1. Mechanism Design Graphical Method
Ken Youssefi
Mechanical & Aerospace Engineering Dept. SJSU

2. Mechanical & Aerospace Engineering Dept. SJSU
Mechanism Synthesis
Design 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
– How many links should the
mechanism have? How many degrees of freedom are desired?
Number Synthesis
Dimensional Synthesis
– deals with determining the length of all links, gear diameter, cam profile.
Ken Youssefi
Mechanical & Aerospace Engineering Dept. SJSU

3. Mechanical & Aerospace Engineering Dept. SJSU
Mechanism Synthesis
Type Synthesis
The 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. Mechanical & Aerospace Engineering Dept. SJSU
Mechanism Synthesis
Type 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)
Max. transmission angle
Min. transmission angle
The minimum transmission angle should be greater than 40o to avoid locking or jamming the mechanism
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 MechanismA
O4B = 2(O2A)
rin = rout
µ = 60O, v = 5O
M.A. = 20
Ken Youssefi
Mechanical & Aerospace Engineering Dept. SJSU

10. Mechanical & Aerospace Engineering Dept. SJSU
Mechanism Synthesis
Dimensional Synthesis
Graphical Methods
– provide the designer with a quick straightforward method but parameters cannot easily be manipulated to create new solutions.
Analytical Methods
– this approach is suitable for automatic computation. Once a mechanism is modeled and coded for computer, parameters are easily manipulated to create new designs.
Ken Youssefi
Mechanical & Aerospace Engineering Dept. SJSU

11. Graphical Synthesis – Motion Generation Mechanism
Two positions, coupler as the output B1
Draw the link AB in its two desired positions, A1B1 and A2B2
Draw two lines perpendicular to A1 A2 and B1B2 at the midpoint (midnormals).
Connect A1 to A2 and B1 to B2.
Measure the length of all links,
O2A = link 2, AB = link 3,
O4B = link 4 and O2 O4 = link 1 A2 A1 B2 O2 O4
Select two fixed pivot points, O2 and O4, anywhere on the two midnormals.
Ken Youssefi
Mechanical & Aerospace Engineering Dept. SJSU

12. Graphical Synthesis – Motion Generation Mechanism
Three positions, coupler as the output
Same procedure as for two positions.
Draw the link AB in three desired positions. A2 B1 A1
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. A3 O2 O4 B2
Check the accuracy of the mechanism, Grashof condition and the transmission angle. B3
Change the second position of link AB to vary the locations of the fixed points
Ken Youssefi
Mechanical & Aerospace Engineering Dept. SJSU

13. Graphical Synthesis – Motion Generation Mechanism
Adding a Dyad to a non-Grashof mechanism.
Draw the four bar in both positions B1 C1 C2
Select any point C on link 2. 3 A2 A1
Connect C1 to C2 and extend. B2 D2
Draw a circle with radius C1C2 / 2. The radius is the length of the sixth link. 2 O6
Select any location on this line for third fixed pivot, O6. 5 6
Measure O6D = link 6, DC = link 5 4 O2 O4
Ken Youssefi
Mechanical & Aerospace Engineering Dept. SJSU

14. Graphical Synthesis – Motion Generation Mechanism
6-Bar Grashof mechanism B1 A A1 5 2 3 B 4 C D O2 O4 6 O6
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
Draw the link CD in its two desired positions, C1D1 and C2D2 D1
Connect C1 to C2 and D1 to D2 and draw two midnormals to C1C2 and D1D2 C2 C1 B1 B2
Select point B1 anywhere on link O4C1 and locate B2 so O4B1= O4B2 D2 O4
The intersection of the two midnormals is the fixed pivot point O4. A2
Draw a circle with radius B1 B2 / 2, point A is the intersection of the circle with the B1 B2 extension. O2
Connect B1 to B2 and extend. Select any location on this line for fixed pivot point O2.
O2A = B1B2 / 2
Measure the length of all links, O2A = link 2, AB = link 3, O4CD = link 4 and O2 O4 = link 1
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 C2 C1 D2 B2 A2 O2 O4
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 Mechanism
Three positions with specified fixed pivot points,
coupler as the output
O’2
O’4
Draw the link CD in its three desired positions, C1D1, C2D2 and C3D3 and locate the fixed pivot points O2 and O4.
Draw an arc from C1 with radius O2C2 and another arc from D1 with radius O2D2. Locate the intersection, O’2.
Draw an arc from C1 with radius O4C2 and another arc from D1 with radius O4D2. Locate the intersection, O’4. C2 D2 D1 D3 C1 C3 O2
O’4 O4
O’2
Ken Youssefi
Mechanical & Aerospace Engineering Dept. SJSU

21. Graphical Synthesis – Motion Generation Mechanism
Three positions with specified fixed pivot points,
coupler as the output
Draw an arc from C1 with radius O2C3 and another arc from D1 with radius O2D3. Locate the intersection, O”2.
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 C2 D2 D1 D3 C1 C3
O”2 O2
O”4
O’4 O4
O’2
Ken Youssefi
Mechanical & Aerospace Engineering Dept. SJSU

