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Example Problems
AutoCAD Verification:
REMOTE POSITIONING MECHANISM
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Figure 4.1: Schematic of the remote positioner with basic dimension labels.

4.0 Problem Description

The remote positioner is a mechanical linkage that positions point P in two-dimensional space. Point P is meant to remain in a fixed location while the angular orientation of Part 5 varies. This model demonstrates the use of two open loops with two closed loop constraints.

This model includes 14 independent variables, and solves for six kinematic variables. In addition, two open loops allow us to solve for additional assembly variations.

Table 4.1: Manufactured Variables (Independent).

Variable Name Basic Size Initial Tolerance (+/-)
gamma1 90.00[[ring]] .02[[ring]]
A 22.000 in .005 in
B 10.400 in .005 in
C 22.000 in .005 in
D 5.200 in .003 in
E 9.0067 in .004 in
gamma2 30.00[[ring]] .02[[ring]]
gamma3 42.60[[ring]] .02[[ring]]
F 12.900 in .005 in
G 49.300 in .010 in
H 12.900 in .005 in
I 49.300 in .010 in
gamma4 42.60[[ring]] .02[[ring]]
J 22.000 in .005 in

4.1 Design Requirements

Table 4.2: Assembly Variables (Dependent).

Variable Name Basic Size Upper Spec. Limit(USL) Lower Spec. Limit(LSL)
q1 60.0[[ring]] -- --
q2 120.0[[ring]] -- --
q3 0.0[[ring]] -- --
q4 47.4[[ring]] -- --
q5 132.6[[ring]] -- --
q6 47.4[[ring]] -- --
DeltaX1 0.0 in .1 in -.1 in
DeltaY1 0.0 in .1 in -.1 in
Deltatheta1 0.0[[ring]] -- --
DeltaX2 0.0 in -- --
DeltaY2 0.0 in -- --
Deltatheta2 0.0[[ring]] .05 in (.26[[ring]]) -.05 in (-.26[[ring]])

Remarks>> DeltaX1 and DeltaY1 are the Cartesian coordinate locations of point P relative to Ground and are used to calculate the position variation. Deltatheta2 is the variation in the angular orientation of Part 5 relative to Part 1 and is used to calculate the parallelism variation. Deltatheta1, DeltaX2, and DeltaY2 can also be solved for from the open loops, but they are not necessary to estimate the parallelism and position assembly variations.

4.2 Modeling Considerations

Part 1.

4.3 Design Goal

The object of this problem is to calculate the variation in the position of point P relative to Ground, as well as the parallelism between Part 1 and Part 5 and optimize the tolerances to meet the parallelism specification limits.

4.4 Part Names and DRFs

Figure 4.2: Diagram showing the location of the part DRFs.

4.5 Kinematic Joints

Seven joints are required to model the remote positioner. All of them are revolute joints in the physical device. However, with all joints free to rotate, the system is indeterminate, and CATS cannot solve for the variations. Therefore, one joint must be designated the input angle and its rotational degree of freedom removed. This is done by either replacing that revolute joint with a rigid joint (in AutoCats) or by "turning off" that joint's rotational degree of freedom (in any of the workstation-based analyzers). For this problem, the input angle (gamma1) was at joint 1, so joint 1 was modeled as a rigid joint.

Figure 4.3: Kinematic joint diagram.

Table 4.3: Kinematic Joints of the Remote Positioner.

Joint Number Part One Part Two Joint Type
1 Ground Part 1 rigid
2 Part 1 Part 2 revolute
3 Part 2 Part 3 revolute
4 Part 3 Ground revolute
5 Part 3 Part 4 revolute
6 Part 4 Part 5 revolute
7 Part 5 Part 2 revolute

4.6 Network Diagram, Vector Loops, and Design Specifications

Two closed loops are necessary to constrain the remote positioner assembly. A location specification relative to joint 1 has been applied to point P, as well as a parallelism specification relative to length A (Part 1). Therefore two open loops are also needed, one for each design specification.

Figure 4.4: Network diagram and open and closed loops for the remote positioner.

Remarks>> Open loops are analyzed in the same manner as closed loops. They are more sensitive to modeling errors than closed loops are, so correct placement of loop endpoints and part DRFs is critical when calculating variations with open loops.

