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- 1. Mechanism Design Graphical Method
- 2. Mechanism Synthesis <ul><li>– deals with determining the length of all links, gear diameter, cam profile. </li></ul><ul><li>Dimensional Synthesis </li></ul>Design a mechanism to obtain a specified motion or force. – How many links should the mechanism have? How many degrees of freedom are desired? <ul><li>Number Synthesis </li></ul>– given the required performance, what type of mechanism is suitable? Linkages, gears, cam and follower, belt and pulley and chain and sprocket. <ul><li>Type Synthesis </li></ul>
- 3. 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
- 4. Mechanism Synthesis Type Synthesis - The Associated Linkage Concept (6-Bar) 6-Bar
- 5. Limiting Conditions – 4 Bar Mechanism Toggle positions of a crank-rocker mechanism. Links 2 and 3 become collinear.
- 6. Transmission Angle – 4 Bar Mechanism The angle between link 3 and link 4 is defined as the transmission angle T 4 = F 34 sin(µ) x (O 4 D)
- 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 40 o to avoid locking or jamming the mechanism µ Min. transmission angle Max. transmission angle
- 8. Mechanical Advantage – 4 Bar Mechanism
- 9. Mechanical Advantage – 4 Bar Mechanism O 4 B = 2( O 2 A ) r in = r out µ = 60 O , v = 5 O M.A. = 20 µ A B
- 10. Mechanism Synthesis Dimensional Synthesis – 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 Graphical Methods – provide the designer with a quick straightforward method but parameters cannot easily be manipulated to create new solutions.
- 11. Graphical Synthesis – Motion Generation Mechanism Two positions, coupler as the output A 1 A 2 B 1 B 2 <ul><li>Draw the link AB in its two desired positions, A 1 B 1 and A 2 B 2 </li></ul>O 2 O 4 <ul><li>Select two fixed pivot points, O 2 and O 4 , anywhere on the two midnormals. </li></ul><ul><li>Measure the length of all links, </li></ul><ul><li>O 2 A = link 2, AB = link 3, </li></ul><ul><li>O 4 B = link 4 and O 2 O 4 = link 1 </li></ul><ul><li>Connect A 1 to A 2 and B 1 to B 2 . </li></ul><ul><li>Draw two lines perpendicular to A 1 A 2 and B 1 B 2 at the midpoint (midnormals). </li></ul>
- 12. Graphical Synthesis – Motion Generation Mechanism Three positions, coupler as the output A 1 A 2 A 3 B 1 B 2 B 3 <ul><li>Same procedure as for two positions. </li></ul><ul><li>Draw the link AB in three desired positions. </li></ul><ul><li>Draw the midnormals to A 1 A 2 and A 2 A 3 , the intersection locates the fixed pivot point O 2 . Same for point B to obtain second pivot point O 4 . </li></ul><ul><li>Check the accuracy of the mechanism, Grashof condition and the transmission angle. </li></ul><ul><li>Change the second position of link AB to vary the locations of the fixed points </li></ul>O 4 O 2
- 13. Graphical Synthesis – Motion Generation Mechanism Adding a Dyad to a non-Grashof mechanism. A 1 A 2 B 1 B 2 O 2 O 4 2 3 4 <ul><li>Draw the four bar in both positions </li></ul>O 6 <ul><li>Select any location on this line for third fixed pivot, O 6. </li></ul>D 2 <ul><li>Draw a circle with radius C 1 C 2 / 2. The radius is the length of the sixth link. </li></ul>C 1 C 2 <ul><li>Select any point C on link 2. </li></ul><ul><li>Connect C 1 to C 2 and extend. </li></ul>5 6 <ul><li>Measure O 6 D = link 6, DC = link 5 </li></ul>
