Designing Design Engineers

Designing (passionately) Design Engineers Prof. Alexander H. Slocum MacVicar Faculty Teaching Fellow Department of Mechanical Engineering Massachusetts Institute of Technology 77 Massachusetts Avenue, Room 3-445 Cambridge, MA 02139 617.253.0012 617-258-6427 (fax) slocum@mit.edu http://pergatory.mit.edu Precision Engineering Research Group, MIT 1 10/2/2002 Working with Industry to Create Precision Machines •Moore Tool PAMT for Defense Logistics Agency •Moore Tool 5-axis Contour Mill •Moore Nanotech 150 Aspheric Grinder •Weldon 1632 Gold Cylindrical Grinder •CoorsTek all-ceramic grinder •NCMS Cluster Spindle •OMAX JetMachining™ Centers •Elk Rapids 5 axis cutter grinder •NCMS HydroBushing™ and HydroSpindle™ •Anorad/Dover MiniMill™ •Teradyne K-Dock System, Manipulator & Apollo Sorter Precision Engineering Research Group, MIT 2 10/2/2002 Getting Engineers to THINK! • • "Personal self-satisfaction is the death of the scientist. Collective selfsatisfaction is the the death of research. It is restlessness, anxiety, dissatisfaction, agony of the mind that nourish science" Jacques-Lucien Monod To help generate and create ideas, thought processes can be used as catalysts – Systematic Variation • Consider all possibilities – Persistent Questioning • Continually ask “Who?”, “What?”, “Why?”, “Where”, “How?” – Reversal: Forward Steps • Start with an idea, and vary it in as many ways as possible to create different ideas, until each gets to the end goal • Also called the method of divergent thought – Reversal: Backwards Steps • Start with the end goal and work backwards along as many paths as possible till you get to the beginning – Nature’s Way • How would nature solve the problem? – Exact Constraints • What are the minimum requirements Precision Engineering Research Group, MIT 3 10/2/2002 Thinking: Reversal • Being able to rapidly switch between thought modes is an invaluable skill – Example: Given length equalities indicated by the colored pointy end cylinders, prove that the yellow cylinder is the perpendicular bisector of the purple and red cylinders? • Never be afraid to add your own sketching to a problem that is given you – The thin red and blue lines and vertex labels were added! • If you do not rapidly see how to move forward, try going backwards! As given: After user inflicted clarifying features: A E D F 4 B C 10/2/2002 Precision Engineering Research Group, MIT How Does Good Design Happen? • Good design has mechanical, electrical, and software components – Being able to determine how a design will work before it is built is the premise of modern industry • Deterministic design is the key: – 62.5 grams of prevention is worth a kilogram of cure! – Good mechanics, makes it easier on the mechanics! – “Random Results are the Result of Random Procedures” Geoffe Portes Precision Engineering Research Group, MIT 5 10/2/2002 How Does Good Design Happen? • Good design is based on philosophy, experience, and analysis – Philosophy is how we create our brains’ bio neural nets to give deep insight into problems • It is the hardest thing to teach and learn, and contributes to the idea that design is a “black art” – Experience depends on learning how things have been done (e.g., take-apart & how things work) and doing it, again and again and again… • Human learning begins with touching… – Analysis is taught widely, and established web-based teaching methods exist • Students need philosophy and experience to help them learn how to use analysis and what level of analysis is appropriate Precision Engineering Research Group, MIT 6 10/2/2002 FUNdaMENTAL Principles of Mechanical Design • Imagine the feeling you get when you engage in an activity in which you RULE! – When you MASTER the FUNdaMENTALs of design, you get the same feeling, continuously! • Robot World will help students master the FUNdaMENTALs! • Philosophy, theory, practice! • AND the issues in cost/performance tradeoffs • How fundamentals can be used to identify disruptive technologies • • • • • • • • • • Accuracy, Repeatability, Resolution Sensitive Directions Reference Features Structural Loop Free Body Diagram Centers of Action Exact Constraint Design Elastic Averaging Dimensional Analysis Leading and Bleeding edges • • • • • • • • • • Patterns Occam’s Razor: KISS & MISS Saint-Venant’s Principle Golden Rectangle Abbe’s Principle Maxwell’s Reciprocity Self-Principles Stability