Tolerance analysis of flexible kinematic mechanism using DLM method

Imani, Behnam Moetakef; Pour, Masoud

doi:10.1016/j.mechmachtheory.2008.03.010

Cited by 20 publications

(12 citation statements)

References 3 publications

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“…where S is a sensitivity matrix as mentioned by Leishman et al [14]. All basic principles about calculations for DLM can be reviewed in references [12,13,25]. For velocity and acceleration calculations, Leishman et al [14] showed in detail the procedure, which is based on the differentiation of the position equations without and with variations.…”

Section: Direct Linearization Methods (Dlm)mentioning

confidence: 99%

“…The method is usually expressed by a formulation of Jacobian matrices which allows deterministic and probabilistic error assessments, e.g., worst case error and root-sum-square error. DLM has been applied in different mechanism types by [13,14], from rigid to flexible-body. Their work described how the coupler path of a four-bar mechanisms is affected (shifting in variance and in covariance of positioning errors) and unveiling critical parameters with highest contributions to the variations of assembly specifications.…”

Section: Mathematical Problems In Engineeringmentioning

confidence: 99%

“…According to the traditional mechanism design, the output positions are deterministically predicted. However, when the geometry of the mechanisms varies by different circumstances, the output positions should exist inside an error domain which can be seen as a tolerance as proposed by different studies [13,26,27]. With this purpose, a solution space is established and delimited by five points that belong to the output positions of a mechanism with fixed variations dX.…”

Section: Position Prediction In a Localmentioning

confidence: 99%

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Tolerance Analysis of Planar Mechanisms Based on a Residual Approach: A Complementary Method to DLM

Tinoco

Durango

2019

Mathematical Problems in Engineering

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The kinematic performance of mechanisms is affected by different uncertainty sources involved in the manufacturing and assembling cycle; among these are the geometric variations. It is known that the effects of these variations produce position errors which are not usually included in the design process. With this objective, a complementary method for the tolerance analysis of planar mechanisms that incorporate geometric variations is presented in this paper. The approach is based on Direct Linearization Method (DLM) that does not consider all the kinematically admissible solutions. DLM naturally minimizes a residual functional ; however it is possible to maximize the residual by means of a proposed complementary method called H-Based Residual Method (RMH). From the proposed methodology, local and global error domains can be defined to predict the maximum and minimum position errors caused by the input variations. DLM and RMH were applied in a four-bar mechanism with dimensional and angular variations to estimate positioning errors. The results show intervals where output positions were invariant with respect to angular variations of the crank. These computations were performed through a distance ratio established with the output deviations determined with nominal angular variations. Furthermore, domain errors were predicted for a set of positions generated by a multivariate normal random algorithm with 1000 combinations of input variations (links lengths). These domains delimited all solutions created in each position stage. It means that by applying the proposed methodology it is possible to estimate the geometric errors of any combination of variations.

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Section: Direct Linearization Methods (Dlm)mentioning

confidence: 99%

Section: Mathematical Problems In Engineeringmentioning

confidence: 99%

Section: Position Prediction In a Localmentioning

confidence: 99%

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Tolerance Analysis of Planar Mechanisms Based on a Residual Approach: A Complementary Method to DLM

Tinoco

Durango

2019

Mathematical Problems in Engineering

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“…is used to describe the accumulation of deviations in the assembly. Several DVPMs are developed during past decades, including matrix model [2], [3], Jacobian-Torsor model [4], [5], T-Map model [6], [7], DLM model [8], [9], stream-of-variation (SOV) model [10]- [12] and skin shapes mode [13]- [15]. A summary of the literature is presented as follows:…”

Section: Introductionmentioning

confidence: 99%

Dimensional Variation Analysis for Rigid Part Assembly With an Improvement of Monte Carlo Simulation

Tang

Zhang

2020

IEEE Access

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Dimensional variation has significant effect on the quality of product. Recently, Monte Carlo (MC) simulation is widely used in dimensional variation analysis, with high accuracy and adaptability, but there is the problem of low computational efficiency. Aiming to address this problem, an improvement of MC simulation is proposed through a two-phases solution. In the first phase, surrogate model is used to approximate the locating constraint equations for a 3D part, which reduces the nonlinear coupling between dimensional deviations and avoids large-scale solution of nonlinear equations in dimensional variation analysis on the condition of ensuring the accuracy. In the second phase, random samples used in MC simulation are replaced by low discrepancy sequences, which enable the samples to have better homogeneity and representativeness and reduce the number of samples required in the dimensional variation analysis. Finally, two examples are used to demonstrate the effectiveness of the method, and the results show that the two-phases solution has advantages both in the accuracy and efficiency.

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“…As pointed out in [4], analytic calculation of sensitivities is feasible for very simple mechanisms, while realistic problems can only be solved by algorithmic procedures suitable for software implementation. One of these is the direct linearization method, which builds a Jacobian matrix of the requirements from one or more vector loops identified in the linkage; the approach has been applied to planar and spatial mechanisms in [5][6][7] and recently revised in [8,9] with some modifications allowing to deal with elastic deformations. Planar mechanisms with deformable links are also treated in [10,11] by Monte Carlo simulation guided by statistical methods to limit computational efforts.…”

Section: Introductionmentioning

confidence: 99%

Force analysis as a support to computer-aided tolerancing of planar linkages

Armillotta

2015

Mechanism and Machine Theory

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Tolerance analysis of flexible kinematic mechanism using DLM method

Cited by 20 publications

References 3 publications

Tolerance Analysis of Planar Mechanisms Based on a Residual Approach: A Complementary Method to DLM

Tolerance Analysis of Planar Mechanisms Based on a Residual Approach: A Complementary Method to DLM

Dimensional Variation Analysis for Rigid Part Assembly With an Improvement of Monte Carlo Simulation

Force analysis as a support to computer-aided tolerancing of planar linkages

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