The direction of open loops is important when gap and position specifications are used. CATS assumes the first part is fixed in space and the parts "downstream" all rotate relative to it. This arises due to the non-commutative property of matrix multiplication. To generate the correct open loop direction, create the final endpoint (the moving endpoint) first and the starting endpoint (fixed endpoint) second.

The allowable position specification variation is given as a diameter.

4.7 Geometric Tolerances

True position geometric tolerances have been applied to the seven joints to account for clearance variations. Each position tolerance is modeled as two orthogonal, independent vectors.

Figure 4.5: Geometric tolerance diagram.

Remarks>> Applying position tolerances to the joints in this assembly is not completely accurate. In this case, the position tolerance is not related to the position of the holes (or pins). Instead, it is being used as a way to approximate the variations that occur in the assembly due to the small clearances between the pins and holes.

4.8 Sensitivity Matrices

Constraint Sensitivities

A Matrix

  gamma1 A B C D E gamma2
X1 0.0000 -1.0000 -.50000 1.0000 1.0000 0.0000 0.0000
Y1 0.0000 0.0000 -.86603 0.0000 0.0000 1.0000 0.0000
theta1 1.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
X2 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
Y2 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
theta2 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -1.0000

A Matrix (continued)

  gamma3 F G H I gamma4 J
X1 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
Y1 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
theta1 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
X2 0.0000 -.73610 0.0000 .73610 0.0000 0.0000 0.0000
Y2 0.0000 -.67688 -1.0000 .67688 1.0000 0.0000 0.0000
theta2 1.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

B Matrix

  q1 q2 q3 q4 q5 q6
X1 0.0000 -9.0067 -9.0067 0.0000 0.0000 0.0000
Y1 22.000 27.200 5.2000 0.0000 0.0000 0.0000
theta1 1.0000 1.0000 1.0000 0.0000 0.0000 0.0000
X2 0.0000 0.0000 0.0000 -8.7317 -58.032 -49.300
Y2 0.0000 0.0000 0.0000 9.4957 9.4957 0.0000
theta2 0.0000 1.0000 0.0000 1.0000 1.0000 1.0000

F Matrix

  alpha1 alpha1 alpha2 alpha2 alpha3 alpha3 alpha4
X1 1.0000 0.0000 1.0000 0.0000 1.0000 0.0000 1.0000
Y1 0.0000 1.0000 0.0000 1.0000 0.0000 1.0000 0.0000
theta1 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
X2 1.0000 0.0000 0.0000 0.0000 1.0000 0.0000 0.0000
Y2 0.0000 0.0000 0.0000 0.0000 0.0000 1.0000 0.0000
theta2 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

F Matrix (continued)

  alpha4 alpha5 alpha5 alpha6 alpha6 alpha7 alpha7
X1 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
Y1 1.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
theta1 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
X2 0.0000 1.0000 0.0000 1.0000 0.0000 1.0000 0.0000
Y2 0.0000 0.0000 1.0000 0.0000 1.0000 0.0000 1.0000
theta2 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

C Matrix

  gamma1 A B C D E gamma2
X1 58.307 -1.0000 -.50000 0.0000 0.0000 0.0000 49.300
Y1 -5.2000 0.0000 -.86603 0.0000 0.0000 0.0000 22.000
theta1 1.0000 0.0000 0.0000 0.0000 0.0000 0.0000 1.0000
X2 0.0000 -1.0000 -.50000 0.0000 0.0000 0.0000 49.300
Y2 0.0000 0.0000 -.86603 0.0000 0.0000 0.0000 22.000
theta2 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 1.0000

C Matrix (continued)

  gamma3 F G H I gamma4 J
X1 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 1.0000
Y1 0.0000 0.0000 0.0000 0.0000 -1.0000 -22.000 0.0000
theta1 0.0000 0.0000 0.0000 0.0000 0.0000 -1.0000 0.0000
X2 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 1.0000
Y2 0.0000 0.0000 0.0000 0.0000 -1.0000 -22.000 0.0000
theta2 0.0000 0.0000 0.0000 0.0000 0.0000 -1.0000 0.0000