Superposition Parallel Axis Theorem Precision Engineering Research Group, MIT 7 10/2/2002 Patterns: StrategiesConceptsModulesComponents • Deterministic Design leaves LOTS of room for the wild free creative spirit, and LOTS of room for experimentation and play Deterministic Design is a catalyst to funnel creativity into a successful design 1 2 3 4 5 6 7 4 1 2 3 4 5 6 7 6 • 1 2 3 4 5 6 3 1 2 2 1 2 3 1 1 2 3 4 2 1 2 3 4 5 5 1 2 3 1 1 2 2 • It is OK to iterate… – A goal is to never have to backtrack • A good engineer, however, knows when its time to let go… 8 10/2/2002 Precision Engineering Research Group, MIT Occam’s Razor: KISS & MISS • William of Occam (or Ockham) (1284-1347) was an English philosopher and theologian – Ockham stressed the Aristotelian principle that entities must not be multiplied beyond what is necessary – “Ockham wrote fervently against the papacy in a series of treatises on papal power and civil sovereignty. The medieval rule of parsimony, or principle of economy, frequently used by Ockham came to be known as Ockham's razor. The rule, which said that plurality should not be assumed without necessity (or, in modern English, keep it simple, stupid), was used to eliminate many pseudo-explanatory entities” (http://wotug.ukc.ac.uk/parallel/www/occam/occam-bio.html) • A problem should be stated in its basic and simplest terms • The simplest theory that fits the facts of a problem is the one that should be selected • Limit Analysis is an invaluable way to identify and check simplicity • Use fundamental principles as catalysts to help you – Keep It Super Simple – Make It Super Simple – Because “Silicon is cheaper than cast iron…”(Don Blomquist) Precision Engineering Research Group, MIT 9 10/2/2002 Saint-Venant’s Principle • Saint-Venant’s Principle – Saint-Venant did extensive research in the theory of elasticity, and many times he relied on the assumption that local effects of loading do not affect global strains • e.g., bending strains at the root of a cantilever are not influenced by the local deformations of a point load applied to the end of a cantilever – The engineering application of his general observations are profound for the development of conceptual ideas and initial layouts of designs: Wheel • To NOT be affected by local deformations of a force, be several characteristic Shaft dimensions away – On the city bus, how many seats away from the smelly old drunk do you Sliding want to be? bearing in structure • To have control of an object, apply constraints over several characteristic !!Non Optimal!! dimensions Wheel Shaft – These are just initial layout guidelines, and designs must be optimized using closed-form or finite element analysis Sliding bearing in structure !!Optimal!! Barré de Saint-Venant 1797-1886 Precision Engineering Research Group, MIT 10 10/2/2002 The Golden Rectangle • The proportions of the Golden Rectangle are a natural starting point for preliminary sizing of structures and elements – – Golden Rectangle: A rectangle where when a square is cut from the rectangle, the remaining rectangle has the same proportions as the original rectangle Watch Donald in Mathmagic Land! The greater the ratio of the longitudinal to latitudinal (length to width) spacing: • The smoother the motion will be and the less the chance of walking (yaw error) • First try to design the system so the ratio of the longitudinal to latitudinal spacing of bearing elements is about 2:1 • For the space conscious, the bearing elements can lie on the perimeter of a golden rectangle (ratio about 1.618:1) • The minimum length to width ratio is 1:1 to minimize yaw error α 90.0 80.0 70.0 60.0 roll angle (deg) 50.0 40.0 30.0 20.0 10.0 0.0 5 3 4. 2 4.6 3.8 3.4 2.6 2.2 1.8 1.4 1 0.6 • Example: Bearings: – 1.618:1 1:1 Precision Engineering Research Group, MIT 11 0.2 width/height 10/2/2002 Abbe’s Principle • In the late 1800s, Dr. Ernst Abbe (1840-1905) and Dr. Carl Zeiss (1816-1888) worked together to create one of the world’s foremost precision optics companies: Carl Zeiss, GmbH (http://www.zeiss.com/us/about/history.shtml) The Abbe Principle (Abbe errors) resulted from observations about measurement errors in the manufacture of microscopes: – If errors in parallax are to be avoided, the measuring system must be placed coaxially with the axis along which the displacement is to be measured on the workpiece • Strictly speaking, the term Abbe error only