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Example Problems
AutoCAD Analyzer:
CHAPTER 7: Remote Positioner
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7.0 The remote positioner: An introduction to open loop specifications.

The remote positioner example introduces assembly tolerances requiring open loop definitions. The remote positioning mechanism is used in wind tunnel testing and is to be designed from a set of linkages connected by pins and attached to the wind tunnel. The assembly allows the orientation of the arm inside the tunnel to be linearly controlled by the input linkage located outside the tunnel. A tolerance analysis should be performed with the arm in several positions since it will be oriented to several different angles during wind tunnel testing. This example will only look at the case where the input linkage is rotated 180deg. from the positive X axis.

Figure 7.1 Remote positioner assembly.

Figure 7.2 shows the remote positioner and the open loop assembly specs which are critical to its operation. The figure shows each assembly spec and the datums to which each is referenced. Both the POSition and PARallelism of PART_5 are critical. PART_5 must be parallel to the input linkage, PART_1, within a tolerance bandwidth of .1 in., and the tip of PART_5 must be at its nominal position within a circular tolerance zone of diameter .2 in.

Figure 7.2 Parallelism and true position design specifications.

Figure 7.3 Vector loops for the remote positioner.

Independent Variables

A - PART_1/2-8 = 22.0000 +/- .005 in
B - PART_2/3-15 = 10.4000 +/- .005 in
C - PART_3/4-9 = 22.0000 +/- .005 in
D - GROUND/10-11 = 5.2000 +/- .003 in
E - GROUND/1-10 = 9.0067 +/- .004 in
F - PART_3/12-13 = 12.9000 +/- .005 in
G - PART_4/5-14 = 49.3000 +/- .010 in
H - PART_5/6-16 = 12.9000 +/- .005 in
I - PART_2/15-16 = 49.3000 +/- .010 in
J - PART_5/17-18 = 22.0000 +/- .005 in
gammagamma1 - <JOINT7 = 90.00 +/- .02deg.
gamma2 - <DATUM15 = 30.00 +/- .02deg.
gamma3 - <DATUM12 = 42.60 +/- .02deg.
gamma4 - <DATUM17 = 42.60 +/- .02deg.

Dependent Variables

F1 - JOINT8 = 60.00 +/- ?
F2 - JOINT9 = 120.00 +/- ?
F3 - JOINT11 = 0.00 +/- ?
F4 - JOINT13 = 47.40 +/- ?
F5 - JOINT14 = 132.60 +/- ?
F6 - JOINT16 = 47.40 +/- ?

7.1 Start Up

After creating a vector-loop model of the remote positioner and a CATS neutral file with the AutoCATS 2-D Modeler, execute the 2-D Analyzer and open the neutral file by typing F O REMOTE Y <CR> from the Main Menu. Select the 2D ANALY option to start your analysis. For more specific instructions on getting started, review section 5.1.

7.2 Parameters

Let's assume that we have determined that the optimum acceptance fraction for this particular assembly and its cost-of-rejects is 4.5 sigma. This means that we would like to get only 6.8 rejects per million assemblies. To change the target acceptance fraction (Zasm) from its default value of 3.0, select PARAM from the 2D ANALY submenu.

PARAM MODIFY KINEMAT DESNSPEC ALLOCATE %CONTRIB SENSDIAG XMATSAVE
.... GLOBAL COMMANDS ....
/HELP /UP /TOP /BLOCK /REF < > /SYSTEM
2D> P <CR>

Select a target acceptance fraction of 4.5 sigma, as shown below:

< PARAMETER TABLE >

ANALYSIS TARGET ACCEPTANCE SPECIFICATION SELECTION LIST
MODEL FRACTION (Zasm) TYPE REFERENCE 1 REFERENCE 2
----------------------------------------------------------------------------
__ WC __ 3.00 SIGMA (.9973) 1 X_ PAR DATUM18 DATUM19
X_ RSS __ 2.58 SIGMA (.99) 2 __ POS DATUM20 DATUM21
__ 6-SIG __ 3.29 SIGMA (.999) 3 __
__ 3.89 SIGMA (.9999) 4 __
X_ 4.50 SIGMA (.999993) 5 __
__ 6.00 SIGMA (.999999998) 6 __
_______ User Defined Sigma 7 __
8 __
ALLOCATION OPTIONS 9 __
NOMINALS TOLERANCES 10 __
------------------------------------- 11 __
__ CENTER __ WEIGHT FACTORS 12 __
__ LOWER SPEC LIM X_ PROPOR. SCALING 13 __
__ UPPER SPEC LIM __ PRECIS. FACTOR 14 __
X_ NONE __ MINIMUM COST <<< INSTRUCTIONS >>>
__ NONE Select one option from each column.
Type any character next to the
X_ Include Feature Tolerances selected item.

