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Principles of

Form Synthesis II

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Form Synthesis Principles

1. Triangle Principle2. Tetrahedron Principle3. Hollow Shaft principle4. Mating Surface Principle5. I-Beam Principle6. Supplementary Shape Principle7. Anti-Buckling Principle8. Direct Path Principle

9. Force Flow Principle10. Metal Removal Principle11. Redundancy Avoidance

Principle12. Leverage Principle13. Shape Merging Principle14. Roughly Uniform Size

Principle15. Symmetry Principle.

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Triangle Principle

1. Football stadium structures2. Bicycle frame3. Airplane landing gear 4. Roof trusses5. Automobile frame component

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Tetrahedron Principle

1. Antenna supports2. Drilling platforms3. Jack stands4. Wire spoked wheels5. Guyed power poles

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Hollow Shaft Principle

1. Automobile drive shaft2. Helicopter mast3 ASV drive shaft4. Drill pipe5. Aircraft transmission shafting

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Mating Surface Principle

All lower kinematic pairs (surface contact) Journal bearings Scotch yoke Piston Roller chain Press fit on a shaft V-belt (instead of a gear) Wobble plate shoe

Examples:

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Mating Surface Summary

a)Gears, Camsb)Roller/ball bearingsc)Journal bearingsd)Bolted joint

Very badBadGoodVery good

Hertz stresses and slidingHertz stresses aloneMating surface and slidingMating surface alone

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I-Beam Principle

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Examples of I-Beam Principle

Wrench handleBox beamChannel sectionSandwich constructionFormed sheet.

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Supplementary Shape PrincipleA supplementary shape often can be added to provide a load path leading to a strong stress pattern

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More on Supplementary Shapes

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Anti-Buckling Principle As sections become thin, buckling becomes

possible

Buckling requires: Compressive load Thin or long section

Sources of Buckling Geometry change Material change

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Examples of Buckling

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More Examples of Buckling

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Buckling Stiffeners

Flange stiffeners

Flat plate stiffeners

Wing stiffeners

Buckling stiffeners add a small amount of material to stiffen (not necessarily strengthen) structure

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More Buckling Stiffeners

Tube stiffeners for bending

Tapered column

House floor braces

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More Buckling Stiffeners (cont’d) Derrick boom lacing

Use of internal pressure

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Direct-Path Principle

• Put material in a straight-line path between loads and supports

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Force-Flow Principle

Internal forces flow like fluids in laminar flow

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Example of force flow

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Flow Line examples

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Metal Removal Principle

After selecting a strong stress pattern After visualizing the flow of forces Remove all material where stresses are

low Consider economics, function, and

manufacturing processes

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Examples of Metal Removal

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Examples of Metal Removal (cont’d)

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Another Example of Metal Removal Principle

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Examples of Material Removal

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Redundancy Avoidance Principle

(a) (b)

F F

Identify optimum load paths, and do not put in structure at other places unless absolutely necessary

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Load Leverage Principle

When moments or torques must be carried, regions of force application should be separated as much as possible

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Load Leverage Example

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Limitations on Leverage

1. Weight can increase due to extra length, and supplementary shapes needed to achieve leverage

2. Sections can become so thin that buckling occurs3. Space may be too large to achieve good leverage4. Manufacturing problems caused by the

introduction of leverage may make the part too expensive

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Shape/stiffness MergingWhen a large force must be accommodated and widely

distributed to a general area, use shape merging

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General Regions Involved in Shape Merging1. Compact region where there is a highly concentrated load2. Merge region3. Thin walled region into which the load must be transferred

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Types of Merging Regions Tapered Sections (thickness or diameter changes with

length)

• Fan Sections (width changes with length)

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Types of Merging Regions (cont’d) Ribs (height and possibly thickness changes

with length)

• Branching Ribs

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Roughly Uniform Size Principle Adjoining portions of a part should be roughly the same

size

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Symmetry Principle Unless there is a reason to the contrary,

make a part symmetric

Makes parts easy to machine on a lathe

Makes assembly easier

Reduces inventory needs

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Rules of Thumb for Part Shapes

Rectangular solids Planes with general boundaries Circular cylinders Cones Axisymmetric geometries Spheres General geometries

Ranking according to order of expense

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Limits to Form Synthesis Principles

Space limitations

Cost limitations

Function limitations

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Limits to Form Synthesis Principles (cont’d)

Manufacturing process limitations (e.g., hollow crankshaft)

Fastening constraints; for example, the mounting brackets on engine block

Appearance

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Examples of Limits

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Summary

• Many different principles for Form Synthesis

• Use of each principle depends on the application and the driving factors

• Engineers determine the appropriate principle for the “best” design

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Credits

This module is intended as a supplement to design classes in mechanical engineering. It was developed at The Ohio State University under the NSF sponsored Gateway Coalition (grant EEC-9109794). Contributing members include:

Gary Kinzel ……………………………………..Primary author Walter Starkey……………Primary source of original material Phuong Pham and Matt Detrick ……….…….. Module revisions

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Disclaimer

This information is provided “as is” for general educational purposes; it can change over time and should be interpreted with regards to this particular circumstance. While much effort is made to provide complete information, Ohio State University and Gateway do not guarantee the accuracy and reliability of any information contained or displayed in the presentation. We disclaim any warranty, expressed or implied, including the warranties of fitness for a particular purpose. We do not assume any legal liability or responsibility for the accuracy, completeness, reliability, timeliness or usefulness of any information, or processes disclosed. Nor will Ohio State University or Gateway be held liable for any improper or incorrect use of the information described and/or contain herein and assumes no responsibility for anyone’s use of the information. Reference to any specific commercial product, process, or service by trade name, trademark, manufacture, or otherwise does not necessarily constitute or imply its endorsement.