applies to measurement errors • • When an angular error is amplified by a distance, to create an error in a machine’s position, for example, the strict definition of the error is a sine or cosine error L(1-cos(ε)) ˜ Lε2 /2 L From www.zeiss.com ε 12 Lsin(ε) L Precision Engineering Research Group, MIT 10/2/2002 Abbe’s Principle: Locating Components • • Geometric: Angular errors are amplified by the distance from the source – Measure near the source, and move the bearings and actuator near the work! Thermal: Temperatures are harder to measure further from the source – Measure near the source! • Thinking of Abbe errors, and the system FRs is a powerful catalyst to help develop DPs, where location of motion axes is depicted schematically – Example: Stick figures with arrows indicating motions are a powerful simple means of depicting strategy or concepts Precision Engineering Research Group, MIT 13 10/2/2002 Abbe’s Principle: Cascading Errors • A small angular deflection in one part of a machine quickly grows as subsequent layers of machine are stacked upon it… – A component that tips on top of a component that tips… – If you give a mouse a cookie….. • Error budgeting keeps tracks of errors in cascaded components – Designs must consider not only linear deflections, but angular deflections and their resulting sine errors… Tool R Error Work Motion of a column as it moves and deflects the axis upon which it rides Precision Engineering Research Group, MIT 14 10/2/2002 Maxwell’s Reciprocity • Maxwell’s theory of Reciprocity – Let A and B be any two points of an elastic system. Let the displacement of B in any direction U due to a force P acting in any direction V at A be u; and the displacement of A in the direction V due to a force Q acting in the direction U at B be v. Then Pv = Qu (from Roark and Young Formulas for Stress and Strain) • The principle of reciprocity can be extended in philosophical terms to have a profound effect on measurement and development of concepts – Reversal – Critical Thinking James Clerk Maxwell 1831-1879 Precision Engineering Research Group, MIT 15 10/2/2002 Reciprocity: Reversal • A method that is used to take out repeatable measuring instrument errors from the measurement – See ANSI standards for axis of rotation, straightness and machine tool metrology for excellent tutorials on applying reciprocity to measurement! • • One of the principal methods by which advances in accuracy of mechanical components have been continually made There are many application variations for measurement and manufacturing – Two bearings rails ground side-by-side can be installed end-to-end – A carriage whose bearings are spaced one rail segment apart will not pitch or roll CMM repeatability Z probe before reversal (x) = δ CMM (x) - δ part (x) Z probe after reversal (x) = δ CMM (x) + δ part (x) δ part(x) = Part before reversal -Z probe before reversal (x) + Z probe after reversal (x) 2 δ CMM (x) δ part (x) before reversal Part after reversal after reversal Precision Engineering Research Group, MIT 16 10/2/2002 Kinematic Couplings for Precision Fixturing • James Clerk Maxwell (1831-1879) likes three grooves – Symmetry good for manufacture, dynamic stability – Easy to obtain very high load capacity • William Thomson (later Lord Kelvin) (1824 - 1907) likes ball-groovetetrahedron – More intuitive, and more easily applied to non-planar designs Z Y X Planar Vertical Precision Engineering Research Group, MIT 17 10/2/2002 Canoe-Ball Kinematic Element for high Load Capacity and Repeatability error [ µ m ] “Canoe Ball” 0.10 0.00 Modular microscope for Univ. of Illinois 0 5 10 15 20 25 30 35 40 45 50 Coupling -0.10 -0.20 Measurement system error [ µ m ] 0.10 Repeatability Measurements 0 5 10 15 20 25 30 35 40 45 50 0.00 -0.10 Precision Engineering Research Group, MIT 18 10/2/2002 Kinematic Couplings: Three-Groove Design Guidelines • Keep Hertz contact pressure below 75% of tensile yield – – – – – Material fails in shear below the surface Contact area center should ideally not be closer than one diameter from edge Materials must be non-galling and non-fretting Preload to keep coupling from tipping Split Groove coupling spreads one of the grooves to give appearance of a 4 point mount, and thus provide somewhat greater unpreloaded tipping resistance Ball 1 • Align grooves with coupling triangle angle bisectors Coupling centroid Coupling triangle Angle bisector