2.76 / Lecture 3: Large scale

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1 2.76 / Lecture 3: Large scale Big-small intuition System modeling Big history Big problems Flexures Design experiment 2.76 Multi-scale System Design & Manuacturing itunnel [na] STM surace sensing Gap [Angstroms]

2 ross-scale coupling Function Form Flows Physics Fabrication Function Form Flow Physics Fabrication What Geometry Mass Application ompatibility Who Motion Momentum Modeling Quality Why Interaces Energy Limiting Rate Where onstraints Inormation Dominant ost Etc Etc Etc Etc Etc 2.76 Multi-scale System Design & Manuacturing

3 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 minutes results to me when time is called Bulleted points please 2.76 Multi-scale System Design & Manuacturing

4 Discussion What was the nature o the trouble? omment on Strain ontrol/sensing Momentum Noise What does this tell you about sensitivity and resolution / discretization? 2.76 Multi-scale System Design & Manuacturing

5 Stage 1: Synthesis & selection Big issues Selection Stage 2: Detailed design Analysis Optimization Function Form Flows Physics Fabrication 2.76 Multi-scale System Design & Manuacturing

6 ake Or Death? Is this a diicult decision? Decision making is dierential Dierence is indicated by model Model is supported by relationship What determines quality o model? 2.76 Multi-scale System Design & Manuacturing

7 Modeling and decision making Determinism Does the system obey cause-eect (as observed)? Systematic error, random error Everything Repeatability How identical are repeated results? Accuracy How close is the result to reality? Experience or Relative importance Non-dimensional analysis Qualitative & quantitative Rational process Necessary & Suicient 2.76 Multi-scale System Design & Manuacturing

8 2.76 Multi-scale System Design & Manuacturing I I I I O O O O Input-output mapping ( ) MuSS MuSS I G O = onceptual

9 2.76 Multi-scale System Design & Manuacturing A A A A A A A A A A A A A A A A I I I I O O O O = Input-output mapping ( ) MuSS MuSS I G O = Equivalent

10 What might G look like? O Ideal or perect scale interaction I O O ~ I I G p = O I What does Gp ij / G ij look like? Why is this useul? G = How will we use it? Multi-scale System Design & Manuacturing

11 Example: STM i = e ( 2 K gap) Figure by MIT OW. Is this the whole story? 2.76 Multi-scale System Design & Manuacturing

12 Example: STM Signal Vibration Noise Noise Gain O I O I O I O I i e 2 K gap STM surace sensing Image removed or copyright reasons. Source: itunnel [na] Gap [Angstroms] 2.76 Multi-scale System Design & Manuacturing

13 Figure by MIT OW.

14 2.76 Multi-scale System Design & Manuacturing I I I I O O O O = Purpose o today Mechanical gain actors to make big machines work with little machines

15 What will this be applied to? Function Form Flows Physics Fabrication Function Form Flow Physics Fabrication What Geometry Mass Application ompatibility Who Motion Momentum Modeling Quality Why Interaces Energy Limiting Rate Where onstraints Inormation Dominant ost Etc Etc Etc Etc Etc 2.76 Multi-scale System Design & Manuacturing

16 Early big machines made to work with the small 2.76 Multi-scale System Design & Manuacturing

Motion stability, resolution, repeatability Two diagrams

17 Big machines working with the small What is the most critical requirements or a large-scale machine to live in a MuSS? Motion stability, resolution, repeatability Two diagrams removed or copyright reasons Multi-scale System Design & Manuacturing

18 Strain management Everything is compliant Strain error scales with size Large scale parts are kinematic bullies Generally require reedom to strain to prevent over constraint & energy storage Generally seek to minimize strain Mechanism/ixture/structure design Necessary & suicient constraint topology concepts Exact constraint 2.76 Multi-scale System Design & Manuacturing

