ME 5243:ADVANCED MECHANISM DESIGN

• People’s Choice Awards• Review

– Linkage Fundamentals– Linkage Synthesis– Cam Design– Spatial Mechanisms

Class #26Course Review

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People’s Choice Award – Project Presentations

Honorable Mentions:• Team 3:Boldenow, Koon, Wollner

– Paper Airplane Launcher

• Team 8: Kravik, Pavelka, Pray, Zhang– Volleyball Setter

• Team 2: Boelter, Lucas, Nitz, Reinhardt– Quadcopter Arm

2nd Place:• Team 1: Creswick, Duan, Gorny, Gust

– Bicycle Lift

Winner:• Team 9: Boyce-Erickson, Fulbright, Simmons, Zeilon

– Nerf Gun

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• 42nd Mechanisms and Robotics Conference (MR) – Paper Draft: March 12, 2018

• Student Mechanism Design Competition– http://sites.google.com/site/asmesmrdc/– Letter of Intent: Early April

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Notes• Final Report & Rebuttal Letter: due by 5pm• Final Exam: Tues, Dec 19th, 8:00-10:00 am

– Example Final Posted• Office Hours:

– Today: 11-12– Thursday: 10-11– Monday: 11-12

• Peer Evaluations: Tuesday, Dec 19th

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Fundamentals

• Links: Binary, Ternary, Quaternary, etc.• Joints: Pin, Slider, Roll-Slide, Screw,

Cylindrical, Spherical, Planar• Mobility

– Kutzbach Criterion: General (Spatial)– Gruebler’s Equation: F = 3(n-1) – 2f1 – f2

• F: Degrees of Freedom• n: Number of Links• f1: Number of Full Joints• f2: Number of Half Joints

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Fundamentals: Classification

• Task: Function, Path, Motion• Range of Motion:

– Grashof Criteria: S + L ≤ P + Q– Barker Classification

• Link Sets– Slider-Crank Inversions– Geared 5-bars– 6-bars

• Stephenson: Ternaries Separated• Watt: Ternaries Connected

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Fundamentals: Operation

• Branch vs. Circuit– Branch: Pass through toggle– Circuit: Disassemble to reach inversion

• Transmission Angle: – Acute angle between coupler and output links

• Mechanical Advantage– MA = Fout / Fin = rin/rout * ωin/ωout

– Use Instant Centers for Angular Velocity Ratio

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Synthesis:

• Type Synthesis– Number Synthesis: DOF, # Links, # Link Sets– Topological Synthesis: # Topologies + Isomers– Topological Analysis: Best Inversions?, Alt Joints?

• Dimensional Synthesis– Graphical– Analytical

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Graphical Synthesis: Motion• Pick Moving Pivots (2 & 3 PPs)

• Ground Pivot Specification (3 PPs)1. Pick Gnd Pivots2. Find AO’ and A0” using inversion3. Find A1 at center of A0, A0’,A0”

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Graphical Synthesis: Path (3 PPs)1. Pick Gnd Pivots and A1

2. Find A2, A3

3. Find A0’, A0”4. Locate B0’, B0”

1. A0B0 = A0’B0’2. P2B0 = P1B0’

5. Locate B1

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Graphical Synthesis: Function (3 PPs)1. Pick Gnd Pivots and A1

2. Locate A0’ and A0” w/ -ψj rotation of A0B0 about B0

3. Locate A2’ and A3’1. A0A1 = A0’A2’2. B0A2 = B0A2’

4. Locate B1 at the center of A1, A2’, A3’

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Chebychev Spacing

1. Draw circle with dia = Δx2. Inscribe regular polygon w/ 2n sides

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M & K Circle Construction

PP1

PP2

PP3

P12

P13

P23

1. Find the poles: P12, P23, P132. Find the image pole: P23’

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PP1

PP2

PP3

P12

P13

P23

P23’