between sides 23 and 31 Ball 2 Ball 3 Plane containing the contact force vectors Precision Engineering Research Group, MIT 19 10/2/2002 Kinematic Couplings: Load Capacity of Contacts • 25 mm diameter stainless steel half-sphere on 25 mm diameter cylinders – – – Fmax = 111 N Vertical deflection = 3.2 µm Contact ellipse major diameter = 0.425 mm , minor diameter = 0.269 mm Fmax = 229 N Vertical deflection = 4.7 µm Contact ellipse major diameter = 0.488 mm , minor diameter = 0.488 mm Fmax = 1106 N Vertical deflection = 11 µm Contact ellipse major diameter = 2.695 mm , minor diameter = 0.603 mm Fmax = 16160 N Vertical deflection = 47 µm Contact ellipse major diameter = 4.878 mm , minor diameter = 4.878 mm Heinrich Hertz 1857-1894 • 25 mm diameter stainless steel half-sphere in a Vee – – – • 25 mm contact diameter x 125 mm radius crowned cone in a Vee – – – • 250 mm diameter stainless steel half-sphere in a Vee – – – • Above based on maximum contact pressure of 1.3 GPa, and E=193 GPa Precision Engineering Research Group, MIT 20 10/2/2002 Quasi-Kinematic Couplings for Ford Engine Assembly Prof. Marty Culpepper’s Ph.D. thesis QKC Attributes and Characteristics: • Partial surfaces of Revolution -> Short Line Contact • Weakly Over-constrained • Sub-micron Repeatability • Sealing Contact • High Stiffness without dowel pins Very low cost Spherical Protrusion δinitial δ=0 δfinal PROCESS: Groove Seat • Mating force/displacement applied Side Reliefs • Ball & groove comply • Brinell out surface finish • Elastic recovery restores gap 10/2/2002 Precision Engineering Research Group, MIT 21 Engine Assembly Performance JL Cap Probe 1 st Block Fixture Bedplate Fixture Bedplate JR Cap Probe Axial Cap Probe 2nd Block Fixture Axial CMM Head Sensitive C L QKC Error in Sensitive Direction 2.0 1.5 1.0 0.5 0.0 -0.5 0 -1.0 -1.5 -2.0 1 2 3 4 5 6 7 8 QKC Error in Axial Direction JL δ c, microns δa, microns JR 2.0 1.5 1.0 0.5 0.0 -0.5 0 -1.0 -1.5 -2.0 1 2 3 4 Max x Dislacement 5 6 7 8 Trial # Trial # (Range/2)|AVG = 0.65 µm Precision Engineering Research Group, MIT (Range/2) = 1.35 µm 22 10/2/2002 9 MAGNABOTS: Hosptial Automation?! § Ceiling based trackless system: Zero footprint, high degree of flexibility in motion § Ceiling of thin metal sheets: Can be bent into any shape; easily expandable and scalable § Graduate Students: Shorya Awtar and John Hart Precision Engineering Research Group, MIT 23 10/2/2002 MAGNABOTS: Development Phase I Proof-of-concept Demonstration at CIMIT, Oct 17’01: Steel ceiling installed in CIMIT Simulation Center Operating Room: § Overhead horizontal sections for traversing across the OR § Vertical wall-side section for payload docking Open-loop radio-controlled vehicles: § Three vehicles: simple pendulum and trianglependulum designs § Detachable payload carriers § Two magnetic driving wheels § Passive delrin wheels for guidance along vertical wall section Precision Engineering Research Group, MIT 24 10/2/2002 Linear Motor Magnet Preloaded Bearings FRDPARRC Sheet Topic: Precision Low Cost Linear Motion Stage Functional Requirement (Event) Preload air bearings for minimal cost Design Parameter (description of idea) Preload air bearings using magnetic attractive force of motor, so air bearings need only ride on two surfaces instead of having to wrap around a beam; thus many precision tolerances to establish bearing gap can be eliminated Sketch: Carriage Motor core Magnet track Assume we want even preload pressure per pad Motor preload angle 26.57 Motor attraction force, Fm 4000 Motor width (mm), L 130 Motor thickness 47 Space for motor thickness 65 Supply pressure, Ps (Pa, atm) 600000 bearing efficiency, m 0.35 preload proportion of total load capacity, f 0.5 vertical/horizontal load capacity, vh 2 X direction pads' total area (mm^2), Ax 21994 Y direction pads total area, (mm^2) Ay 43989 Bearing rail Air bearing pad Analysis (physics in words) The magnet attraction force is 5x greater than the motor force, so it can be positioned at an angle such that even preload is applied to all the bearings. As long as the magnet attraction net vertical and horizontal force are proportional to the bearing areas and is applied through the effective centers of the bearings, they will be evenly loaded without any applied moments. 