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2.76 Multi-scale System Design & Manufacturing
2.76 / 2.760 Lecture 3: Large scaleBig-small intuition
System modeling
Big history
Big problems
Flexures
Design experiment2.76 STM surface sensing
0
2
4
6
8
0 2 4 6 8Gap [Angstroms]
i tunnel
[nA
]
2.76 Multi-scale System Design & Manufacturing
Cross-scale couplingMacroMeso
Micro
Nano
FunctionFormFlowsPhysicsFabrication
GeometryMotion
InterfacesConstraints
Form
Etc…
MassMomentum
EnergyInformation
Flow
Etc…
ApplicationModelingLimiting
Dominant
Physics
Etc…
CompatibilityQualityRateCost
Fabrication
Etc…
WhatWhoWhy
Where
Function
Etc…
2.76 Multi-scale System Design & Manufacturing
Short experiment(1) What cross-scale incompatibilities (5Fs) do you notice?
(2) What obstacles must be overcome to enable interaction between large/small?
Time Limit: 5 minutesEmail results to me when time is calledBulleted points please
2.76 Multi-scale System Design & Manufacturing
DiscussionWhat was the nature of the trouble?
Comment onStrainControl/sensingMomentumNoise
What does this tell you about sensitivity and resolution / discretization?
2.76 Multi-scale System Design & Manufacturing
Stage 1: Synthesis & selectionBig issuesSelection
Stage 2: Detailed designAnalysisOptimization
MacroMeso
Micro
Nano
FunctionFormFlowsPhysicsFabrication
2.76 Multi-scale System Design & Manufacturing
CakeOr
Death ?Is this a difficult decision?
Decision making is differentialDifference is indicated by modelModel is supported by relationship
What determines quality of model?
2.76 Multi-scale System Design & Manufacturing
Modeling and decision makingDeterminism
Does the system obey cause-effect (as observed)?Systematic error, random error
RepeatabilityHow identical are repeated results?
AccuracyHow close is the result to reality?
Non-dimensional analysisQualitative & quantitativeRational process
Everything
Necessary & Sufficient
Experienceor
Relative importance
2.76 Multi-scale System Design & Manufacturing
Nano
Micro
Meso
Macro
NanoNano
NanoMicro
NanoMeso
NanoMacro
MicroNano
MicroMicro
MicroMeso
MicroMacro
MesoNano
MesoMicro
MesoMeso
MesoMacro
MacroNano
MacroMicro
MacroMeso
MacroMacro
Nano
Micro
Meso
Macro
I
I
I
I
SRfSRfSRfSRf
SRfSRfSRfSRf
SRfSRfSRfSRf
SRfSRfSRfSRf
O
O
O
O
⋅
⎟⎟⎠
⎞⎜⎜⎝
⎛⎟⎟⎠
⎞⎜⎜⎝
⎛⎟⎟⎠
⎞⎜⎜⎝
⎛⎟⎟⎠
⎞⎜⎜⎝
⎛
⎟⎟⎠