3. Draw lines for centers of m & k1 circles: a. m circle touches P13 and P23b. k circle touches P13 and P23’.

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PP1

PP2

PP3

P12

P13

P23

P23’Center of m-circles

Center of k-circles

4. Draw m circle: P13 Cm P23 = β25. Draw k circle: P23’ Ck P13 = α2-β2

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PP1

PP2

PP3

P12

P13

P23

P23’Cm

Center of m-circles

Center of k-circles

4. Draw m circle: P13 Cm P23 = β25. Draw k circle: P23’ Ck P13 = α2-β2

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PP1

PP2

PP3

P12

P13

P23

P23’Cm

Ck

Center of m-circles

Center of k-circles

4. Draw m circle: P13 Cm P23 = β25. Draw k circle: P23’ Ck P13 = α2-β26. Draw ray from P12 to a point on m-circle (picking β3), label it M

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PP1

PP2

PP3

P12

P13

P23

P23’Cm

Ck

Center of m-circles

Center of k-circles

M

6. Draw ray from P12 to a point on m circle (picking β3), label it M7. Find corresponding point on k1 circle

a. Rotate line P12 M by -β2/2 at Mb. Rotate line P12 M by -α2/2 at P12

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PP1

PP2

PP3

P12

P13

P23

P23’Cm

Ck

Center of m-circles

Center of k-circles

M

6. Draw ray from P12 to a point on m circle (picking β3), label it M7. Find corresponding point on k1 circle

a. Rotate line P12 M by -β2/2 at Mb. Rotate line P12 M by -α2/2 at P12

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PP1

PP2

PP3

P12

P13

P23

P23’Cm

Ck

Center of m-circles

Center of k-circles

M

K

6. Draw ray from P12 to a point on m circle (picking β3), label it M7. Find corresponding point on k1 circle

a. Rotate line P12 M by -β2/2 at Mb. Rotate line P12 M by -α2/2 at P12

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PP1

PP2

PP3

P12

P13

P23

P23’

M

K

8. Draw dyad in 1st and 3rd positions9. Measure β3

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PP1

PP2

PP3

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Parallel Motion 6-bar• Parallel Motion is Useful for Many

Applications– Parallel Motion 4-bars: Only Circular Motion

• Leveraging Cognates Allows Construction of a Parallel Motion 6-bar (Watt I)

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3

4

5

6

7

10

8

9

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Parallel Motion 6-bar• Recognizing that ω2 = ω7

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82

3

4

5

6

7

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Geared 5-bar• A Geared 5-bar Can Create the Coupler Curve of Any 4-bar

αα

α

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Geared 5-bar• A Geared 5-bar Can Create the Coupler Curve of Any 4-bar

α

α

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Cam Design

S

V

A

J

Source: Norton, Design of Machinery

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Fundamental Law of Cam Design:The cam-follower function must have continuous

velocity and acceleration across the entire interval, thus making the jerk finite.

Profile Selection:• Obey fundamental law• Low peak acceleration:

F = ma• Low peak velocity:

KE = 0.5 mv2

• Smoother jerk = lower vibrations

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Common Double-Dwell Functions

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Polynomial Cam Segments

θ

s

θ

v

θ

a

θ

j

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Polynomial Segments

• Minimize the number of segments• Start with the segment you know most about• Use polynomials where possible• Minimize the number of boundary conditions

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Cam Sizing

• Size cam for:– Pressure angle– Radius of curvature– Forces / Stresses

• By adjusting:– Prime circle, RP

– Eccentricity, – Follower radius, RF

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Conveyor Belt Chaser RP = 5 in, Rf = 2 in, ε = -1 in

0 50 100 150 200 250 300 350angle (deg)

-10

0

10

0 50 100 150 200 250 300 350angle (deg)

-5

0

5

0 50 100 150 200 250 300 350angle (deg)

-10

0

10

0 50 100 150 200 250 300 350angle (deg)

-20

0

20

-15 -10 -5 0 5 10 15-15

-10

-5

0

5

10

5 5 5 100 150 60

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14 weeks ago, you told me your goals for this course

• Did you meet your goals? Why/Why not?

11111

222

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46

910

0 2 4 6 8 10 12

Prepare for QualsPrototyping

Basis for Soft MechanismsMechanism Optimization

Improve Design SkillsPass the Course

Computer Synthesis ToolsEarn an A

Mechanism AnalysisExperience for Career

Visualize Mechanism MotionDesign Useful ProjectAdvanced Synthesis

Real-World Applications

chimein.cla.umn.edu or text 1-503-770-6789(text 22616 plus your answer)