22. Graphical Synthesis – Motion Generation Mechanism
Three positions with specified fixed pivot points,
coupler as the output
O”4
O”2
Connect O2 to O’2 and O’2 to O”2 . Draw two midnormals and locate the intersection, G.
Connect O4 to O”4 and O”4 to O’4 . Draw two midnormals and locate the intersection, H.
O2G is link 2 and O4H is link 4.
Construct a link (3) containing GH and CD.
Verify the solution by constructing the mechanism in three position
O’4 C2 D2 D1 H
O’2 G D3 C1 C3 O2 O4
Ken Youssefi
Mechanical & Aerospace Engineering Dept. SJSU

23. Graphical Synthesis – Motion Generation MechanismD2 D1 H D3 G C1 C3 O2 O4
Ken Youssefi
Mechanical & Aerospace Engineering Dept. SJSU

24. Graphical Synthesis – Motion Generation Mechanism
Three positions with specified fixed pivot points, coupler as the output.
Ken Youssefi
Mechanical & Aerospace Engineering Dept. SJSU

25. Graphical Synthesis – Path Generation Mechanism
Three prescribed points.
Design a 4-Bar in such a way that a point on the coupler passes thru three specified points P1 P2 P3
Draw the three desired points, P1, P2, and P3. A1
Select the length of the crank O2A and the coupler side AP. O4 O2
Select the location of the fixed pivot points, O2 and O4. A3 A2
With A1P1 established, locate A2 and A3, A1P1 = A2P2 = A3P3.
Measure angles α1 (O2A1P1), α2 and α3. α1 α2 α3
Ken Youssefi
Mechanical & Aerospace Engineering Dept. SJSU

26. Graphical Synthesis – Path Generation Mechanism
Three prescribed points.
Locate moving pivot B by means of kinematic inversion. Fix coupler AP in position 1 and rotate O2O4.
O”4 B
Draw an arc from O”2 with radius O2O4 , draw another arc from P1 with radius P3O4 , locate the intersection, O”4 .
Connect O4 to O’4 and O’4 to O”4 and draw the midnormals. Locate the intersection, B.
O’2
Rotate A1O2 about A1 by (α2 – α1) to O’2 . P1 P2
Draw an arc from O’2 with radius O2O4 , draw another arc from P1 with radius P2O4 , locate the intersection, O’4 . P3
O”2
Rotate A1O2 about A1 by (α3 – α1) to O”2 . A1 O4 O2
Verify the mechanism.
Ken Youssefi
Mechanical & Aerospace Engineering Dept. SJSU

27. Graphical Synthesis – Path Generation Mechanism with Prescribed Timing
Three prescribed points
Timing requirements:
input crank rotation α, mechanism moves from P1 to P2
input crank rotation β, mechanism moves from P1 to P3 O2
Select location of the fixed pivot point O2.
P’2 α
Rotate O2P2 , in the opposite direction of motion, through angle α, P’2. A P1 P2
Draw midnormals to P1P’2 and P1P’3.and locate the intersection A.
Measure O2A = link 2 and AP. P3
P’3 β
Rotate O2P3 ,in the opposite direction of motion, through angle β, P’3.
Follow the same procedure as before , for without timing, to locate the moving pivot point B.
Note: timing takes away the free choices of the crank length and coupler length AP.
Ken Youssefi
Mechanical & Aerospace Engineering Dept. SJSU

28. Graphical Synthesis; Quick – Return Mechanism
4-Bar crank-Rocker mechanism
Advance stroke – mechanism operates under the load.
Return stroke – mechanism operates under no load.
Q = time of advance stroke / time of return stroke
Q > 1 quick-return mechanism
Ken Youssefi
Mechanical & Aerospace Engineering Dept. SJSU

29. Quick – Return Mechanism
Consider the two toggle positions of a crank-rocker mechanism. C
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 - (r3 – r2) = 2r2
r3 – r2 O4 O2 B1 2 3 4 A1 B2 A2
Ken Youssefi
Mechanical & Aerospace Engineering Dept. SJSU

30. Quick – Return MechanismB1 B2 A2 α 3 4
180 – α, Return stroke A1 2 O2 O4
Q = advance / Return = (180 + α) / (180 – α), Time Ratio
Ken Youssefi
Mechanical & Aerospace Engineering Dept. SJSU

31. Synthesis of a Quick – Return Mechanism
Known or selected; Rocker angle, φ Rocker length, r4 Time ratio, Q
Determine; r1, r2, r3
Construct the line YY’ through point B2 making an angle α with XX’. Y Y’ α
Draw the two toggle positions, knowing r4 and φ. B1 B2 φ O4
Select the location for the fixed pivot point, O4. X
Construct an arbitrary line XX’ through point B1. X’
Calculate the angle α from known time ratio Q =
(180 + α) / (180 – α) O2
The intersection of XX’ and YY’ is the other fixed pivot, O2
Ken Youssefi
Mechanical & Aerospace Engineering Dept. SJSU

32. Synthesis of a Quick – Return Mechanism
Locate point C on YY’ so O2C = O2 B1. C O2 X Y’ O4 X’ Y B1 B2
Measure length B2 C, Link 2 = r2 = (B2 C) /2
2r2 A1 r2 A2
Calculate the length of link 3, AB = r3 = O2 B1 – r2 A O4 O2 B
Verify the motion of the mechanism and check the minimum transmission angle.
Ken Youssefi
Mechanical & Aerospace Engineering Dept. SJSU