⎞⎜⎜⎝
⎛⎟⎟⎠
⎞⎜⎜⎝
⎛⎟⎟⎠
⎞⎜⎜⎝
⎛⎟⎟⎠
⎞⎜⎜⎝
⎛
⎟⎟⎠
⎞⎜⎜⎝
⎛⎟⎟⎠
⎞⎜⎜⎝
⎛⎟⎟⎠
⎞⎜⎜⎝
⎛⎟⎟⎠
⎞⎜⎜⎝
⎛
⎟⎟⎠
⎞⎜⎜⎝
⎛⎟⎟⎠
⎞⎜⎜⎝
⎛⎟⎟⎠
⎞⎜⎜⎝
⎛⎟⎟⎠
⎞⎜⎜⎝
⎛
←
44434241
34333231
24232221
14131211
Input-output mapping
( ) MuSSMuSS ISRGO ⋅=
Conceptual
2.76 Multi-scale System Design & Manufacturing
Nano
Micro
Meso
Macro
A
NanoNano
A
NanoMicro
A
NanoMeso
A
NanoMacro
A
MicroNano
A
MicroMicro
A
MicroMeso
A
MicroMacro
A
MesoNano
A
MesoMicro
A
MesoMeso
A
MesoMacro
A
MacroNano
A
MacroMicro
A
MacroMeso
A
MacroMacro
Nano
Micro
Meso
Macro
I
I
I
I
SRCSRCSRCSRC
SRCSRCSRCSRC
SRCSRCSRCSRC
SRCSRCSRCSRC
O
O
O
O
⋅
⎟⎟⎠
⎞⎜⎜⎝
⎛⋅⎟⎟
⎠
⎞⎜⎜⎝
⎛⋅⎟⎟
⎠
⎞⎜⎜⎝
⎛⋅⎟⎟
⎠
⎞⎜⎜⎝
⎛⋅
⎟⎟⎠
⎞⎜⎜⎝
⎛⋅⎟⎟
⎠
⎞⎜⎜⎝
⎛⋅⎟⎟
⎠
⎞⎜⎜⎝
⎛⋅⎟⎟
⎠
⎞⎜⎜⎝
⎛⋅
⎟⎟⎠
⎞⎜⎜⎝
⎛⋅⎟⎟
⎠
⎞⎜⎜⎝
⎛⋅⎟⎟
⎠
⎞⎜⎜⎝
⎛⋅⎟⎟
⎠
⎞⎜⎜⎝
⎛⋅
⎟⎟⎠
⎞⎜⎜⎝
⎛⋅⎟⎟
⎠
⎞⎜⎜⎝
⎛⋅⎟⎟
⎠
⎞⎜⎜⎝
⎛⋅⎟⎟
⎠
⎞⎜⎜⎝
⎛⋅
=
44434241
34333231
24232221
14131211
44434241
34333231
24232221
14131211
Input-output mapping
( ) MuSSMuSS ISRGO ⋅=
Equivalent
2.76 Multi-scale System Design & Manufacturing
Nano
Micro
Meso
Macro
Nano
Micro
Meso
Macro
I
I
I
I
O
O
O
O
⋅
−−−
−−
−
0369
3036
6303
9630
10101010
10101010
10101010
10101010
~
What might G look like?
0369
3036
6303
9630
10101010
10101010
10101010
10101010
−−−
−−
−
=pG
What does | Gp ij / G ij | look like?
Why is this useful?
How will we use it?
“Ideal” or perfectscale interaction
0369
3036
6303
2063100
10101010
10101010
10101010
10101010
−−−
−−
−
=G
2.76 Multi-scale System Design & Manufacturing
Example: STM
( )gapKeCi ⋅⋅−⋅= 2
Is this the whole story?Figure by MIT OCW.
Nano
Micro
Meso
Macro
NanoNano
NanoMicro
NanoMeso
NanoMacro
MicroNano
MicroMicro
MicroMeso
MicroMacro
MesoNano
MesoMicro
MesoMeso
MesoMacro
MacroNano
MacroMicro
MacroMeso
MacroMacro
Nano
Micro
Meso
Macro
I
I
I
I
SRfSRfSRfSRf
SRfSRfSRfSRf
SRfSRfSRfSRf
SRfSRfSRfSRf
O
O
O
O
44434241
34333231
24232221
14131211
Example: STM Signal
NanoNano
NanoMicro
NanoMeso
NanoMacro
MicroNano
MicroMicro
MicroMeso
MicroMacro
MesoNano
MesoMicro
MesoMeso
MesoMacro
SRfSRfSRfSRf
SRfSRfSRfSRf
SRfSRfSRfSRf
44f44f43f43f42f42f41f41f
34f34f33f33f32f32f31f31f
24f24f23f23f22f22f21f21f
Image removed for copyright reasons.Source: http://www.almaden.ibm.com
gapKeCi 2
Vibration Noise Noise
Nano
Micro
Meso
ONanoONano
OMicroOMicro
OMesoOMeso
2.76 STM surface sensing
0
2
4
6
8
0 2 4 6 8Gap [Angstroms]
i tunnel
[nA
]
Gain
2.76 Multi-scale System Design & Manufacturing
Figure by MIT OCW.