D Matrix

  q1 q2 q3 q4 q5 q6
X1 58.307 0.0000 0.0000 0.0000 0.0000 0.0000
Y1 16.8000 0.0000 0.0000 0.0000 0.0000 -22.000
theta1 1.0000 0.0000 0.0000 0.0000 0.0000 -1.0000
X2 58.307 0.0000 0.0000 0.0000 0.0000 0.0000
Y2 16.8000 0.0000 0.0000 0.0000 0.0000 -22.000
theta2 0.0000 0.0000 0.0000 0.0000 0.0000 -1.0000

G Matrix

  alpha1 alpha1 alpha2 alpha2 alpha3 alpha3 alpha4
X1 1.0000 0.0000 1.0000 0.0000 0.0000 0.0000 0.0000
Y1 0.0000 1.0000 0.0000 1.0000 0.0000 0.0000 0.0000
theta1 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
X2 1.0000 0.0000 1.0000 0.0000 0.0000 0.0000 0.0000
Y2 0.0000 1.0000 0.0000 1.0000 0.0000 0.0000 0.0000
theta2 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

 

G Matrix (continued)

  alpha4 alpha5 alpha5 alpha6 alpha6 alpha7 alpha7
X1 0.0000 0.0000 0.0000 0.0000 0.0000 -1.0000 0.0000
Y1 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -1.0000
theta1 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
X2 0.0000 0.0000 0.0000 0.0000 0.0000 -1.0000 0.0000
Y2 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -1.0000
theta2 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

 

Tolerance Sensitivities

-B-1A Matrix

  gamma1 A B C D E gamma2
q1 -1.0000 .11103 .05551 -.11103 -.11103 2.52E-18 0.0000
q2 1.0000 -.08479 -.00303 .08479 .08479 -.04545 0.0000
q3 -1.0000 -.02624 -.05249 .02624 .02624 .04545 0.0000
q4 -1.0000 .08479 .00303 -.08479 -.08479 .04545 1.0000
q5 1.0000 -.08479 -.00303 .08479 .08479 -.04545 -1.0000
q6 -1.0000 .08479 .00303 -.08479 -.08479 .04545 1.0000

 

-B-1A Matrix (continued)

  gamma3 F G H I gamma4 J
q1 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
q2 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
q3 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
q4 -1.0000 .02756 .01865 -.02756 -.01865 0.0000 0.0000
q5 1.0000 .04373 .08666 -.04373 -.08666 0.0000 0.0000
q6 -1.0000 -.07128 -.10531 .07128 .10531 0.0000 0.0000

-B-1F Matrix

  alpha1 alpha1 alpha2 alpha2 alpha3 alpha3 alpha4
q1 -.11103 2.52E-18 -.11103 2.52E-18 -.11103 2.52E-18 -.11103
q2 .08479 -.04545 .08479 -.04545 .08479 -.04545 .08479
q3 .02624 .04545 .02624 .04545 .02624 .04545 .02624
q4 -.08479 .04545 -.08479 .04545 -.10507 .02680 -.08479
q5 .08479 -.04545 .08479 -.04545 .10507 -.13211 .08479
q6 -.08479 .04545 -.08479 .04545 -.08479 .15077 -.08479

-B-1F Matrix (continued)

  alpha4 alpha5 alpha5 alpha6 alpha6 alpha7 alpha7
q1 2.52E-18 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
q2 -.04545 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
q3 .04545 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
q4 .04545 -.02028 -.01865 -.02028 -.01865 -.02028 -.01865
q5 -.04545 .02028 -.08666 .02028 -.08666 .02028 -.08666
q6 .04545 1.80E-17 .10531 1.80E-17 .10531 1.80E-17 .10531

C-DB-1A Matrix

  gamma1 A B C D E gamma2
DeltaX1 0.0000 5.4737 2.7369 -6.4737 -6.4737 1.47E-16 49.300
DeltaY1 -2.1E-14 2.22E-16 -5.6E-16 -2.2E-16 -2.2E-16 -1.0000 1.07E-14
Deltatheta1 1.0000 .02624 .05249 -.02624 -.02624 -.04545 8.88E-16
DeltaX2 -58.307 5.4737 2.7369 -6.4737 -6.4737 1.47E-16 49.300
DeltaY2 5.2000 2.22E-16 -5.6E-16 -2.2E-16 -2.2E-16 -1.0000 1.42E-14
Deltatheta2 -8.9E-16 .02624 .05249 -.02624 -.02624 -.04545 8.88E-16