- 14. Graphical Synthesis – Motion Generation Mechanism A 1 A B 1 O 4 O 6 C D O 2 B 3 2 4 5 6 6-Bar Grashof mechanism
- 15. Three Position, 6-Bar Grashof ,Motion Generation Mechanism
- 16. Three Position, 6-Bar Grashof ,Motion Generation Mechanism
- 17. Graphical Synthesis – Motion Generation Mechanism Two positions Grashof 4-Bar mechanism with rocker as the output D 1 C 1 C 2 D 2 O 2 <ul><li>Connect B 1 to B 2 and extend. Select any location on this line for fixed pivot point O 2 . </li></ul>O 2 A = B 1 B 2 / 2 7. Measure the length of all links, O 2 A = link 2, AB = link 3, O 4 CD = link 4 and O 2 O 4 = link 1 <ul><li>Draw the link CD in its two desired positions, C 1 D 1 and C 2 D 2 </li></ul><ul><li>Connect C 1 to C 2 and D 1 to D 2 and draw two midnormals to C 1 C 2 and D 1 D 2 </li></ul>O 4 <ul><li>The intersection of the two midnormals is the fixed pivot point O 4 . </li></ul>B 1 B 2 <ul><li>Select point B 1 anywhere on link O 4 C 1 and locate B 2 so O 4 B 1 = O 4 B 2 </li></ul>A 2 <ul><li>Draw a circle with radius B 1 B 2 / 2, point A is the intersection of the circle with the B 1 B 2 extension. </li></ul>
- 18. Graphical Synthesis – Motion Generation Mechanism Two positions Grashof 4-Bar mechanism with rocker as the output D 1 C 1 C 2 A 2 O 2 B 2 D 2 O 4
- 19. Two Position, 4-Bar Grashof Motion Generation Mechanism
- 20. Graphical Synthesis – Motion Generation Mechanism Three positions with specified fixed pivot points, coupler as the output C 1 D 1 C 2 C 3 D 2 D 3 O 2 <ul><li>Draw the link CD in its three desired positions, C 1 D 1 , C 2 D 2 and C 3 D 3 and locate the fixed pivot points O 2 and O 4 . </li></ul><ul><li>Draw an arc from C 1 with radius O 2 C 2 and another arc from D 1 with radius O 2 D 2 . Locate the intersection, O’ 2 . </li></ul><ul><li>Draw an arc from C 1 with radius O 4 C 2 and another arc from D 1 with radius O 4 D 2 . Locate the intersection, O’ 4 . </li></ul>O 4 O ’ 4 O ’ 2 O’ 2 O’ 4
- 21. Graphical Synthesis – Motion Generation Mechanism C 1 D 1 C 2 C 3 D 2 D 3 O 2 Three positions with specified fixed pivot points, coupler as the output <ul><li>Draw an arc from C 1 with radius O 2 C 3 and another arc from D 1 with radius O 2 D 3 . Locate the intersection, O” 2 . </li></ul><ul><li>Draw an arc from C 1 with radius O 4 C 3 and another arc from D 1 with radius O 4 D 3 . Locate the intersection, O” 4 . </li></ul>O 4 O ’ 2 O ’ 4 O ” 2 O ” 4 O” 2 O” 4
- 22. Graphical Synthesis – Motion Generation Mechanism C 1 D 1 C 2 C 3 D 2 O 2 O ” 2 O ” 4 O ’ 2 O ’ 4 Three positions with specified fixed pivot points, coupler as the output D 3 <ul><li>Connect O 2 to O’ 2 and O’ 2 to O” 2 . Draw two midnormals and locate the intersection, G. </li></ul><ul><li>Connect O 4 to O” 4 and O” 4 to O’ 4 . Draw two midnormals and locate the intersection, H. </li></ul><ul><li>O 2 G is link 2 and O 4 H is link 4. </li></ul><ul><li>Construct a link (3) containing GH and CD. </li></ul><ul><li>Verify the solution by constructing the mechanism in three position </li></ul>O 4 G H
- 23. Graphical Synthesis – Motion Generation Mechanism C 1 D 1 C 2 C 3 D 2 O 2 G H D 3 O 4
- 24. Graphical Synthesis – Motion Generation Mechanism Three positions with specified fixed pivot points, coupler as the output.