2.76 Multi-scale System Design & Manufacturing
Nano
Micro
Meso
Macro
NanoNano
NanoMicro
NanoMeso
NanoMacro
MicroNano
MicroMicro
MicroMeso
MicroMacro
MesoNano
MesoMicro
MesoMeso
MesoMacro
MacroNano
MacroMicro
MacroMeso
MacroMacro
Nano
Micro
Meso
Macro
I
I
I
I
SRfSRfSRfSRf
SRfSRfSRfSRf
SRfSRfSRfSRf
SRfSRfSRfSRf
O
O
O
O
⋅
⎟⎟⎠
⎞⎜⎜⎝
⎛⎟⎟⎠
⎞⎜⎜⎝
⎛⎟⎟⎠
⎞⎜⎜⎝
⎛⎟⎟⎠
⎞⎜⎜⎝
⎛
⎟⎟⎠
⎞⎜⎜⎝
⎛⎟⎟⎠
⎞⎜⎜⎝
⎛⎟⎟⎠
⎞⎜⎜⎝
⎛⎟⎟⎠
⎞⎜⎜⎝
⎛
⎟⎟⎠
⎞⎜⎜⎝
⎛⎟⎟⎠
⎞⎜⎜⎝
⎛⎟⎟⎠
⎞⎜⎜⎝
⎛⎟⎟⎠
⎞⎜⎜⎝
⎛
⎟⎟⎠
⎞⎜⎜⎝
⎛⎟⎟⎠
⎞⎜⎜⎝
⎛⎟⎟⎠
⎞⎜⎜⎝
⎛⎟⎟⎠
⎞⎜⎜⎝
⎛
=
44434241
34333231
24232221
14131211
Purpose of today
Mechanical gain factors to make big machineswork with little machines
2.76 Multi-scale System Design & Manufacturing
What will this be applied to?MacroMeso
Micro
Nano
FunctionFormFlowsPhysicsFabrication
GeometryMotion
InterfacesConstraints
Form
Etc…
MassMomentum
EnergyInformation
Flow
Etc…
ApplicationModelingLimiting
Dominant
Physics
Etc…
CompatibilityQualityRateCost
Fabrication
Etc…
WhatWhoWhy
Where
Function
Etc…
2.76 Multi-scale System Design & Manufacturing
Early big machines made to
work with the small
2.76 Multi-scale System Design & Manufacturing
Big machines working with the smallWhat is the most critical requirements for a large-scale machine to live in a MuSS?
Motion stability, resolution, repeatability
Two diagrams removedfor copyright reasons.