Press <ESC> Q to exit, <ESC> H for help, <ESC> C to update

7.3 Kinematic Assembly Variables

In this assembly there are six revolute (pin) joints, each defining a dependent kinematic assembly angle. The KINEMAT option shows how much each of these angles will vary due to the tolerances on each controlled dimension.

PARAM MODIFY KINEMAT DESNSPEC ALLOCATE %CONTRIB SENSDIAG XMATSAVE
.... GLOBAL COMMANDS ....
/HELP /UP /TOP /BLOCK /REF < > /SYSTEM
2D> K <CR>

< CLOSED LOOP ANALYSIS RESULTS >
Assembly Name: REMOTE No. Closed Loops: 2
Feature Tolerances: Applied
Target Acceptance Fraction (Zasm): 4.50
Loop Names: LOOP_2 LOOP_1

Controlled Dimensions:
Nominal Symmetric Standard
Part Name/Dimen Dimension Tolerance Deviation (RSS)
---------------:-------------:-----------:-----------
<JOINT7 : .00000 : .02000 : .00012
PART_1/2-8 : 22.00000 : .00500 : .00167
PART_2/3-9 : 10.40000 : .00500 : .00167
<DATUM15 : 30.00000 : .02000 : .00012
PART_2/15-16 : 49.30000 : .01000 : .00333
PART_5/6-16 : 12.90000 : .00500 : .00167
<DATUM17 : -42.60000 : .02000 : .00012
PART_5/17-18 : 22.00000 : .00500 : .00167
PART_4/5-14 : 49.30000 : .01000 : .00333
PART_3/12-13 : 12.90000 : .00500 : .00167
<DATUM12 : -42.60000 : .02000 : .00012
PART_3/4-9 : 22.00000 : .00500 : .00167
GROUND/1-10 : 9.00666 : .00400 : .00133
GROUND/10-11 : 5.20000 : .00300 : .00100
---------------:-------------:-----------:-----------

Kinematic Assembly Variables:
Variations
Variable Name DEG of FDM Worst Case RSS Case 6-SIG Case
--------------:-------------:-----------:-----------:-----------
JOINT8 : ROTATION : .11859 : .08270 : .11027
JOINT16 : ROTATION : .29593 : .15599 : .20798
JOINT14 : ROTATION : .25877 : .13369 : .17826
JOINT13 : ROTATION : .17159 : .08290 : .11053
JOINT9 : ROTATION : .09443 : .06540 : .08720
JOINT11 : ROTATION : .06500 : .04419 : .05892
--------------:-------------:-----------:-----------:-----------

Results to file REMOTE.OUT (y/N)? Y <CR>

Notice that manufactured angles such as gamma2 (<DATUM15) are indicated by a "<" in front of the node at which they occur. Also, since our target acceptance fraction is set at 4.50 sigma, the angular variations shown for each joint are 4.5[[sigma]] variations. For example, the RSS angular variation at JOINT8 is .08270deg.. Thus, its standard deviation ([[sigma]]) is .08270/4.5 or .018938deg..

7.4 Analysis of Design Specifications

As mentioned in section 7.0, there is both a PARallelism spec and a POSition spec for this assembly. DESNSPEC will show us how many rejects can be expected with the original specified tolerances.

PARAM MODIFY KINEMAT DESNSPEC ALLOCATE %CONTRIB SENSDIAG XMATSAVE
.... GLOBAL COMMANDS ....
/HELP /UP /TOP /BLOCK /REF < > /SYSTEM
2D> D <CR>