- 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 O 4 O 2 <ul><li>Select the location of the fixed pivot points, O 2 and O 4 . </li></ul><ul><li>Measure angles α 1 (O 2 A 1 P 1 ), α 2 and α 3 . </li></ul>α 1 α 2 α 3 P 1 P 2 P 3 <ul><li>Draw the three desired points, P 1 , P 2 , and P 3 . </li></ul>A 1 <ul><li>Select the length of the crank O 2 A and the coupler side AP. </li></ul>A 3 A 2 <ul><li>With A 1 P 1 established, locate A 2 and A 3 , A 1 P 1 = A 2 P 2 = A 3 P 3 . </li></ul>
- 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 O 2 O 4 . O 2 P 1 P 2 P 3 A 1 <ul><li>Verify the mechanism. </li></ul><ul><li>Draw an arc from O’ 2 with radius O 2 O 4 , draw another arc from P 1 with radius P 2 O 4 , locate the intersection, O’ 4 . </li></ul>O 4 B O” 4 O’ 2 <ul><li>Rotate A 1 O 2 about A 1 by (α 2 – α 1 ) to O’ 2 . </li></ul>O’ 4 O” 2 <ul><li>Rotate A 1 O 2 about A 1 by (α 3 – α 1 ) to O” 2 . </li></ul><ul><li>Draw an arc from O” 2 with radius O 2 O 4 , draw another arc from P 1 with radius P 3 O 4 , locate the intersection, O” 4 . </li></ul><ul><li>Connect O 4 to O’ 4 and O’ 4 to O” 4 and draw the midnormals. Locate the intersection, B. </li></ul>
- 27. Graphical Synthesis – Path Generation Mechanism with Prescribed Timing Three prescribed points Timing requirements: input crank rotation α, mechanism moves from P 1 to P 2 input crank rotation β, mechanism moves from P 1 to P 3 P 1 P 2 P 3 <ul><li>Follow the same procedure as before , for without timing, to locate the moving pivot point B. </li></ul>Note: timing takes away the free choices of the crank length and coupler length AP. O 2 <ul><li>Select location of the fixed pivot point O 2 . </li></ul>A P’ 2 α <ul><li>Rotate O 2 P 2 , in the opposite direction of motion, through angle α , P’ 2 . </li></ul>P’ 3 β <ul><li>Rotate O 2 P 3 ,in the opposite direction of motion, through angle β , P’ 3 . </li></ul><ul><li>Draw midnormals to P 1 P’ 2 and P 1 P’ 3 .and locate the intersection A. </li></ul><ul><li>Measure O 2 A = link 2 and AP. </li></ul>
- 28. Graphical Synthesis; Quick – Return Mechanism Advance stroke – mechanism operates under the load. Return stroke – mechanism operates under no load. 4-Bar crank-Rocker mechanism Q = time of advance stroke / time of return stroke Q > 1 quick-return mechanism
- 29. Quick – Return Mechanism Consider the two toggle positions of a crank-rocker mechanism. O 4 O 2 B 1 2 3 4 A 1 B 2 A 2 C Locate point C to satisfy the following two conditions; 1) C is on extension of line A 2 B 2 . 2) O 2 C = O 2 B 1 = r 2 + r 3 B 2 C = r 2 +r 3 - (r 3 – r 2 ) = 2r 2 r 3 – r 2
- 30. Quick – Return Mechanism O 4 O 2 B 1 2 3 4 A 1 Q = advance / Return = (180 + α) / (180 – α), Time Ratio B 2 A 2 C α 180 – α, Return stroke
- 31. Synthesis of a Quick – Return Mechanism Known or selected; Rocker angle, φ Rocker length, r 4 Time ratio, Q Determine; r 1 , r 2 , r 3 O 4 <ul><li>Select the location for the fixed pivot point, O 4. </li></ul>O 2 <ul><li>The intersection of XX’ and YY’ is the other fixed pivot, O 2 </li></ul>X <ul><li>Construct an arbitrary line XX’ through point B 1 . </li></ul>X’ <ul><li>Construct the line YY’ through point B 2 making an angle α with XX’. </li></ul>Y Y’ α <ul><li>Draw the two toggle positions, knowing r 4 and φ. </li></ul>B 1 B 2 φ <ul><li>Calculate the angle α from known time ratio Q = </li></ul>(180 + α) / (180 – α)
- 32. Synthesis of a Quick – Return Mechanism <ul><li>Calculate the length of link 3, AB = r 3 = O 2 B 1 – r 2 </li></ul>O 2 X Y’ O 4 X’ Y B 1 B 2 <ul><li>Locate point C on YY’ so O 2 C = O 2 B 1 . </li></ul>C <ul><li>Measure length B 2 C, Link 2 = r 2 = (B 2 C) /2 </li></ul>2r 2 A 1 r 2 A 2 A O 4 O 2 B <ul><li>Verify the motion of the mechanism and check the minimum transmission angle. </li></ul>

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