2.76 Multi-scale System Design & Manufacturing
Strain managementEverything is compliant
•Strain error scales with size•Large scale parts are kinematic bullies
Generally require “freedom to strain” to prevent over constraint & energy storage
Generally seek to minimize strain
Mechanism/fixture/structure design• Necessary & sufficient constraint topology → concepts• Exact constraint
2.76 Multi-scale System Design & Manufacturing
History of compliant machinesHooke
Early1900s1800s 2002
Reciprocity & relative stiffness
Screw theory (instant centers)Basic linear modular 4B modules
Exact constraint
Elastic elements/mechanisms
CoMeT synthesisConstraint metrics
Constraint topology
Hinge-specific researchModular constraint rules
Non-linear 4BM
Reconfigure
Imperfect constraint
Late1900s1600s 1700s
Instruments
Beam theoryF ~ k x
2.76 Multi-scale System Design & Manufacturing
History of compliant machinesBernoulli, Euler
Early1900s1800s 2002
Reciprocity & relative stiffness
Screw theory (instant centers)Basic linear modular 4B modules
Exact constraint
Elastic elements/mechanisms
CoMeT synthesisConstraint metrics
Constraint topology
Hinge-specific researchModular constraint rules
Non-linear 4BM
Reconfigure
Imperfect constraint
Late1900s1600s 1700s
Instruments
Beam theoryF ~ k x
2.76 Multi-scale System Design & Manufacturing
History of compliant machinesWillis, Kelvin, Maxwell
Early1900s1800s 2002
Reciprocity & relative stiffness
Screw theory (instant centers)Basic linear modular 4B modules
Exact constraint
Elastic elements/mechanisms
CoMeT synthesisConstraint metrics
Constraint topology
Hinge-specific researchModular constraint rules
Non-linear 4BM
Reconfigure
Imperfect constraint
Late1900s1600s 1700s
Instruments
Beam theoryF ~ k x
2.76 Multi-scale System Design & Manufacturing
History of compliant machinesMaxwell
6 DOF
Early1900s1800s 2002
Reciprocity & relative stiffness
Screw theory (instant centers)Basic linear modular 4B modules
Elastic elements/mechanisms
CoMeT synthesisConstraint metrics
Constraint topology
Hinge-specific researchModular constraint rules
Non-linear 4BM
Reconfigure
Imperfect constraint
Late1900s
Exact constraint
1600s 1700s
Instruments
Beam theoryF ~ k x
2.76 Multi-scale System Design & Manufacturing
History of compliant machinesAfter R.V. Jones
1600s 1700sEarly1900s1800s 2002
Instruments
Reciprocity & relative stiffness
Screw theory (instant centers)
Beam theory
Basic linear modular 4B modules
Exact constraint
F ~ k x
Elastic elements/mechanisms
CoMeT synthesisConstraint metrics
Constraint topology
Hinge-specific researchModular constraint rules
Non-linear 4BM
Reconfigure
Imperfect constraint
Late1900s
2.76 Multi-scale System Design & Manufacturing
History of compliant machinesBlanding, Hale, Slocum
1600s 1700sEarly1900s1800s 2002
Instruments
Reciprocity & relative stiffness
Screw theory (instant centers)
Beam theory
Basic linear modular 4B modules
Exact constraint
F ~ k x
Elastic elements/mechanisms
CoMeT synthesisConstraint metrics
Constraint topology
Hinge-specific researchModular constraint rules
Non-linear 4BM
Reconfigure
Imperfect constraint
Late1900s
2.76 Multi-scale System Design & Manufacturing
History of compliant machines
Late1900s
Early1900s1800s 2002
Reciprocity & relative stiffness
Screw theory (instant centers)Basic linear modular 4B modules
Exact constraint
Elastic elements/mechanisms
CoMeT synthesisConstraint metrics
Constraint topology
Hinge-specific researchModular constraint rules
Culpepper, Slocum,. Shaikh, ‘98 ASME IMECCulpepper, Ph.D. 2000
Non-linear 4BM
Reconfigure
Imperfect constraint
⊥
=KK
CMi||
180
270
θr0
K||
x
y
K┴
1600s 1700s
Instruments
Beam theoryF ~ k x
2.76 Multi-scale System Design & Manufacturing
History of compliant machinesCulpepper, Petri 2001
Early1900s1800s 2002
Reciprocity & relative stiffness
Screw theory (instant centers)Basic linear modular 4B modules
Exact constraint
Elastic elements/mechanisms
CoMeT synthesisConstraint metrics
Constraint topology
Hinge-specific researchModular constraint rules
Non-linear 4BM
Reconfigure
Imperfect constraint
Late1900s1600s 1700s
Instruments
Beam theoryF ~ k x
2.76 Multi-scale System Design & Manufacturing
History of compliant machinesAwtar, Slocum, 2002
Early1900s1800s 2002
Reciprocity & relative stiffness
Screw theory (instant centers)Basic linear modular 4B modules
Exact constraint
Elastic elements/mechanisms
CoMeT synthesisConstraint metrics
Constraint topology
Hinge-specific researchModular constraint rules
Non-linear 4BM
Reconfigure
Imperfect constraint
4B modules: 1-5 DOF
Late1900s1600s 1700s
Instruments
Beam theoryF ~ k x
Diagram removedfor copyright
reasons.
