems for Imprecise Probability

Suo¹,

Cheng²,

Zeng³

et al. 2012

IJEM

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In the situation that unit failure probability is imprecise when calculation the failure probability of system, classical probability method is not applicable, and the analysis result of interval method is coarse. To calculate the reliability of series and parallel systems in above situation, D-S evidence theory was used to represent the unit failure probability. Multi-sources information was fused, and belief and plausibility function were used to calculate the reliability of series and parallel systems by evidential reasoning. By this mean, lower and upper bounds of probability distribution of system failure probability were obtained. Simulation result shows that the proposed method is preferable to deal with the imprecise probability in reliability calculation, and can get additional information when compare with interval analysis method.

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Uncertainty analysis and allocation of joint tolerances in robot manipulators based on interval analysis

Cited by 96 publications

References 20 publications

Tolerance Design of Robot Parameters Using Generalized Reduced Gradient Algorithm

Tolerance Design of Robot Parameters Using Generalized Reduced Gradient Algorithm

Convergence to equilibrium for some nonlinear evolution equations with dynamical boundary condition

Calculation of Failure Probability of Series and Parallel Systems for Imprecise Probability

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