mechanism synthesis, graphical
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Ken Youssefi Mechanical & Aerospace Engineering Dept. SJSU 1
Mechanism Design Graphical Method
Ken Youssefi Mechanical & Aerospace Engineering Dept. SJSU 2
• Dimensional Synthesis
Mechanism SynthesisDesign a mechanism to obtain a specified motion or force.
– How many links should themechanism have? How many degrees of freedom are desired?
• Number Synthesis
– given the required performance, what type of mechanism is suitable? Linkages, gears, cam and follower, belt and pulley and chain and sprocket.
• Type Synthesis
– deals with determining the length of all links, gear diameter, cam profile.
Ken Youssefi Mechanical & Aerospace Engineering Dept. SJSU 3
Mechanism SynthesisType SynthesisThe Associated Linkage Concept
It is desired to derive various types of mechanisms for driving a slider with a linear translation along a fixed path in a machine. Also, assume that the slider must move with a reciprocating motion.
4-Bar
Ken Youssefi Mechanical & Aerospace Engineering Dept. SJSU 4
Mechanism SynthesisType Synthesis - The Associated Linkage Concept (6-Bar)
6-Bar
Ken Youssefi Mechanical & Aerospace Engineering Dept. SJSU 5
Limiting Conditions – 4 Bar Mechanism
Toggle positions of a crank-rocker mechanism. Links 2 and 3 become collinear.
Ken Youssefi Mechanical & Aerospace Engineering Dept. SJSU 6
Transmission Angle – 4 Bar Mechanism
The angle between link 3 and link 4 is defined as the transmission angle
T4 = F34sin(µ) x (O4D)
Ken Youssefi Mechanical & Aerospace Engineering Dept. SJSU 7
Minimum Transmission Angle – 4 Bar Mechanism
Minimum transmission angle occurs when link 2 (crank) becomes collinear with link 1 (ground link)
The minimum transmission angle should be greater than 40o to avoid locking or jamming the mechanism
µ
Min. transmission angle
Max. transmission angle
Ken Youssefi Mechanical & Aerospace Engineering Dept. SJSU 8
Mechanical Advantage – 4 Bar Mechanism
Ken Youssefi Mechanical & Aerospace Engineering Dept. SJSU 9
Mechanical Advantage – 4 Bar Mechanism
O4B = 2(O2A)
rin = rout
µ = 60O, v = 5O
M.A. = 20
µ
A
B
Ken Youssefi Mechanical & Aerospace Engineering Dept. SJSU 10
Mechanism SynthesisDimensional Synthesis
Graphical Methods – provide the designer with a quick straightforward method but parameters cannot easily be manipulated to create new 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
Ken Youssefi Mechanical & Aerospace Engineering Dept. SJSU 11
O2
O44. Select two fixed pivot points, O2 and O4, anywhere on the two midnormals.
Graphical Synthesis – Motion Generation MechanismTwo positions, coupler as the output
A1A2
B1
B2
1. Draw the link AB in its two desired positions, A1B1 and A2B2
5. Measure the length of all links,
O2A = link 2, AB = link 3,
O4B = link 4 and O2 O4 = link 1
2. Connect A1 to A2 and B1 to B2.
3. Draw two lines perpendicular to A1 A2 and B1B2 at the midpoint (midnormals).
Ken Youssefi Mechanical & Aerospace Engineering Dept. SJSU 12
O4O2
Graphical Synthesis – Motion Generation Mechanism
Three positions, coupler as the output
A1
A2
A3
B1
B2
B3
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 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
Ken Youssefi Mechanical & Aerospace Engineering Dept. SJSU 13
O6
4. Select any location on this line for third fixed pivot, O6.
D2
5. Draw a circle with radius C1C2 / 2. The radius is the length of the sixth link.
Graphical Synthesis – Motion Generation MechanismAdding a Dyad to a non-Grashof mechanism.