2.76 Multi-scale System Design & Manufacturing
History of compliant machinesCulpepper, 2002
Early1900s1800s 2002
Reciprocity & relative stiffness
Screw theory (instant centers)Basic linear modular 4B modules
Exact constraint
Elastic elements/mechanisms
CoMeT synthesisConstraint metrics
Constraint topology
Hinge-specific researchModular constraint rules
Non-linear 4BM
Reconfigure
Imperfect constraint
Late1900s1600s 1700s
Instruments
Beam theoryF ~ k x
2.76 Multi-scale System Design & Manufacturing
Principles of cross-scale motion and constraint
2.76 Multi-scale System Design & Manufacturing
Design for compliant constraint1.Stability
Maximize passive stability“Self-help” (symmetry & cancellation)
2. EnvelopeStrain errors (compliance, thermal)Packaging
3.ManufacturingMonolithicMinimum information
4. ConstraintMaximize linear independenceParasitic errors
yx
z
yx
z
2.76 Multi-scale System Design & Manufacturing
Principle of symmetryStart-up thermal drift
0 10 20 30-6
-4
-2
0
2
4
6x y zθx θy θz
-30
30
Time [ minutes ]
Line
ar [
nm ]
Angular [ µradians
]
20
10
0
-10
-20
Thermal strain error
Over constraint → Force
2.76 Multi-scale System Design & Manufacturing
Principle of cancellationKinematic path building blocks
Straight linesRotation (instant centers)
+ =Kstiff
Kcompliant
δ1
δ2 δdesired
Kdesired
2.76 Multi-scale System Design & Manufacturing
Principle of center of stiffnessLoading mattersCenter of stiffness: Load = no rotation
Tuning Block
Figure by MIT OCW. After R. V. Jones.
2.76 Multi-scale System Design & Manufacturing
Actuator sensitivity & calibrationSource of errors
Tolerance (5000 nm vs 1nm?)MountingMaterial propsStress stiffeningLinear assumptions
Calibration and mapping…
“Perfectly” Calibrated
6
5
4
3
2
1
321
654
654
654
321
321
000000000000
000000
∆∆∆∆∆∆
=
zzz
yyy
xxx
zzz
yyy
xxx
z
y
x
CCCCCCCCCCCC
CCCCCC
zyx
θθθ
θθθ
θθθ
θθθ
ActuatorStage C ∆⋅=δ
Tab load [N]
Displacement calibration plots
Dis
plac
emen
t [ µ
m ] Rotation [ µ radians ]
-2400
-2000
-1600
-1200
-800
-400
-60
-40
-20
0
20
40
60
0 0.5 1.0 1.5 2.0
0
Measured x Measured zMeasured θx Measured θzLines = CoMeT
2.76 Multi-scale System Design & Manufacturing
Constraint-basedcompliant mechanism design
2.76 Multi-scale System Design & Manufacturing
Rules of constraintDOC = # of linearly independent constraints
DOF = 6 - DOC
Constraints have lines of action
Lines of action intersect at instant centers
Instant centers (via constraint) define motion
2.76 Multi-scale System Design & Manufacturing
Basic elements
Bars Beams Plates
Cross Beam Hinge Notch Hinge
Diagrams removed for copyright reasons.Source: Blanding, D. L. Exact Constraint: Machine Design using Kinematic
Principles. New York: ASME Press, 1999. ISBN: 0791800857
2.76 Multi-scale System Design & Manufacturing
Common precision constraint typesConstraints
5 DOF
3 planar DOF
Diagrams removed for copyright reasons.Source: Blanding, D. L. Exact Constraint: Machine Design using Kinematic
Principles. New York: ASME Press, 1999. ISBN: 0791800857
2.76 Multi-scale System Design & Manufacturing
Constraint and FreedomWhen connecting in series
Add degrees of freedom with exception of redundant degreesExamples:
Rod at end of plate & Rod on Rod
Front View Side View Front View Side View
2.76 Multi-scale System Design & Manufacturing
Example: Constraint-based designConstraint-based compliant mechanism design
STEP 2: Motion path decomposition
STEP 3:Kinematic parametric concepts
STEP 4:Constraint-motion addition rules
STEP 5: Topology concept generation
STEP 6: Concept selection phase I
STEP 7: Size and shape optimization
STEP 8: Concept selection phase II
STEP 1: Design requirements
Arcs, lines, rotation pts. sub-paths
Motions, constraint metric, symmetry, etc.
