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Mechanism Design Graphical Method

Mechanism Design Graphical Method. Type Synthesis. – given the required performance, what type of mechanism is suitable? Linkages, gears, cam and follower, belt and pulley and chain and sprocket. Number Synthesis.

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Mechanism Design Graphical Method

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

  2. Type Synthesis – given the required performance, what type of mechanism is suitable? Linkages, gears, cam and follower, belt and pulley and chain and sprocket. • Number Synthesis – How many links should the mechanism have? How many degrees of freedom are desired? Mechanism Synthesis Design a mechanism to obtain a specified motion or force. – deals with determining the length of all links, gear diameter, cam profile. • Dimensional Synthesis Mechanical & Aerospace Engineering Dept. SJSU

  3. 4-Bar 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. Mechanical & Aerospace Engineering Dept. SJSU

  4. Mechanism Synthesis Type Synthesis - The Associated Linkage Concept (6-Bar) 6-Bar Mechanical & Aerospace Engineering Dept. SJSU

  5. Limiting Conditions – 4 Bar Mechanism Toggle positions of a crank-rocker mechanism. Links 2 and 3 become collinear. 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) Mechanical & Aerospace Engineering Dept. SJSU

  7. Max. transmission angle Min. transmission angle Minimum Transmission Angle – 4 Bar Mechanism Minimum transmission angle occurs when link 2 (crank) becomes collinear with link 1 (ground link) µ The minimum transmission angle should be greater than 40o to avoid locking or jamming the mechanism Mechanical & Aerospace Engineering Dept. SJSU

  8. Mechanical Advantage – 4 Bar Mechanism Mechanical & Aerospace Engineering Dept. SJSU

  9. Mechanical Advantage – 4 Bar Mechanism B µ A O4B = 2(O2A) rin = rout µ = 60O, v = 5O M.A. = 20 Mechanical & Aerospace Engineering Dept. SJSU

  10. Graphical Methods – provide the designer with a quick straightforward method but parameters cannot easily be manipulated to create new solutions. Mechanism Synthesis Dimensional Synthesis 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. Mechanical & Aerospace Engineering Dept. SJSU

  11. Connect A1 to A2 and B1 to B2. • Draw two lines perpendicular to A1 A2 and B1B2 at the midpoint (midnormals). O2 O4 • Select two fixed pivot points, O2 and O4, anywhere on the two midnormals. • Measure the length of all links, • O2A = link 2, AB = link 3, • O4B = link 4 and O2 O4 = link 1 Graphical Synthesis – Motion Generation Mechanism Two positions, coupler as the output B1 • Draw the link AB in its two desired positions, A1B1 andA2B2 A2 A1 B2 Mechanical & Aerospace Engineering Dept. SJSU

  12. O2 O4 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 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 Mechanical & Aerospace Engineering Dept. SJSU

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

  15. Three Position, 6-Bar Grashof ,Motion Generation Mechanism Mechanical & Aerospace Engineering Dept. SJSU

  16. Three Position, 6-Bar Grashof ,Motion Generation Mechanism Mechanical & Aerospace Engineering Dept. SJSU

  17. Draw the link CD in its two desired positions, C1D1 andC2D2 • Connect C1 to C2 and D1 to D2 and draw two midnormals to C1C2 and D1D2 B1 B2 • The intersection of the two midnormals is the fixed pivot point O4. A2 O2 O2A = B1B2 / 2 • Select point B1 anywhere on link O4C1 and locate B2 so O4B1= O4B2 O4 • Connect B1 to B2 and extend. Select any location on this line for fixed pivot point O2. • Draw a circle with radius B1 B2 / 2, point A is the intersection of the circle with the B1 B2 extension. 7. Measure the length of all links, O2A = link 2, AB = link 3, O4CD = link 4 and O2 O4 = link 1 Graphical Synthesis – Motion Generation Mechanism Two positions Grashof 4-Bar mechanism with rocker as the output D1 C2 C1 D2 Mechanical & Aerospace Engineering Dept. SJSU

  18. O4 Graphical Synthesis – Motion Generation Mechanism Two positions Grashof 4-Bar mechanism with rocker as the output D1 C2 C1 D2 B2 A2 O2 Mechanical & Aerospace Engineering Dept. SJSU

  19. Two Position, 4-Bar Grashof Motion Generation Mechanism Mechanical & Aerospace Engineering Dept. SJSU

  20. O’4 O’2 O4 O’4 O’2 Three positions with specified fixed pivot points, coupler as the output Graphical Synthesis – Motion Generation Mechanism • Draw the link CD in its three desired positions, C1D1, C2D2 andC3D3 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 Mechanical & Aerospace Engineering Dept. SJSU

  21. O”4 O”2 O”2 O4 O’4 O”4 O’2 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. C2 D2 D1 D3 C1 C3 O2 Mechanical & Aerospace Engineering Dept. SJSU

  22. H G O4 Three positions with specified fixed pivot points, coupler as the output Graphical Synthesis – Motion Generation Mechanism 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 D3 O’2 C1 C3 O2 Mechanical & Aerospace Engineering Dept. SJSU

  23. O4 Graphical Synthesis – Motion Generation Mechanism C2 D2 D1 H D3 G C1 C3 O2 Mechanical & Aerospace Engineering Dept. SJSU

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

  25. Draw the three desired points, P1, P2, and P3. P1 P2 • Select the location of the fixed pivot points, O2 and O4. P3 A2 • Select the length of the crank O2Aand the coupler side AP. A1 α2 α1 A3 α3 • With A1P1 established, locate A2 and A3, A1P1 = A2P2 = A3P3. O2 O4 • Measure angles α1 (O2A1P1), α2 and α3. Three prescribed points. Graphical Synthesis – Path Generation Mechanism Design a 4-Bar in such a way that a point on the coupler passes thru three specified points Mechanical & Aerospace Engineering Dept. SJSU

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

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

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

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

  30. C α B2 180 – α, Return stroke A2 Quick – Return Mechanism B1 4 3 A1 2 O4 O2 Q = advance / Return = (180 + α) / (180 – α), Time Ratio Mechanical & Aerospace Engineering Dept. SJSU

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

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

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