 

C-DB-1A Matrix (continued)

  gamma3 F G H I gamma4 J
DeltaX1 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 1.0000
DeltaY1 22.000 1.5682 2.3168 -1.5682 -3.3168 -22.000 0.0000
Deltatheta1 1.0000 .07128 .10531 -.07128 -.10531 -1.0000 0.0000
DeltaX2 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 1.0000
DeltaY2 22.000 1.5682 2.3168 -1.5682 -3.3168 -22.000 0.0000
Deltatheta2 1.0000 -.04545 -.02624 -.04545 -.02624 -1.0000 0.0000

G-DB-1F Matrix

  alpha1 alpha1 alpha2 alpha2 alpha3 alpha3 alpha4
DeltaX1 -5.4737 1.47E-16 -5.4737 1.47E-16 -6.4737 1.47E-16 -6.4737
DeltaY1 -2.2E-16 8.88E-16 -2.2E-16 8.88E-16 -4.4E-16 -3.3168 -2.2E-16
Deltatheta1 -.02624 -.04545 -.02624 -.04545 -.02624 -.15077 -.02624
DeltaX2 -5.4737 -5.4737 -5.4737 1.47E-16 -6.4737 1.47E-16 -6.4737
DeltaY2 -2.2E-16 8.88E-16 -2.2E-16 8.88E-16 -4.4E-16 -3.3168 -2.2E-16
Deltatheta2 -.02624 -.04545 -.02624 -.04545 -.02624 -.15077 -.02624
                                                   

G-DB-1F Matrix (continued)

  alpha4 alpha5 alpha5 alpha6 alpha6 alpha7 alpha7
DeltaX1 1.47E-16 0.0000 0.0000 0.0000 0.0000 -1.0000 0.0000
DeltaY1 -1.0000 -4.0E-16 -2.3168 -4.0E-16 -2.3168 -4.0E-16 -3.3168
Deltatheta1 -.04545 -1.8E-17 -.10531 -1.8E-17 -.10531 -1.8E-17 -.10531
DeltaX2 1.47E-16 0.0000 0.0000 0.0000 0.0000 -1.0000 0.0000
DeltaY2 -1.0000 -4.0E-16 -2.3168 -4.0E-16 -2.3168 -4.0E-16 -3.3168
Deltatheta2 -.04545 -1.8E-17 -.10531 -1.8E-17 -.10531 -1.8E-17 -.10531

 

4.9 Predicted Assembly Variation

Table 4.4: Independent Variable Tolerances and Control Factors

Dim.Name +/- Tol. Std. Dev. Cp Dk Cpk Sk Wt. Factor
Tol. Basic Fixed
gamma1 .02deg. .0067 1 0.25 0.75 0 0 0 Yes
A .005 in .0017 1 0.25 0.75 0 3 1 No
B .005 in .0017 1 0.25 0.75 0 2 1 No
C .005 in .0017 1 0.25 0.75 0 3 1 No
D .003 in .0010 1 0.25 0.75 0 2 1 No
E .004 in .0013 1 0.25 0.75 0 2 1 No
gamma2 .02deg. .0067 1 0.25 0.75 0 0 0 Yes
gamma3 .02deg. .0067 1 0.25 0.75 0 0 0 Yes
F .005 in .0017 1 0.25 0.75 0 2 1 No
G .010 in .0033 1 0.25 0.75 0 4 1 No
H .005 in .0017 1 0.25 0.75 0 2 1 No
I .010 in .0033 1 0.25 0.75 0 4 1 No
gamma4 .02deg. .0067 1 0.25 0.75 0 0 0 Yes
J .005 in .0017 1 0.25 0.75 0 3 1 No

 

Table 4.5: Kinematic Assembly Variables (No Geometric Tolerances)

Variable Name Degree of Freedom +/- Assembly Variations (ZASM = 4.500)
Worst Case RSS Case Six-Sigma
q1 Rotation ([[ring]]) .11860 .08271 .11028
q2 Rotation ([[ring]]) .09444 .06541 .08721
q3 Rotation ([[ring]]) .06500 .04419 .05892
q4 Rotation ([[ring]]) .17160 .08290 .11054
q5 Rotation ([[ring]]) .25879 .13371 .17828
q6 Rotation ([[ring]]) .29596 .15601 .20801