19 History o compliant machines 1600s Instruments F ~ k x Beam theory 1700s Hooke 2.76 Multi-scale System Design & Manuacturing Exact constraint Reciprocity & relative stiness onstraint topology Elastic elements/mechanisms Screw theory (instant centers) Basic linear modular 4B modules Hinge-speciic research Modular constraint rules Imperect constraint onstraint metrics omet synthesis Early Late 1800s 1900s 1900s 2002 Non-linear 4BM Reconigure

20 History o compliant machines 1600s Instruments F ~ k x Beam theory 1700s 2.76 Multi-scale System Design & Manuacturing Bernoulli, Euler Exact constraint Reciprocity & relative stiness onstraint topology Elastic elements/mechanisms Screw theory (instant centers) Basic linear modular 4B modules Hinge-speciic research Modular constraint rules Imperect constraint onstraint metrics omet synthesis Early Late 1800s 1900s 1900s 2002 Non-linear 4BM Reconigure

21 History o compliant machines 1600s Instruments F ~ k x Beam theory 1700s 2.76 Multi-scale System Design & Manuacturing Willis, Kelvin, Maxwell Exact constraint Reciprocity & relative stiness onstraint topology Elastic elements/mechanisms Screw theory (instant centers) Basic linear modular 4B modules Hinge-speciic research Modular constraint rules Imperect constraint onstraint metrics omet synthesis Early Late 1800s 1900s 1900s 2002 Non-linear 4BM Reconigure

22 History o compliant machines 1600s Instruments F ~ k x Beam theory 1700s Maxwell 2.76 Multi-scale System Design & Manuacturing Exact constraint Reciprocity & relative stiness 6 DOF onstraint topology Elastic elements/mechanisms Screw theory (instant centers) Basic linear modular 4B modules Hinge-speciic research Modular constraint rules Imperect constraint onstraint metrics omet synthesis Early Late 1800s 1900s 1900s 2002 Non-linear 4BM Reconigure

23 History o compliant machines 1600s Instruments F ~ k x Beam theory 1700s 2.76 Multi-scale System Design & Manuacturing Ater R.V. Jones Exact constraint Reciprocity & relative stiness onstraint topology Elastic elements/mechanisms Screw theory (instant centers) Basic linear modular 4B modules Hinge-speciic research Modular constraint rules Imperect constraint onstraint metrics omet synthesis Early Late 1800s 1900s 1900s 2002 Non-linear 4BM Reconigure

24 History o compliant machines 1600s Instruments F ~ k x Beam theory 1700s 2.76 Multi-scale System Design & Manuacturing Blanding, Hale, Slocum Exact constraint Reciprocity & relative stiness onstraint topology Elastic elements/mechanisms Screw theory (instant centers) Basic linear modular 4B modules Hinge-speciic research Modular constraint rules Imperect constraint onstraint metrics omet synthesis Early Late 1800s 1900s 1900s 2002 Non-linear 4BM Reconigure

25 History o compliant machines 1600s Instruments F ~ k x Beam theory 1700s 2.76 Multi-scale System Design & Manuacturing ulpepper, Slocum,. Shaikh, 98 ASME IME ulpepper, Ph.D Exact constraint Reciprocity & relative stiness onstraint topology Elastic elements/mechanisms Screw theory (instant centers) Basic linear modular 4B modules Hinge-speciic research Modular constraint rules Imperect constraint onstraint metrics omet synthesis Early Late 1800s 1900s 1900s 2002 K y 270 K θ r 0 K M i = K Non-linear 4BM x Reconigure

26 History o compliant machines 1600s Instruments F ~ k x Beam theory 1700s 2.76 Multi-scale System Design & Manuacturing ulpepper, Petri 2001 Exact constraint Reciprocity & relative stiness onstraint topology Elastic elements/mechanisms Screw theory (instant centers) Basic linear modular 4B modules Hinge-speciic research Modular constraint rules Imperect constraint onstraint metrics omet synthesis Early Late 1800s 1900s 1900s 2002 Non-linear 4BM Reconigure