< DESIGN SPEC ANALYSIS RESULTS >
Assembly Name: REMOTE
Analysis Model: RSS
Target Acceptance Fraction (Zasm): 4.50
-----< Spec # 1 >------------------------------------<< OUTPUTS >>---------
Spec Type : PARALLELISM : With Feature :Without Feature
References: DATUM18 DATUM19 : Tolerances : Tolerances
--------------------------------------------:--------------:---------------p>:
Mean: .00000 Computed Variation: B= .05579: B= .05579
Nominal: .00000 :
Bandwidth: .10000 Upper Tail Z (sigma): 8.07: 8.07
Lower Tail Z (sigma): 8.07: 8.07
USL Rejects (ppm): .0: .0
LSL Rejects (ppm): .0: .0
--------------------------------------------:--------------:---------------p>
TOTAL REJECTS (PPM): .0: .0
--------------------------------------------:--------------:---------------p>

Do you want this written to REMOTE.OUT (y/N)? Y <CR>

Notice that the specified tolerance zone for the PARallelism design specification is a bandwidth .1 in wide. The predicted variation bandwidth, however, is only +/-.055786 in. Notice that this will result in an 8-sigma quality level--much higher than we need. However, we must also take into account the POSition spec. Go to the PARAMeter table and choose the POSition spec from the specification selection list.

PARAM MODIFY KINEMAT DESNSPEC ALLOCATE %CONTRIB SENSDIAG XMATSAVE
.... GLOBAL COMMANDS ....
/HELP /UP /TOP /BLOCK /REF < > /SYSTEM
2D> P <CR>

< PARAMETER TABLE >
ANALYSIS TARGET ACCEPTANCE SPECIFICATION SELECTION LIST
MODEL FRACTION (Zasm) TYPE REFERENCE 1 REFERENCE 2
----------------------------------------------------------------------------
__ WC __ 3.00 SIGMA (.9973) 1 __ PAR DATUM18 DATUM19
X_ RSS __ 2.58 SIGMA (.99) 2 X_ POS DATUM20 DATUM21
__ 6-SIG __ 3.29 SIGMA (.999) 3 __
__ 3.89 SIGMA (.9999) 4 __
X_ 4.50 SIGMA (.999993) 5 __
__ 6.00 SIGMA (.999999998) 6 __
_______ User Defined Sigma 7 __
8 __
ALLOCATION OPTIONS 9 __
NOMINALS TOLERANCES 10 __
------------------------------------- 11 __
__ CENTER __ WEIGHT FACTORS 12 __
__ LOWER SPEC LIM X_ PROPOR. SCALING 13 __
__ UPPER SPEC LIM __ PRECIS. FACTOR 14 __
X_ NONE __ MINIMUM COST <<< INSTRUCTIONS >>>
__ NONE Select one option from each column.
Type any character next to the
X_ Include Feature Tolerances selected item.

Press <ESC> Q to exit, <ESC> H for help, <ESC> C to update

<ESC> Q

PARAM MODIFY KINEMAT DESNSPEC ALLOCATE %CONTRIB SENSDIAG XMATSAVE
.... GLOBAL COMMANDS ....
/HELP /UP /TOP /BLOCK /REF < > /SYSTEM
2D> D <CR>

< DESIGN SPEC ANALYSIS RESULTS >
Assembly Name: REMOTE
Analysis Model: RSS
Target Acceptance Fraction (Zasm): 4.50

-----< Spec # 2 >------------------------------------<< OUTPUTS >>---------
Spec Type : POSITION : With Feature :Without Feature
References: DATUM20 DATUM21 : Tolerances : Tolerances
--------------------------------------------:--------------:---------------p>:
Mean: .00000 Computed Variation: X= .15536: X= .15536
Nominal: .00000 Y= .13054: Y= .13054
Diam Tol: .20000 Upper Tail Z (sigma): N/A: N/A
Lower Tail Z (sigma): N/A: N/A
USL Rejects (ppm): .3: .3
LSL Rejects (ppm): .0: .0
--------------------------------------------:--------------:---------------p>
TOTAL REJECTS (PPM): .3: .3
--------------------------------------------:--------------:---------------p>
Do you want this written to REMOTE.OUT (y/N)? Y <CR>

The POSition spec is unique. Since it takes into account variations in both the X and Y directions, its distribution is elliptically bivariate. In addition, any covariance (a measure of X and Y's interdependency) rotates the distribution's principal axes away from the global X and Y axes. Thus, rejects must be calculated with a double integration algorithm, and Z scores are not applicable (N/A).

Notice that the specified tolerance zone is a circle with a diameter of .2 in. The 4.5[[sigma]] variations in both the X and Y directions are given to compare with the specified tolerance. Both variations are smaller than the .2 in diameter, and result in only .30 rejects per million. For a normal univariate distribution, this would represent nearly a 5.25 sigma quality level. Again, this is much higher than we need.