Serial, parallel, hybrid
Path & constraint driven
Path errors & over constraint
Stiffness, load capacity, efficiency, etc…
Direct comparison with design requirements
Motion path, stiffness, load capacity, etc…Diagram of automobile steering column,
rack and rotor - removedfor copyright reasons.
2.76 Multi-scale System Design & Manufacturing
Example: Constraint-based designConstraint-based compliant mechanism design
STEP 2: Motion path decomposition
STEP 3:Kinematic parametric concepts
STEP 4:Constraint-motion addition rules
STEP 5: Topology concept generation
STEP 6: Concept selection phase I
STEP 7: Size and shape optimization
STEP 8: Concept selection phase II
STEP 1: Design requirements
Arcs, lines, rotation pts. sub-paths
Motions, constraint metric, symmetry, etc.
Serial, parallel, hybrid
Path & constraint driven
Path errors & over constraint
Stiffness, load capacity, efficiency, etc…
Direct comparison with design requirements
Motion path, stiffness, load capacity, etc…
=
2.76 Multi-scale System Design & Manufacturing
1
3 2δ2(r)→
┴
||
Example: Constraint-based designConstraint-based compliant mechanism design
STEP 2: Motion path decomposition
STEP 3:Kinematic parametric concepts
STEP 4:Constraint-motion addition rules
STEP 5: Topology concept generation
STEP 6: Concept selection phase I
STEP 7: Size and shape optimization
STEP 8: Concept selection phase II
STEP 1: Design requirements
Arcs, lines, rotation pts. sub-paths
Motions, constraint metric, symmetry, etc.
Serial, parallel, hybrid
Path & constraint driven
Path errors & over constraint
Stiffness, load capacity, efficiency, etc…
Direct comparison with design requirements
Motion path, stiffness, load capacity, etc…
2.76 Multi-scale System Design & Manufacturing
1
3 2δ2(r)→
K┴ -3K||-3
θ
δ┴ -2 δ||-2
θ
┴
||
Example: Constraint-based designConstraint-based compliant mechanism design
STEP 2: Motion path decomposition
STEP 3:Kinematic parametric concepts
STEP 4:Constraint-motion addition rules
STEP 5: Topology concept generation
STEP 6: Concept selection phase I
STEP 7: Size and shape optimization
STEP 8: Concept selection phase II
STEP 1: Design requirements
Arcs, lines, rotation pts. sub-paths
Motions, constraint metric, symmetry, etc.
Serial, parallel, hybrid
Path & constraint driven
Path errors & over constraint
Stiffness, load capacity, efficiency, etc…
Direct comparison with design requirements
Motion path, stiffness, load capacity, etc…1
||
||
2.76 Multi-scale System Design & Manufacturing
Example: Constraint-based designConstraint-based compliant mechanism design
STEP 2: Motion path decomposition
STEP 3:Kinematic parametric concepts
STEP 4:Constraint-motion addition rules
STEP 5: Topology concept generation
STEP 6: Concept selection phase I
STEP 7: Size and shape optimization
STEP 8: Concept selection phase II
STEP 1: Design requirements
Arcs, lines, rotation pts. sub-paths
Motions, constraint metric, symmetry, etc.