1.5 raw accuracy:2.44 raw repeat:0.5 Analysis   θ = arctan  AV     AH  References: Vee & Flat bearings used on many common machine tools where gravity provides preload. NEAT uses two magnet tracks, one horizontal and one vertical, to provide horizontal and vertical preload force. Patent search revealed no other relevant art. -0.5 F F V H = F magnets sin θ = F magnets cos θ V H V H pitch error [arc sec] at 10 mm/s F F = A A 1 = tan θ 0.5 0 -1 -1.5 0 50 100 150 200 position [mm] 250 300 Risks: The magnet pitch may cause the carriage to pitch as the motor’s iron core windings pass over the magnets Countermeasures: Add steel out of phase with motor core position, or if the error is repeatable, map it and compensate for it in other axes Precision Engineering Research Group, MIT 25 10/2/2002 Linear Motor Magnet Preloaded Bearings • Primary research challenges – Carriage pitch caused by magnets is acceptable for modest precision or wafer transport systems – Two-axis proof-of-concept grinding machine designed and built (in 2 months) at Overbeck Machine Tool Corp. 1.5 Top Blocks Top Plate Top Jack Screws pitch error [arc sec] at 10 mm/s raw accuracy:2.44 raw repeat:0.5 1 0.5 0 -0.5 -1 -1.5 0 50 100 150 200 position [mm] 250 300 Side “L” Blocks Replicating Fixturing Side Jack Screws Removal Fixturing Precision Engineering Research Group, MIT 26 10/2/2002 Low-Cost Actuator/Bearing Structures • • Can preload of a nut on a screw be done in three-dimensions instead of just one… Can threaded-rods, the cheapest machine elements, can be made a precision bearing and actuator? 1”-14 Greased Threaded Rods Adjustable Preload Nuts Precision Engineering Research Group, MIT Additional Flexures 27 10/2/2002 Low-Cost Actuator/Bearing Structures • Preliminary tests were very encouraging! Full Scale Error Budget FR (Full Scale) δx Accuracy δy δx Repeatability δy Prototype Error Budget Prototype Results .02 .02 ±.02 ±.02 .006 .010 ±.009 ±.014 .010 .004 ±.019 ±.021 .007 .001 ±.0012 ±.00065 Flexures Precision Engineering Research Group, MIT 28 Preload Fixed Brass 10/2/2002 Nut Next: Personal Fabricators • How can we create low cost precision technologies to bring manufacturing to under-developed regions – Rolled threaded rod with preloaded nuts…. • Bits to atoms on a large scale…..? Precision Engineering Research Group, MIT 29 10/2/2002 MEMS: Wafer Alignment • Alexis Weber’s SM thesis was to see how repeatable are legos (several microns) and can we learn from them and other work on kinematic couplings to create a new means to precisely stack up wafers: – 4-inch double-sided polished (100) wafers were used and the convex features and cantilever flexures are fabricated through a backside KOH etch. – The individual flexures are released through a front-side DRIE. – The concave features are bulk micro-machined through a KOH etch. 3 µm feature size reference alignment marks were patterned initially using a custom mask. – Chrome masks made from emulsion transparencies were used to create the alignment features. – Testing of the passive alignment features was done on an Electronic Vision Group TBM8 wafer alignment inspection system, and wafer-to-wafer alignment on the order of 1 micron was achieved, and repeatability was in the submicron range – This alignment technique is not (YET!) compatible with anodic bonding due to the rough surface finish left by the KOH etch. It can however be used for eutectic bonding, among other bonding methods. Precision Engineering Research Group, MIT 30 10/2/2002 MEMS • Flexures have been used for centuries as a means to create extremely high accuracy small range of motion instrument stages – Prof. Sridhar Kota at UMI has an entire laboratory devoted to the design of compliant mechanisms • From staples to windshield washer blades to sophisticated MEMs devices • He has created field-search algorithms to find “optimum” flexural linkage designs to meet user defined FRs constraints • http://www.engin.umich.edu/labs/csdl/index.htm – Much of the work in MicroElectroMechanical Systems (MEMS) is based on the use of tiny silicon flexures Precision Engineering Research Group, MIT 31 10/2/2002 MEMS: Relays • • Jin Qiu’s Ph.D. thesis has led to a bistable double-beam flexure – It is bistable without any initial preload In trying to help us make it better, Prof. Michael Brenner (formally of MIT) developed an entirely new way of looking at optimization problems – When design engineers and applied mathematicians get together to play, it’s a productive day! Precision Engineering Research Group, MIT 32 10/2/2002 