7.5 Tolerance Allocation

As explained in section 5.7, tolerances can only be allocated to satisfy one design specification at a time. Let's perform a simple proportional scaling for each design specification and compare the results. Because POSition is the PARAMeter table's currently selected spec, we'll allocate tolerances to meet it first. Select ALLOCATE from the 2D ANALY menu.

PARAM MODIFY KINEMAT DESNSPEC ALLOCATE %CONTRIB SENSDIAG XMATSAVE
.... GLOBAL COMMANDS ....
/HELP /UP /TOP /BLOCK /REF < > /SYSTEM
2D> A <CR>

< ALLOCATION RESULTS >
Assembly: REMOTE
Analysis Model: RSS
Target Acceptance Fraction (Zasm): 4.50
Tolerance Allocation Option: Proportional Scaling
Nominal Allocation Option : None

-----< Spec # 2 >---------------------------------------------------------
Spec Type : POSITION Nominal: .00000
References: DATUM20 DATUM21 Diam Tol: .20000
--------------------------------------------------------------------------<> :
PECIFIED VALUES : ALLOCATED VALUES : Optimized Perc
Part Name/Dimen : Nominal +/-Tol : Nominal +/-Tol : Std Dev Cont
--------------- : --------- ------- : --------- ------- : --------- ------
<JOINT7 : .0000 .02000 : .0000 .02498 : .00015
PART_1/2-8 : 22.0000 .00500 : 22.0000 .00624 : .00208
PART_2/3-9 : 10.4000 .00500 : 10.4000 .00625 : .00208
<DATUM15 : 30.0000 .02000 : 30.0000 .02498 : .00015
PART_2/15-16 : 49.3000 .01000 : 49.3000 .01249 : .00416
PART_5/6-16 : 12.9000 .00500 : 12.9000 .00625 : .00208
<DATUM17 : -42.6000 .02000 : -42.6000 .02498 : .00015
PART_5/17-18 : 22.0000 .00500 : 22.0000 .00624 : .00208
PART_4/5-14 : 49.3000 .01000 : 49.3000 .01249 : .00416
PART_3/12-13 : 12.9000 .00500 : 12.9000 .00625 : .00208
<DATUM12 : -42.6000 .02000 : -42.6000 .02498 : .00015
PART_3/4-9 : 22.0000 .00500 : 22.0000 .00624 : .00208
GROUND/1-10 : 9.0067 .00400 : 9.0067 .00500 : .00167
GROUND/10-11 : 5.2000 .00300 : 5.2000 .00375 : .00125
--------------- : ----------------- : ----------------- : --------- ------
COMPUTED ASSEMBLY VARIATION -- POSITION
Mean +/- Var : .0000 X: .1554 : .0000 X: .1941 :
: Y: .1305 : Y: .1631 :
----------------:-------------------:-------------------:-----------------
REJECTS Z PPM : Z PPM :
Upper: N/A .3 : N/A 6.8 :
Lower: N/A .0 : N/A .0 :Total: .3 6.8
* = Fixed Tolerance

Do you want this written to REMOTE.OUT (y/N)? Y

These allocation results show that to have a 4.5[[sigma]] quality level for the POSition spec, the original tolerances must be increased by a factor of 1.25. To compare the allocated values required to meet the POSition spec with those required to meet the PARallelism spec, return to the analysis menu and go to the PARAMeter table to select the PARallelism spec.

PARAM MODIFY KINEMAT DESNSPEC ALLOCATE %CONTRIB SENSDIAG XMATSAVE
.... GLOBAL COMMANDS ....
/HELP /UP /TOP /BLOCK /REF < > /SYSTEM
2D> P <CR>

Select the PARallelism spec from the ALLOCATION SPECIFICATION LIST, as shown below

