sintesis grafica mecanismos

Mechanism Design Graphical Method

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

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
Draw the link AB in its two desired positions, A 1 B 1 and A 2 B 2
O 2 O 4
Select two fixed pivot points, O 2 and O 4 , anywhere on the two midnormals.
Measure the length of all links,
O 2 A = link 2, AB = link 3,
O 4 B = link 4 and O 2 O 4 = link 1
Connect A 1 to A 2 and B 1 to B 2 .
Draw two lines perpendicular to A 1 A 2 and B 1 B 2 at the midpoint (midnormals).

Graphical Synthesis – Motion Generation Mechanism Three positions, coupler as the output A 1 A 2 A 3 B 1 B 2 B 3
Same procedure as for two positions.
Draw the link AB in three desired positions.
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 .
Check the accuracy of the mechanism, Grashof condition and the transmission angle.
Change the second position of link AB to vary the locations of the fixed points
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
Draw the four bar in both positions
O 6
Select any location on this line for third fixed pivot, O 6.
D 2
Draw a circle with radius C 1 C 2 / 2. The radius is the length of the sixth link.
C 1 C 2
Select any point C on link 2.
Connect C 1 to C 2 and extend.
5 6
Measure O 6 D = link 6, DC = link 5

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
Connect B 1 to B 2 and extend. Select any location on this line for fixed pivot point O 2 .
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
Draw the link CD in its two desired positions, C 1 D 1 and C 2 D 2
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
O 4
The intersection of the two midnormals is the fixed pivot point O 4 .
B 1 B 2
Select point B 1 anywhere on link O 4 C 1 and locate B 2 so O 4 B 1 = O 4 B 2
A 2
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.

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
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 .
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 .
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 .
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
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 .
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 .
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
Connect O 2 to O’ 2 and O’ 2 to O” 2 . Draw two midnormals and locate the intersection, G.
Connect O 4 to O” 4 and O” 4 to O’ 4 . Draw two midnormals and locate the intersection, H.
O 2 G is link 2 and O 4 H is link 4.
Construct a link (3) containing GH and CD.
Verify the solution by constructing the mechanism in three position
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
Select the location of the fixed pivot points, O 2 and O 4 .
Measure angles α 1 (O 2 A 1 P 1 ), α 2 and α 3 .
α 1 α 2 α 3 P 1 P 2 P 3
Draw the three desired points, P 1 , P 2 , and P 3 .
A 1
Select the length of the crank O 2 A and the coupler side AP.
A 3 A 2
With A 1 P 1 established, locate A 2 and A 3 , A 1 P 1 = A 2 P 2 = A 3 P 3 .

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
Verify the mechanism.
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 .
O 4 B O” 4 O’ 2
Rotate A 1 O 2 about A 1 by (α 2 – α 1 ) to O’ 2 .
O’ 4 O” 2
Rotate A 1 O 2 about A 1 by (α 3 – α 1 ) to O” 2 .
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 .
Connect O 4 to O’ 4 and O’ 4 to O” 4 and draw the midnormals. Locate the intersection, B.

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
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. O 2
Select location of the fixed pivot point O 2 .
A P’ 2 α
Rotate O 2 P 2 , in the opposite direction of motion, through angle α , P’ 2 .
P’ 3 β
Rotate O 2 P 3 ,in the opposite direction of motion, through angle β , P’ 3 .
Draw midnormals to P 1 P’ 2 and P 1 P’ 3 .and locate the intersection A.
Measure O 2 A = link 2 and AP.

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
Select the location for the fixed pivot point, O 4.
O 2
The intersection of XX’ and YY’ is the other fixed pivot, O 2
X
Construct an arbitrary line XX’ through point B 1 .
X’
Construct the line YY’ through point B 2 making an angle α with XX’.
Y Y’ α
Draw the two toggle positions, knowing r 4 and φ.
B 1 B 2 φ
Calculate the angle α from known time ratio Q =
(180 + α) / (180 – α)

Synthesis of a Quick – Return Mechanism
Calculate the length of link 3, AB = r 3 = O 2 B 1 – r 2
O 2 X Y’ O 4 X’ Y B 1 B 2
Locate point C on YY’ so O 2 C = O 2 B 1 .
C
Measure length B 2 C, Link 2 = r 2 = (B 2 C) /2
2r 2 A 1 r 2 A 2 A O 4 O 2 B
Verify the motion of the mechanism and check the minimum transmission angle.

sintesis grafica mecanismos

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