Force Displacement Curve For The Switch Force Ratio is 2:1…. Precision Engineering Research Group, MIT 33 10/2/2002 The Optimization: Changing Beam Shape Improves Performance Better Force Ratio Precision Engineering Research Group, MIT 34 10/2/2002 Optimized Switch Force Ratio is 1:1 ! Precision Engineering Research Group, MIT 35 10/2/2002 Nanogate • The Nanogate is a device that precisely meters the flow of tiny amounts of fluid. – – Precise control of the flow restriction is accomplished by deflecting a highly polished cantilevered plate. The opening is adjustable on a sub-nanometer scale, limited by the roughness of the polished plates. This research grew out of understanding of flow metering garnered from years of hydrostatic bearing research • The Nanogate can be fabricated on a macro-, meso- or micro- (MEMs) scale. – • This research was funded by an NSF award, number 9900792, and James White is a recipient of a a Hertz Fellowship Possible fuel injector application? Precision Engineering Research Group, MIT 36 10/2/2002 Nanogate Operation 100 620 667 641 640 650 682b 681b 665 667 • • • • The outer diameter of the “gate plate 620” is forced down The annular thin wall structure 630 acts like a torsion spring pivot The gate plate surface 641 lifts up creating a gap 777 Fluid can then flow from source 670a to sink 670b 601a 668 630 601b 682a 670b 670a 681a 622 668 100 F 667 777 620 641 640 650 665 682b 681b F ∆ δ 601a 668 630 601b 682d 682e 670b 682c 670a 682a 681a 622 Fig. 7 Precision Engineering Research Group, MIT 37 10/2/2002 Molecular Sensing and Filtration Using the Nanogate The Nanogate is micro-mechanical device that can accurately and repeatably control a nanometer sized gap. Precise control of the gate opening is accomplished by deflecting a cantilevered plate that is anchored by an annular torsion spring. The opening is adjustable on a subnanometer scale using a piezoelectric actuator. The ability to control flow channels at nanometer length scales may enable sensing and filtration of large molecules such as proteins and DNA. Graduate students James White and Hong Ma are building instrumentation around the Nanogate to precisely measure the gate opening and to image the flow of molecules in these constrained conditions. The actuation is achieved by a Nu Focus Picomotor actuator while the displacement sensing will be implemented using a Zygo single point optical probe interferometer. 10/2/2002 Figure 2: Schematic of the Nanogate Instrumentation Precision Engineering Research Group, MIT 38 Nanogate Molecular Sieve? • • • Flowrate of large molecules is nonlinearly dependent on the gap size, and modulation frequency, for very small gaps How does the mobility of a protein depend on the size and surface properties of the channel? Can proteins be mechanically filtered based on size? What dynamic effects would play a role? Can adsorption be controlled? Can we accomplish small gap chromatography? Proteins • • Precision Engineering Research Group, MIT 39 10/2/2002 AFM and the Nanogate § 0.5-dimensional probe § Interact with a few molecules at a time § Low throughput § Elastic forces ~ molecular attraction Precision Engineering Research Group, MIT § Molecules are constrained in a 2.5dimensional space. § Interact with many molecules § Higher throughput § Elastic forces >> molecular attraction 40 10/2/2002 Nanogate Instrumentation é Planned fluid connections ì Instrument schematic è First version - Super Invar flexure, piezoelectric motor, Michaelson interferometer for displacement measurement. Precision Engineering Research Group, MIT 41 10/2/2002 Results: 2nm Resolution! Displacement due to 2 steps 105 100 displacement (nm) 95 raw data Averaged 90 85 80 0 0.02 0.04 0.06 time (s) 0.08 0.1 0.12 Precision Engineering Research Group, MIT 42 10/2/2002 Results: Opening and Closing the Gate Mechanical Characteristics 140 120 Displacement (nm) 100 80 Going up (gate closing) 60 Going Down (Gate Opening) 40 20 0 0 5 10 15 20 25 30 Picomotor Steps Conclusion: Very good relative repeatability Precision Engineering Research Group, MIT 43 10/2/2002 Conclusions • • The fundamental principles of design can be applied at all scales – Deterministic design is most important! What we do on a large scale, often provides insight on the small scale – There is no shortage of engineering challenges at ALL scales Precision Engineering Research Group, MIT 44 10/2/2002