Table 4.6: Geometric Tolerances

Feat. Joint Part Name Feature Type Tolerance Band Char. Length
alpha1 1 Part 1 True Position .001 in N/A
alpha2 2 Part 1 True Position .001 in N/A
alpha3 3 Part 3 True Position .001 in N/A
alpha4 4 Part 3 True Position .001 in N/A
alpha5 5 Part 4 True Position .001 in N/A
alpha6 6 Part 4 True Position .001 in N/A
alpha7 7 Part 5 True Position .001 in N/A

 

Table 4.7: Kinematic Assembly Variables (Geometric Tolerances Included)

Variable Name Degree of Freedom +/- Assembly Variations (ZASM = 4.500)
Worst Case RSS Case Six-Sigma
q1 Rotation ([[ring]]) .13133 .08326 .11069
q2 Rotation ([[ring]]) .10936 .06593 .08761
q3 Rotation ([[ring]]) .07322 .04442 .05910
q4 Rotation ([[ring]]) .18992 .08337 .11089
q5 Rotation ([[ring]]) .28597 .13426 .17870
q6 Rotation ([[ring]]) .32295 .15655 .20842

Table 4.8: Six-Sigma Percent Rejects (Parallelism Specification)

Spec. Name Spec. Type Nominal Dimension (+/-) Computed
Variation
With Geometric Tolerances Without Geometric Tolerances
P Parallelism 0.0000 .03725 Z Rej. Z Rej.
ZASM = 4.500 USL 0.05 Upper Tail 6.04 7.8e-4 6.05 7.3e-4

(Rejects in PPM)

LSL -0.05 Lower Tail -6.04 7.8e-4 -6.05 7.3e-4

Remarks>> The variation in the assembly due to the small gaps in the pin joints is relatively insignificant. For tolerance allocation, the effects of the gaps (represented by the true position geometric tolerances) will be ignored.

Table 4.9: Six-Sigma Percent Contributions To Parallelism Of P
(No Geometric Tolerances)

Variable Name Variance Six-Sigma
G 2.191e-7 38.80
I 2.191e-7 38.80
F 2.509e-8 4.44
H 2.509e-8 4.44
gamma3 2.407e-8 4.26
gamma4 2.407e-8 4.26
B 1.360e-8 2.41
E 6.530e-9 1.16
other 8.026e-9 1.43

Table 4.10: Six-Sigma Percent Rejects (True Position)

Spec. Name Spec. Type Nominal Dimension (+/-) Computed Variation With Geometric Tolerances Without Geometric Tolerances
P True Pos. 0.0000 X: .10398 Y: .08715 Z Rej. Z Rej.
ZASM = 4.500 X-rad. .100 Upper Tail N/A 59.4 N/A 55.2

(Rejects in PPM)

Y-rad. .100 Lower Tail N/A 59.4 N/A 55.2


4.10 Tolerance And Nominal Allocation

Weight Factor Tolerance Allocation

Table 4.11: Six-Sigma Weight Factor Tolerance Allocation
(Parallelism, No Geometric Tolerances)