27 History o compliant machines 1600s Instruments F ~ k x Beam theory 1700s 2.76 Multi-scale System Design & Manuacturing Awtar, Slocum, 2002 Diagram removed or copyright reasons. Exact constraint Reciprocity & relative stiness onstraint topology 4B modules: 1-5 DOF Elastic elements/mechanisms Screw theory (instant centers) Basic linear modular 4B modules Hinge-speciic research Modular constraint rules Imperect constraint onstraint metrics omet synthesis Early Late 1800s 1900s 1900s 2002 Non-linear 4BM Reconigure

28 History o compliant machines 1600s Instruments F ~ k x Beam theory 1700s 2.76 Multi-scale System Design & Manuacturing ulpepper, 2002 Exact constraint Reciprocity & relative stiness onstraint topology Elastic elements/mechanisms Screw theory (instant centers) Basic linear modular 4B modules Hinge-speciic research Modular constraint rules Imperect constraint onstraint metrics omet synthesis Early Late 1800s 1900s 1900s 2002 Non-linear 4BM Reconigure

29 Principles o cross-scale motion and constraint 2.76 Multi-scale System Design & Manuacturing

31 Design or compliant constraint 1.Stability Maximize passive stability Sel-help (symmetry & cancellation) 2. Envelope Strain errors (compliance, thermal) Packaging x z y 3.Manuacturing Monolithic Minimum inormation x z y 4. onstraint Maximize linear independence Parasitic errors 2.76 Multi-scale System Design & Manuacturing

33 Principle o symmetry Thermal strain error Over constraint Force Linear [ nm ] Start-up thermal drit x y z θx θy θz Time [ minutes ] Angular [ µradians ] 2.76 Multi-scale System Design & Manuacturing

34 Principle o cancellation Kinematic path building blocks Straight lines Rotation (instant centers) K compliant δ 1 + = K desired K sti δ 2 δ desired 2.76 Multi-scale System Design & Manuacturing

35 Principle o center o stiness Loading matters enter o stiness: Load = no rotation Tuning Block Figure by MIT OW. Ater R. V. Jones Multi-scale System Design & Manuacturing

40 Actuator sensitivity & calibration Source o errors Tolerance (5000 nm vs 1nm?) Mounting Material props Stress stiening Linear assumptions alibration and mapping Displacement [ µm ] 60 Displacement calibration plots Measured x Measured θx 0 Lines = omet Tab load [N] Measured z Measured θz Rotation [ µ radians ] x y z θ θ θ x y z = Perectly alibrated δstage = Actuator x1 y1 θz1 x2 y2 θz2 x3 y θz z4 θx4 θy4 0 z5 θx5 θy5 0 z6 θx6 θy Multi-scale System Design & Manuacturing

41 onstraintbased compliant mechanism design 2.76 Multi-scale System Design & Manuacturing

43 Rules o constraint DO = # o linearly independent constraints DOF = 6 - DO onstraints have lines o action Lines o action intersect at instant centers Instant centers (via constraint) deine motion 2.76 Multi-scale System Design & Manuacturing

44 Basic elements Diagrams removed or copyright reasons. Source: Blanding, D. L. Exact onstraint: Machine Design using Kinematic Principles. New York: ASME Press, ISBN: Bars Beams Plates ross Beam Hinge Notch Hinge 2.76 Multi-scale System Design & Manuacturing

45 ommon precision constraint types onstraints 5 DOF Diagrams removed or copyright reasons. Source: Blanding, D. L. Exact onstraint: Machine Design using Kinematic Principles. New York: ASME Press, ISBN: planar DOF 2.76 Multi-scale System Design & Manuacturing

46 onstraint and Freedom When connecting in series Add degrees o reedom with exception o redundant degrees Examples: Rod at end o plate & Rod on Rod Front View Side View Front View Side View 2.76 Multi-scale System Design & Manuacturing