< PARAMETER TABLE >
ANALYSIS TARGET ACCEPTANCE SPECIFICATION SELECTION LIST
MODEL FRACTION (Zasm) TYPE REFERENCE 1 REFERENCE 2
----------------------------------------------------------------------------
__ WC __ 3.00 SIGMA (.9973) 1 X_ PAR DATUM18 DATUM19
X_ RSS __ 2.58 SIGMA (.99) 2 __ POS DATUM20 DATUM21
__ 6-SIG __ 3.29 SIGMA (.999) 3 __
__ 3.89 SIGMA (.9999) 4 __
X_ 4.50 SIGMA (.999993) 5 __
__ 6.00 SIGMA (.999999998) 6 __
_______ User Defined Sigma 7 __
8 __
ALLOCATION OPTIONS 9 __
NOMINALS TOLERANCES 10 __
------------------------------------- 11 __
__ CENTER __ WEIGHT FACTORS 12 __
__ LOWER SPEC LIM X_ PROPOR. SCALING 13 __
__ UPPER SPEC LIM __ PRECIS. FACTOR 14 __
X_ NONE __ MINIMUM COST <<< INSTRUCTIONS >>>
__ NONE Select one option from each column.
Type any character next to the
X_ Include Feature Tolerances selected item.

Press <ESC> Q to exit, <ESC> H for help, <ESC> C to update

Select ALLOCATE to see proportional scaling allocation results for the PARallelism spec.

PARAM MODIFY KINEMAT DESNSPEC ALLOCATE %CONTRIB SENSDIAG XMATSAVE
.... GLOBAL COMMANDS ....
/HELP /UP /TOP /BLOCK /REF < > /SYSTEM
2D> A <CR>

< ALLOCATION RESULTS >
Assembly: REMOTE
Analysis Model: RSS
Target Acceptance Fraction (Zasm): 4.50
Tolerance Allocation Option: Proportional Scaling
Nominal Allocation Option : None

-----< Spec # 1 >---------------------------------------------------------
Spec Type : PARALLELISM Nominal: .00000
References: DATUM18 DATUM19 Bandwidth: .10000
--------------------------------------------------------------------------<> :
SPECIFIED VALUES : ALLOCATED VALUES : Optimized Perc
Part Name/Dimen : Nominal +/-Tol : Nominal +/-Tol : Std Dev Cont
--------------- : --------- ------- : --------- ------- : --------- ------
<JOINT7 : .0000 .02000 : .0000 .03583 : .00021 .00
PART_1/2-8 : 22.0000 .00500 : 22.0000 .00896 : .00299 .60
PART_2/3-9 : 10.4000 .00500 : 10.4000 .00896 : .00299 2.41
<DATUM15 : 30.0000 .02000 : 30.0000 .03583 : .00021 .00
PART_2/15-16 : 49.3000 .01000 : 49.3000 .01791 : .00597 38.80
PART_5/6-16 : 12.9000 .00500 : 12.9000 .00896 : .00299 4.45
<DATUM17 : -42.6000 .02000 : -42.6000 .03583 : .00021 4.26
PART_5/17-18 : 22.0000 .00500 : 22.0000 .00896 : .00299 .00
PART_4/5-14 : 49.3000 .01000 : 49.3000 .01791 : .00597 38.80
PART_3/12-13 : 12.9000 .00500 : 12.9000 .00896 : .00299 4.45
<DATUM12 : -42.6000 .02000 : -42.6000 .03583 : .00021 4.26
PART_3/4-9 : 22.0000 .00500 : 22.0000 .00896 : .00299 .60
GROUND/1-10 : 9.0067 .00400 : 9.0067 .00717 : .00239 1.16
GROUND/10-11 : 5.2000 .00300 : 5.2000 .00537 : .00179 .22
--------------- : ----------------- : ----------------- : --------- ------
COMPUTED ASSEMBLY VARIATION -- PARALLELISM .01110 100.00
Mean +/- Var : .0000 B: .0558 : .0000 B: .0999 :
: : :
----------------:-------------------:-------------------:-----------------
REJECTS Z PPM : Z PPM :
Upper: 8.07 .0 : 4.50 3.4 :
Lower: 8.07 .0 : 4.50 3.4 :
Total: .0 6.8
* = Fixed Tolerance

Do you want this written to REMOTE.OUT (y/N)? Y

In contrast to the POSition spec, notice that in this simple proportional scaling allocation, each tolerance is increased by a factor of 1.79. This means that in order to meet both specs, the allocated values obtained for the POSition spec must be used, since they are tighter. However, if weight factor allocation were used instead of proportional scaling, the allocated tolerances on some dimensions might have been increased by a greater factor than others. So, due to their various sensitivities, one dimension's tolerance might be constrained by one spec and another dimension's tolerance might be constrained by the other spec.


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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