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
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
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.
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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
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.
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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
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