Serial, parallel, hybrid
Path & constraint driven
Path errors & over constraint
Stiffness, load capacity, efficiency, etc…
Direct comparison with design requirements
Motion path, stiffness, load capacity, etc…
2.76 Multi-scale System Design & Manufacturing
Example: Constraint-based designConstraint-based compliant mechanism design
STEP 2: Motion path decomposition
STEP 3:Kinematic parametric concepts
STEP 4:Constraint-motion addition rules
STEP 5: Topology concept generation
STEP 6: Concept selection phase I
STEP 7: Size and shape optimization
STEP 8: Concept selection phase II
STEP 1: Design requirements
Arcs, lines, rotation pts. sub-paths
Motions, constraint metric, symmetry, etc.
Serial, parallel, hybrid
Path & constraint driven
Path errors & over constraint
Stiffness, load capacity, efficiency, etc…
Direct comparison with design requirements
Motion path, stiffness, load capacity, etc…
CoMeT: Compliant Mechanism Tool
2.76 Multi-scale System Design & Manufacturing
Example: Constraint-based designConstraint-based compliant mechanism design
STEP 2: Motion path decomposition
STEP 3:Kinematic parametric concepts
STEP 4:Constraint-motion addition rules
STEP 5: Topology concept generation
STEP 6: Concept selection phase I
STEP 7: Size and shape optimization
STEP 8: Concept selection phase II
STEP 1: Design requirements
Arcs, lines, rotation pts. sub-paths
Motions, constraint metric, symmetry, etc.
Serial, parallel, hybrid
Path & constraint driven
Path errors & over constraint
Stiffness, load capacity, efficiency, etc…
Direct comparison with design requirements
Motion path, stiffness, load capacity, etc…
T
θ
2.76 Multi-scale System Design & Manufacturing
Example: Constraint-based designConstraint-based compliant mechanism design
STEP 2: Motion path decomposition
STEP 3:Kinematic parametric concepts
STEP 4:Constraint-motion addition rules
STEP 5: Topology concept generation
STEP 6: Concept selection phase I
STEP 7: Size and shape optimization
STEP 8: Concept selection phase II
STEP 1: Design requirements
Arcs, lines, rotation pts. sub-paths
Motions, constraint metric, symmetry, etc.
Serial, parallel, hybrid
Path & constraint driven
Path errors & over constraint
Stiffness, load capacity, efficiency, etc…
Direct comparison with design requirements
Motion path, stiffness, load capacity, etc…
2.76 Multi-scale System Design & Manufacturing
Example: Constraint-based designConstraint-based compliant mechanism design
STEP 2: Motion path decomposition
STEP 3:Kinematic parametric concepts
STEP 4:Constraint-motion addition rules
STEP 5: Topology concept generation
STEP 6: Concept selection phase I
STEP 7: Size and shape optimization
STEP 8: Concept selection phase II
STEP 1: Design requirements
Arcs, lines, rotation pts. sub-paths
Motions, constraint metric, symmetry, etc.
Serial, parallel, hybrid
Path & constraint driven
Path errors & over constraint
Stiffness, load capacity, efficiency, etc…
Direct comparison with design requirements
Motion path, stiffness, load capacity, etc…
2.76 Multi-scale System Design & Manufacturing
Design activity
2.76 Multi-scale System Design & Manufacturing
ProblemDesign a mechanical filter which:
Gij = 0.05 (factor of 20 filtering)Range of 0.5 mm with less than 5 micron PEEnvelope: 5 x 5 x 0.125 inches
Give us enough information to:Understand your constraint topologyFabricate itAssume it is aluminum
Email journal file at end of class
You may ask any question at any time…
2.76 Multi-scale System Design & Manufacturing
AssignmentForm teams of 4 now, email members to TA
by 5pm Friday
Flexure reading (pp. 67-82 & 174-205)
CoMeT tutorials 1 - 3
Learn a CAD package (3 wks!!!)
Create CoMeT model of your flexure, send to TA by Monday 9am
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