Synthesis of linkages Graphical Method

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Mechanism SynthesisDesign or creation of a mechanism to obtain a specified motion or force.

– Given the required performance, what type of mechanism is suitable? Linkages, gears, cam and follower, belt and pulley and chain and sprocket.

• Type Synthesis

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• Dimensional Synthesis

– How many links should themechanism have? How many degrees of freedom are desired?

• Number Synthesis

sprocket.

– Deals with determining the length of all links, gear diameter, cam profile.

Mechanism SynthesisFunction Generation, Path Generation, Body Guidance

Path Generation-

Function Generation- Design requirement is that of causingout put member to rotate, oscillate, or reciprocate according toa specified function of time or function of the input motion.

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Path Generation- Refers to a problem in which a coupler point is to generate a path having prescribed shape. i.e. circular arc, elliptical, or straight line

Body Guidance- Deals with moving an object from oneposition to another. May be simple translation orcombination of translation and rotation. i.e. MovingBulldozer blades.

Mechanism SynthesisDimensional and position Synthesis

Graphical Methods – provide the designer with a quick straightforward method but parameters cannot easily be manipulated to create new solutions.

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solutions.

– this approach is suitable for automatic computation. Once a mechanism is modeled and coded for computer, parameters are easily manipulated to create new designs.

Analytical Methods

Mechanism Synthesis

Graphical position Synthesis

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Graphical position Synthesis

Two position synthesis of slider crank mechanism

•Stroke B1B2 = 2* r2

•Limiting positions B1 and B2 = r3+r2 and r3- r2

•For centered slider crank mechanism r3> r2

•Whenr = r Called as Isosceles

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(a) Centered slider-crank mechanism.

•Whenr3= r2 Called as Isosceles slider crank mechanism

Two position synthesis of slider crank mechanism

•Stroke B1B2 is always > 2* r2

•Limiting positions B1 and B2 = r3+r2 and r3- r2

• Crank angle required to executive the forward stroke is different from that for the

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General or offset slider-crank mechanism

different from that for the return stroke.

•This feature can be used in quick return mechanisms

Limiting Conditions – 4 Bar Mechanism

Toggle positions of a crank-rocker mechanism. Links 2 and 3 become collinear.

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Two position synthesis of crank and rocker mechanism

•Limiting positions B1 and B2 = r3+r2 and r3- r2

• Crank and coupler form a single straight line at each extreme position.

•Forward stroke- Crank

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The extreme positions of the crank-and-rocker mechanism

•Forward stroke- Crank executive the angle y ,y ,y ,y ,Rocker executive the angle Ø

•Return stroke - Crank executive the angle 360 -y ,y ,y ,y ,Rocker executive the same angle Ø

Mechanism Synthesis

Graphical Dimension Synthesis

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Graphical Dimension Synthesis

Graphical Synthesis; Quick – Return Mechanism

Q = time of advance stroke / time of return stroke

Advance stroke – mechanism operates under the load.

Return stroke – mechanism operates under no load.

4-Bar crank-Rocker mechanism

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Q = time of advance stroke / time of return stroke

Q > 1 quick-return mechanism

Graphical Synthesis; Quick – Return Mechanism, Crank and rocker

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0

0

180

180Q

αα

+=−

Equation for timer ratio of the forward and backward motions of the rocker is

Quick – Return Mechanism

Consider the two toggle positions of a crank-rocker mechanism.

B1B2

C

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O4O2

2

3 4

A1

A2

Locate point C to satisfy the following two conditions;

1) C is on extension of line A2B2.

2) O2C = O2B1 = r2 + r3 B2C = r2 +r3 - (r 3 – r2) = 2r2

Quick – Return Mechanism

B1

2

3 4

A1

B2

C

α

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O4O2A2

180 –α, Return stroke

Q = advance / Return = (180 + α) / (180 –α), Time Ratio

Synthesis of a Quick – Return Mechanism

Known or selected; Rocker angle, φ Rocker length, r4

Time ratio, Q

Determine; r1, r2, r3

1. Select the location for the fixed pivot point, O4.

X’

Y’

2. Draw the two toggle positions, knowing r and φ.

B1

B2

φ

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O4O2

6. The intersection of XX’ and YY’ is the other fixed pivot, O2

X4. Construct an arbitrary line XX’

through point B1.

5. Construct the line YY’ through point B2 making an angle α with XX’.

Y

αknowing r4 and φ. φ

3. Calculate the angle α from known time ratio Q =(180 + α) / (180 –α)

Synthesis of a Quick – Return Mechanism

Y’

X’

B1

B2

7. Locate point C on YY’ so O2C = O2 B1.

C

9. Calculate the length of link 3, AB = r3 = O2 B1 – r2

8. Measure length B2 C, Link 2 = r2 = (B2 C) /22r2

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O2

X

O4

Y

A1

r2

A2

A

O4O2

B

10. Verify the motion of the mechanism and check the minimum transmission angle.

Two- Position synthesis of crank-and-rocker mechanisms

17The extreme positions of the crank-and rocker-mechanism

Crank rocker mechanism Hall and Soni method

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Layout showing all possible

locations of B1 and B2.Determination of the link lengths

for one of the possible crank-

rocker mechanisms

Draw O2O4 1. Locate point C defined by angle (f/2–

a)and f/22. Locate point C’ symmetrical about O2O4

3. Then using C as centre and CO2 as radius draw circular arc from O2 showing locus of B2

4. Using C’ as centre and CO2 as radius draw circular arc from O2 showing locus of B1

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circular arc from O2 showing locus of B1

Layout showing all possible

locations of B1 and B2.

Determination of the link lengths

for one of the possible crank-

rocker mechanisms

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1. Choose any point B1 on the locus of B12. Draw an arc about O4 to locate B2 on the locus of the B23. Once points B1 and B2 are defined methods of the preceding

section are used to locate A1 and A2 together with r2 and r3

Graphical Synthesis – Motion Generation Mechanism

O2

Two positions, coupler as the output

A1A2

B1

B2

1. Draw the link AB in its two desired positions, A1B1 andA2B2

2. Connect A1 to A2 and B1 to B2.

3. Draw two lines perpendicular to A1 A2 and B1B2 at the midpoint

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O2

O44. Select two fixed pivot points, O2and O4, anywhere on the two midnormals.

5. Measure the length of all links,

O2A = link 2, AB = link 3,

O4B = link 4 and O2 O4 = link 1

A1 A2 and B1B2 at the midpoint (midnormals).

Graphical Synthesis – Motion Generation Mechanism

O4O2

Three positions, coupler as the output

A1

A2

A3

B1

Same procedure as for two positions.

1. Draw the link AB in three desired positions.

2. Draw the midnormals to A1A2 and A2A3, the intersection locates the fixed pivot

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B2

B3

point O2. Same for point B to obtain second pivot point O4.

3. Check the accuracy of the mechanism, Grashof condition and the transmission

angle.

4. Change the second position of link AB to vary the locations of the fixed points