48 Example: onstraint-based design onstraint-based compliant mechanism design STEP 1: Design requirements Motion path, stiness, load capacity, etc STEP 2: Motion path decomposition Arcs, lines, rotation pts. sub-paths Diagram o automobile steering column, rack and rotor - removed or copyright reasons. STEP 3:Kinematic parametric concepts Motions, constraint metric, symmetry, etc. STEP 4:onstraint-motion addition rules Serial, parallel, hybrid STEP 5: Topology concept generation Path & constraint driven STEP 6: oncept selection phase I Path errors & over constraint STEP 7: Size and shape optimization Stiness, load capacity, eiciency, etc STEP 8: oncept selection phase II Direct comparison with design requirements 2.76 Multi-scale System Design & Manuacturing

49 Example: onstraint-based design onstraint-based compliant mechanism design STEP 1: Design requirements Motion path, stiness, load capacity, etc STEP 2: Motion path decomposition Arcs, lines, rotation pts. sub-paths STEP 3:Kinematic parametric concepts Motions, constraint metric, symmetry, etc. STEP 4:onstraint-motion addition rules Serial, parallel, hybrid STEP 5: Topology concept generation Path & constraint driven STEP 6: oncept selection phase I Path errors & over constraint = STEP 7: Size and shape optimization Stiness, load capacity, eiciency, etc STEP 8: oncept selection phase II Direct comparison with design requirements 2.76 Multi-scale System Design & Manuacturing

50 Example: onstraint-based design onstraint-based compliant mechanism design STEP 1: Design requirements Motion path, stiness, load capacity, etc STEP 2: Motion path decomposition Arcs, lines, rotation pts. sub-paths STEP 3:Kinematic parametric concepts Motions, constraint metric, symmetry, etc. STEP 4:onstraint-motion addition rules Serial, parallel, hybrid STEP 5: Topology concept generation Path & constraint driven STEP 6: oncept selection phase I Path errors & over constraint STEP 7: Size and shape optimization Stiness, load capacity, eiciency, etc 3 δ 2 2 (r) 1 STEP 8: oncept selection phase II Direct comparison with design requirements 2.76 Multi-scale System Design & Manuacturing

51 Example: onstraint-based design onstraint-based compliant mechanism design STEP 1: Design requirements Motion path, stiness, load capacity, etc STEP 2: Motion path decomposition Arcs, lines, rotation pts. sub-paths 1. Series topology: Add DOF 2. Parallel topology: Add onstraints K 3. Over constraint: K δ M δ k M δ << 1 STEP 3:Kinematic parametric concepts Motions, constraint metric, symmetry, etc. STEP 4:onstraint-motion addition rules Serial, parallel, hybrid STEP 5: Topology concept generation Path & constraint driven 3 δ 2 2 (r) STEP 6: oncept selection phase I Path errors & over constraint STEP 7: Size and shape optimization Stiness, load capacity, eiciency, etc K -3 K -3 θ 1 δ -2 θ δ -2 STEP 8: oncept selection phase II Direct comparison with design requirements 2.76 Multi-scale System Design & Manuacturing

52 Example: onstraint-based design onstraint-based compliant mechanism design STEP 1: Design requirements Motion path, stiness, load capacity, etc STEP 2: Motion path decomposition Arcs, lines, rotation pts. sub-paths STEP 3:Kinematic parametric concepts Motions, constraint metric, symmetry, etc. STEP 4:onstraint-motion addition rules Serial, parallel, hybrid STEP 5: Topology concept generation Path & constraint driven STEP 6: oncept selection phase I Path errors & over constraint STEP 7: Size and shape optimization Stiness, load capacity, eiciency, etc STEP 8: oncept selection phase II Direct comparison with design requirements 2.76 Multi-scale System Design & Manuacturing

Example: onstraint-based design onstraint-based compliant mechanism design omet: ompliant Mechanism Tool STEP 1: Design requirements Motion path, stiness, load capacity, etc STEP 2: Motion path