A1A2
B1
B2
O2
O4
2
3
4
1. Draw the four bar in both positions
C1 C2
2. Select any point C on link 2.
3. Connect C1 to C2 and extend.
56
6. Measure O6D = link 6, DC = link 5
Ken Youssefi Mechanical & Aerospace Engineering Dept. SJSU 14
Graphical Synthesis – Motion Generation Mechanism
A1A
B1
O4
O6
CDO2
B32 4
5
6
6-Bar Grashof mechanism
Ken Youssefi Mechanical & Aerospace Engineering Dept. SJSU 15
Three Position, 6-Bar Grashof ,Motion Generation Mechanism
Ken Youssefi Mechanical & Aerospace Engineering Dept. SJSU 16
Three Position, 6-Bar Grashof ,Motion Generation Mechanism
Ken Youssefi Mechanical & Aerospace Engineering Dept. SJSU 17
Graphical Synthesis – Motion Generation Mechanism
Two positions Grashof 4-Bar mechanism with rocker as the output
D1
C1C2
D2
O2
5. Connect B1 to B2 and extend. Select any location on this line for fixed pivot point O2.
O2A = B1B2 / 2
7. Measure the length of all links, O2A = link 2, AB = link 3, O4CD = link 4 and O2 O4 = link 1
1. Draw the link CD in its two desired positions, C1D1 and C2D2
2. Connect C1 to C2 and D1 to D2 and draw two midnormals to C1C2 and D1D2
O4
3. The intersection of the two midnormals is the fixed pivot point O4.
B1 B2
4. Select point B1 anywhere on link O4C1 and locate B2 so O4B1= O4B2
A2
6. Draw a circle with radius B1 B2 / 2, point A is the intersection of the circle with the B1 B2 extension.
Ken Youssefi Mechanical & Aerospace Engineering Dept. SJSU 18
Graphical Synthesis – Motion Generation Mechanism
Two positions Grashof 4-Bar mechanism
with rocker as the output
D1
C1C2
A2
O4
O2
B2D2
Ken Youssefi Mechanical & Aerospace Engineering Dept. SJSU 19
Two Position, 4-Bar Grashof Motion Generation Mechanism
Ken Youssefi Mechanical & Aerospace Engineering Dept. SJSU 20
Graphical Synthesis – Motion Generation MechanismThree positions with specified fixed pivot points,coupler as the output
C1
D1
C2
C3
D2
D3
O4
O2
1. Draw the link CD in its three desired positions, C1D1, C2D2 and C3D3 and locate the fixed pivot points O2 and O4.
2. Draw an arc from C1 with radius O2C2 and another arc from D1 with radius O2D2. Locate the intersection, O’2.
3. Draw an arc from C1 with radius O4C2 and another arc from D1 with radius O4D2. Locate the intersection, O’4.
O’4O’
2
O’2
O’4
Ken Youssefi Mechanical & Aerospace Engineering Dept. SJSU 21
Graphical Synthesis – Motion Generation Mechanism
C1
D1
C2
C3
D2
D3
O4
O2
O’2
O’4
Three positions with specified fixed pivot points,coupler as the output
4. Draw an arc from C1 with radius O2C3 and another arc from D1 with radius O2D3. Locate the intersection, O”2.
5. Draw an arc from C1 with radius O4C3 and another arc from D1 with radius O4D3. Locate the intersection, O”4.
O”2
O”4
O”2
O”4
Ken Youssefi Mechanical & Aerospace Engineering Dept. SJSU 22
C1
D1
C2
C3
D2
O4
O2
O”2
O”4
O’2
O’4
G
H
Graphical Synthesis – Motion Generation MechanismThree positions with specified fixed pivot points,coupler as the output
D3
6. Connect O2 to O’2 and O’2 to O”2 . Draw two midnormals and locate the intersection, G.
7. Connect O4 to O”4 and O”4 to O’4 . Draw two midnormals and locate the intersection, H.
8. O2G is link 2 and O4H is link 4.
9. Construct a link (3) containing GH and CD.
10. Verify the solution by constructing the mechanism in three position
Ken Youssefi Mechanical & Aerospace Engineering Dept. SJSU 23
Graphical Synthesis – Motion Generation Mechanism
C1
D1
C2
C3
D2
O4
O2
G
H
D3
Ken Youssefi Mechanical & Aerospace Engineering Dept. SJSU 24
Graphical Synthesis – Motion Generation MechanismThree positions with specified fixed pivot points, coupler as the output.
Ken Youssefi Mechanical & Aerospace Engineering Dept. SJSU 25
O4O2
2. Select the location of the fixed pivot points, O2 and O4.
Graphical Synthesis – Path Generation MechanismThree prescribed points.