Assembly Specs. Nom. USL LSL +/- ZASM
Parallelism (P) 0.0000 0.0500 -0.0500 4.500
Dimension Name Specified Values Allocated Values
Nom. +/-Tol. Nom. +/-Tol. STDEV % Cont.
gamma1 ([[ring]]) 90.0000 .02000 90.0000 .02000 .00889 1.9e-30 *
A (in) 22.0000 .00500 22.0000 .00545 .00242 0.40
B (in) 10.4000 .00500 10.4000 .00364 .00162 0.70
C (in) 22.0000 .00500 22.0000 .00545 .00242 0.40
D (in) 5.2000 .00300 5.2000 .00218 .00097 0.06
E (in) 9.0067 .00400 9.0067 .00291 .00129 0.34
gamma2 ([[ring]]) 30.0000 .02000 30.0000 .02000 .00889 1.9e-30 *
gamma3 ([[ring]]) 42.6000 .02000 42.6000 .02000 .00889 2.36 *
F (in) 12.9000 .00500 12.9000 .00364 .00162 1.30
G (in) 49.3000 .01000 49.3000 .01454 .00646 45.39
H (in) 12.9000 .00500 12.9000 .00364 .00162 1.30
I (in) 49.3000 .01000 49.3000 .01454 .00646 45.39
gamma4 ([[ring]]) 42.6000 .02000 42.6000 .02000 .00889 2.36 *
J (in) 22.0000 .00500 22.0000 .00545 .00242 0.00
Assem. Total Nom. +/-Var. Nom. +/-Var. STDEV 100.00
P (in) 0.0000 .03720 0.0000 .05000 .01111  
Min./Max. -.03720 .03720 -.0500 .0500 * Fixed Nom./Tol.
  Before Optimization After Optimization
Rejects Z PPM Z PPM
Upper Tail 6.05 7.3e-4 4.5 3.4
Lower Tail -6.05 7.3e-4 -4.5 3.4
  Total Rejects 1.5e-3 Total Rejects 6.8

Proportional Scaling Tolerance Allocation

 

Table 4.12: Six-Sigma Proportional Scaling Tolerance Allocation

(Parallelism, No Geometric Tolerances)

Assembly Specs. Nom. USL LSL +/- ZASM
Parallelism (P) 0.0000 0.0500 -0.0500 4.500
Dimension Name Specified Values Allocated Values
Nom. +/-Tol. Nom. +/-Tol. STDEV % Cont.
gamma1 ([[ring]]) 90.0000 .02000 90.0000 .02000 .00889 1.9e-30 *
A (in) 22.0000 .00500 22.0000 .00686 .00305 0.63
B (in) 10.4000 .00500 10.4000 .00686 .00305 2.51
C (in) 22.0000 .00500 22.0000 .00686 .00305 0.63
D (in) 5.2000 .00300 5.2000 .00412 .00183 0.23
E (in) 9.0067 .00400 9.0067 .00549 .00243 1.20
gamma2 ([[ring]]) 30.0000 .02000 30.0000 .02000 .00889 1.9e-30 *
gamma3 ([[ring]]) 42.6000 .02000 42.6000 .02000 .00889 2.36 *
F (in) 12.9000 .00500 12.9000 .00686 .00305 4.63
G (in) 49.3000 .01000 49.3000 .01372 .00610 40.41
H (in) 12.9000 .00500 12.9000 .00686 .00305 4.63
I (in) 49.3000 .01000 49.3000 .01372 .00610 40.41
gamma4 ([[ring]]) 42.6000 .02000 42.6000 .02000 .00889 2.36 *
J (in) 22.0000 .00500 22.0000 .00686 .00305 0.00
Assem. Total Nom. +/-Var. Nom. +/-Var. STDEV 100.00
P (in) 0.0000 .03720 0.0000 .05000 .01111  
Min./Max. -.03720 .03720 -.0500 .0500 * Fixed Nom./Tol.
  Before Optimization After Optimization
Rejects Z PPM Z PPM
Upper Tail 6.05 7.3e-4 4.5 3.4
Lower Tail -6.05 7.3e-4 -4.5 3.4
  Total Rejects 1.5e-3 Total Rejects 6.8

Remarks>> Comparison of the two tables above shows some of the differences between weight factor and proportional scaling allocation. Proportional scaling adjusts all non-fixed dimension tolerances proportional to their original tolerances. Weight factor allocation distributes the assembly variable variance pool among the non-fixed dimension tolerances proportional to their weight factors. If all weight factors are set equal, weight factor allocation becomes equivalent to proportional scaling.


PRO-E

Modeler: Clutch | Stack Blocks | Remote Positioner
Analyzer: Clutch | Stack Blocks | Remote Positioner
Verification: Clutch | Stack Blocks | Remote Positioner | Bike Crank | Parallel Blocks | NFOV

AutoCAD

Modeler: Clutch | Stack Blocks | Remote Positioner
Analyzer: Clutch | Stack Blocks | Remote Positioner
Verification: Clutch | Stack Blocks | Remote Positioner | Bike Crank | Ratchet | Parallel Blocks | NFOV

CATIA

Modeler: Crank Slider

 

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