53 Example: onstraint-based design onstraint-based compliant mechanism design omet: ompliant Mechanism Tool STEP 1: Design requirements Motion path, stiness, load capacity, etc STEP 2: Motion path decomposition Arcs, lines, rotation pts. sub-paths STEP 3:Kinematic parametric concepts Motions, constraint metric, symmetry, etc. STEP 4:onstraint-motion addition rules Serial, parallel, hybrid STEP 5: Topology concept generation Path & constraint driven STEP 6: oncept selection phase I Path errors & over constraint STEP 7: Size and shape optimization Stiness, load capacity, eiciency, etc STEP 8: oncept selection phase II Direct comparison with design requirements 2.76 Multi-scale System Design & Manuacturing

54 Example: onstraint-based design onstraint-based compliant mechanism design T STEP 1: Design requirements Motion path, stiness, load capacity, etc STEP 2: Motion path decomposition Arcs, lines, rotation pts. sub-paths STEP 3:Kinematic parametric concepts Motions, constraint metric, symmetry, etc. θ STEP 4:onstraint-motion addition rules Serial, parallel, hybrid STEP 5: Topology concept generation Path & constraint driven STEP 6: oncept selection phase I Path errors & over constraint STEP 7: Size and shape optimization Stiness, load capacity, eiciency, etc STEP 8: oncept selection phase II Direct comparison with design requirements 2.76 Multi-scale System Design & Manuacturing

Example: onstraint-based design onstraint-based compliant mechanism design STEP 1: Design requirements Motion path, stiness, load capacity, etc STEP 2: Motion path

STEP 4:onstraint-motion addition rules Serial, parallel, hybrid STEP 5: Topology concept generation Path & constraint driven STEP 6: oncept selection phase I Path errors

55 Example: onstraint-based design onstraint-based compliant mechanism design STEP 1: Design requirements Motion path, stiness, load capacity, etc STEP 2: Motion path decomposition Arcs, lines, rotation pts. sub-paths STEP 3:Kinematic parametric concepts Motions, constraint metric, symmetry, etc. STEP 4:onstraint-motion addition rules Serial, parallel, hybrid STEP 5: Topology concept generation Path & constraint driven STEP 6: oncept selection phase I Path errors & over constraint STEP 7: Size and shape optimization Stiness, load capacity, eiciency, etc STEP 8: oncept selection phase II Direct comparison with design requirements 2.76 Multi-scale System Design & Manuacturing

56 Example: onstraint-based design onstraint-based compliant mechanism design STEP 1: Design requirements Motion path, stiness, load capacity, etc STEP 2: Motion path decomposition Arcs, lines, rotation pts. sub-paths STEP 3:Kinematic parametric concepts Motions, constraint metric, symmetry, etc. STEP 4:onstraint-motion addition rules Serial, parallel, hybrid STEP 5: Topology concept generation Path & constraint driven STEP 6: oncept selection phase I Path errors & over constraint STEP 7: Size and shape optimization Stiness, load capacity, eiciency, etc STEP 8: oncept selection phase II Direct comparison with design requirements 2.76 Multi-scale System Design & Manuacturing

58 Design activity 2.76 Multi-scale System Design & Manuacturing

59 Problem Design a mechanical ilter which: Gij = 0.05 (actor o 20 iltering) Range o 0.5 mm with less than 5 micron PE Envelope: 5 x 5 x inches Give us enough inormation to: Understand your constraint topology Fabricate it Assume it is aluminum journal ile at end o class You may ask any question at any time 2.76 Multi-scale System Design & Manuacturing

60 Assignment Form teams o 4 now, members to TA by 5pm Friday Flexure reading (pp & ) omet tutorials 1-3 Learn a AD package (3 wks!!!) reate omet model o your lexure, send to TA by Monday 9am 2.76 Multi-scale System Design & Manuacturing

2.76 / Lecture 5: Large/micro scale

2.76 / Lecture 5: Large/micro scale 2.76 / 2.760 Lecture 5: Large/micro scale Constraints Micro-fabrication Micro-physics scaling Assignment Nano Micro Meso Macro Nano Nano Nano Micro Nano Meso Nano Macro Micro Nano Micro Micro Micro Meso