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Research Papers

Direct Linearization Method Kinematic Variation Analysis

[+] Author and Article Information
Robert C. Leishman1

Department of Mechanical Engineering, Brigham Young University, Provo, UT 84602rleish@gmail.com

Kenneth W. Chase

Department of Mechanical Engineering, Brigham Young University, Provo, UT 84602chasek@byu.edu

1

Corresponding author.

J. Mech. Des 132(7), 071003 (Jun 09, 2010) (9 pages) doi:10.1115/1.4001531 History: Received July 23, 2009; Revised March 15, 2010; Published June 09, 2010; Online June 09, 2010

Velocity and acceleration analysis is an important tool for predicting the motion of mechanisms. The results, however, may be inaccurate when applied to manufactured products due to the process variations that occur in production. Small changes in mechanism dimensions can accumulate and propagate, causing a significant variation in the performance of the mechanism. A new application of statistical analysis is presented for predicting the effects of variation on mechanism kinematic performance. The new method is an extension of the direct linearization method developed for static assemblies. This method provides a solution that is a closed form. It may be applied to two-dimensional mechanisms to predict variation in velocity and acceleration due to dimensional variations. It is also shown how form, orientation, and position variations may be included in the analysis to analyze variations that occur within the joints. Only two assemblies are analyzed to characterize the distribution: The first determines the mean, and the second estimates the variance. The system is computationally efficient and well suited for design iteration.

Copyright © 2010 by American Society of Mechanical Engineers
Topics: Velocity , Equations
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References

Figures

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Figure 2

Nominal values of θ3 and θ4 versus θ2

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Figure 3

Variations in θ3 and θ4 versus θ2

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Figure 4

Nominal values of ω3 and ω4 versus θ2

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Figure 5

Variations in ω3 and ω4 versus θ2

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Figure 6

Nominal values of α3 and α4 versus θ2

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Figure 7

Variations in α3 and α4 versus θ2

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Figure 8

Percent contributions at certain points for position, velocity, and acceleration

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Figure 9

Variations resulting from each feature exhibited in each 2D joint type (12)

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Figure 10

Crank-slider mechanism

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Figure 15

Nominal values of α3 and a4 versus θ2

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Figure 16

Variations in α3 and a4 versus θ2

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Figure 17

Percent contributions of dimensional and geometric feature variation at θ2=6.144 rad

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Figure 1

Four-bar crank and rocker mechanism

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Figure 11

Nominal values of θ3 and r4 versus θ2

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Figure 12

Variations in θ3 and r4 versus θ2

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Figure 13

Nominal values of ω3 and v4 versus θ2

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Figure 14

Variations in ω3 and v4 versus θ2

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