sintesis grafica mecanismos

Mechanism Design Graphical Method

Mechanism Synthesis ,[object Object],[object Object],Design a mechanism to obtain a specified motion or force. – How many links should the mechanism have? How many degrees of freedom are desired? ,[object Object],– given the required performance, what type of mechanism is suitable? Linkages, gears, cam and follower, belt and pulley and chain and sprocket. ,[object Object]

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

Mechanism Synthesis Type Synthesis - The Associated Linkage Concept (6-Bar) 6-Bar

Limiting Conditions – 4 Bar Mechanism Toggle positions of a crank-rocker mechanism. Links 2 and 3 become collinear.

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)

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

Mechanical Advantage – 4 Bar Mechanism

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

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.

Graphical Synthesis – Motion Generation Mechanism Two positions, coupler as the output A 1 A 2 B 1 B 2 ,[object Object],O 2 O 4 ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Graphical Synthesis – Motion Generation Mechanism Three positions, coupler as the output A 1 A 2 A 3 B 1 B 2 B 3 ,[object Object],[object Object],[object Object],[object Object],[object Object],O 4 O 2

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 ,[object Object],O 6 ,[object Object],D 2 ,[object Object],C 1 C 2 ,[object Object],[object Object],5 6 ,[object Object]

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

Three Position, 6-Bar Grashof ,Motion Generation Mechanism

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 ,[object Object],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 ,[object Object],[object Object],O 4 ,[object Object],B 1 B 2 ,[object Object],A 2 ,[object Object]

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

Two Position, 4-Bar Grashof Motion Generation Mechanism

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 ,[object Object],[object Object],[object Object],O 4 O ’ 4 O ’ 2 O’ 2 O’ 4

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 ,[object Object],[object Object],O 4 O ’ 2 O ’ 4 O ” 2 O ” 4 O” 2 O” 4

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 ,[object Object],[object Object],[object Object],[object Object],[object Object],O 4 G H

Graphical Synthesis – Motion Generation Mechanism C 1 D 1 C 2 C 3 D 2 O 2 G H D 3 O 4

Graphical Synthesis – Motion Generation Mechanism Three positions with specified fixed pivot points, coupler as the output.

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 ,[object Object],[object Object],α 1 α 2 α 3 P 1 P 2 P 3 ,[object Object],A 1 ,[object Object],A 3 A 2 ,[object Object]

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 ,[object Object],[object Object],O 4 B O” 4 O’ 2 ,[object Object],O’ 4 O” 2 ,[object Object],[object Object],[object Object]

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 ,[object Object],Note: timing takes away the free choices of the crank length and coupler length AP. O 2 ,[object Object],A P’ 2 α ,[object Object],P’ 3 β ,[object Object],[object Object],[object Object]

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

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

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

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 ,[object Object],O 2 ,[object Object],X ,[object Object],X’ ,[object Object],Y Y’ α ,[object Object],B 1 B 2 φ ,[object Object],(180 + α) / (180 – α)

Synthesis of a Quick – Return Mechanism ,[object Object],O 2 X Y’ O 4 X’ Y B 1 B 2 ,[object Object],C ,[object Object],2r 2 A 1 r 2 A 2 A O 4 O 2 B ,[object Object]

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