5. Measure angles α1 (O2A1P1), α2 and α3.
α1α2 α3
P1 P2
P3
1. Draw the three desired points, P1, P2, and P3.
A13. Select the length of the crank O2A
and the coupler side AP. A3
A2
4. With A1P1 established, locate A2 and A3, A1P1 = A2P2 = A3P3.
Design a 4-Bar in such a way that a point on the coupler passes thru three specified points
Ken Youssefi Mechanical & Aerospace Engineering Dept. SJSU 26
Graphical Synthesis – Path Generation MechanismThree prescribed points.Locate moving pivot B by means of kinematic inversion. Fix coupler AP in position 1 and rotate O2O4.
O4O2
P1 P2
P3
A1
11. Verify the mechanism.
B
O”4
O’2
6. Rotate A1O2 about A1 by (α2 – α1) to O’2 .
O’4
7. Draw an arc from O’2 with radius O2O4 , draw another arc from P1
with radius P2O4 , locate the intersection, O’4 .
O”2
8. Rotate A1O2 about A1 by (α3 – α1) to O”2 .
9. Draw an arc from O”2 with radius O2O4 , draw another arc from P1
with radius P3O4 , locate the intersection, O”4 .
10. Connect O4 to O’4 and O’4 to O”4 and draw the midnormals. Locate the intersection, B.
Ken Youssefi Mechanical & Aerospace Engineering Dept. SJSU 27
O2
1. Select location of the fixed pivot point O2.
Graphical Synthesis – Path Generation Mechanismwith Prescribed Timing
Three prescribed pointsTiming requirements: input crank rotation α, mechanism moves from P1 to P2 input crank rotation β, mechanism moves from P1 to P3
P1 P2
P3
6. Follow the same procedure as before , for without timing, to locate the moving pivot point B.
A
Note: timing takes away the free choices of the crank length and coupler length AP.
P’2
α
2. Rotate O2P2 , in the opposite direction
of motion, through angle α, P’2.P’3
β
3. Rotate O2P3 ,in the opposite direction of motion, through angle β, P’3.
4. Draw midnormals to P1P’2 and P1P’3.and locate the intersection A.
5. Measure O2A = link 2 and AP.
Ken Youssefi Mechanical & Aerospace Engineering Dept. SJSU 28
Graphical Synthesis; Quick – Return Mechanism
Q = time of advance stroke / time of return stroke
Q > 1 quick-return mechanism
Advance stroke – mechanism operates under the load.
Return stroke – mechanism operates under no load.
4-Bar crank-Rocker mechanism
Ken Youssefi Mechanical & Aerospace Engineering Dept. SJSU 29
Quick – Return Mechanism
Consider the two toggle positions of a crank-rocker mechanism.
O4O2
B1
2
3 4
A1
B2
A2
C
Locate point C to satisfy the following two conditions;
1) C is on extension of line A2B2.
2) O2C = O2B1 = r2 + r3B2C = r2 +r3 - (r3 – r2) = 2r2
r 3 – r 2
Ken Youssefi Mechanical & Aerospace Engineering Dept. SJSU 30
Quick – Return Mechanism
O4O2
B1
2
3 4
A1
B2
A2
C
α
180 – α, Return stroke
Q = advance / Return = (180 + α) / (180 – α), Time Ratio
Ken Youssefi Mechanical & Aerospace Engineering Dept. SJSU 31
Synthesis of a Quick – Return MechanismKnown or selected; Rocker angle, φ Rocker length, r4
Time ratio, Q
Determine; r1, r2, r3
O4
1. Select the location for the fixed pivot point, O4.
O2
6. The intersection of XX’ and YY’ is the other fixed pivot, O2
X4. Construct an arbitrary line XX’
through point B1.
X’
5. Construct the line YY’ through point B2 making an angle α with XX’.
Y
Y’
α
2. Draw the two toggle positions, knowing r4 and φ.
B1
B2
φ
3. Calculate the angle α from known time ratio Q = (180 + α) / (180 – α)
Ken Youssefi Mechanical & Aerospace Engineering Dept. SJSU 32
Synthesis of a Quick – Return Mechanism
O2
X
Y’
O4
X’
Y
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
A1
r2
A2
A
O4O2
B
10. Verify the motion of the mechanism and check the minimum transmission angle.
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