Mechanism Design Graphical Method Ken Youssefi Mechanical Aerospace

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

Mechanism Synthesis Design a mechanism to obtain a specified motion or force. • 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? • Dimensional Synthesis – deals with determining the length of all links, gear diameter, cam profile. Ken Youssefi Mechanical & Aerospace Engineering Dept. SJSU 2

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 Ken Youssefi Mechanical & Aerospace Engineering Dept. SJSU 3

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

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

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) Ken Youssefi Mechanical & Aerospace Engineering Dept. SJSU 6

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

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

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

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

Graphical Synthesis – Motion Generation Mechanism Two positions, coupler as the output 1. Draw the link AB in its two desired positions, A 1 B 1 and A 2 B 2 2. Connect A 1 to A 2 and B 1 to B 2. 3. Draw two lines perpendicular to A 1 A 2 and B 1 B 2 at the midpoint (midnormals). Select two fixed pivot points, O 2 and O 4, anywhere on the two midnormals. 4. 5. B 1 A 2 A 1 B 2 O 4 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 Ken Youssefi Mechanical & Aerospace Engineering Dept. SJSU 11

Graphical Synthesis – Motion Generation Mechanism Three positions, coupler as the output Same procedure as for two positions. 1. Draw the link AB in three desired positions. 2. 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. 3. A 2 B 1 A 3 O 2 O 4 B 2 Check the accuracy of the mechanism, Grashof condition and the transmission angle. 4. Change the second position of link AB to vary the locations of the fixed points Ken Youssefi Mechanical & Aerospace Engineering Dept. SJSU B 3 12

Graphical Synthesis – Motion Generation Mechanism Adding a Dyad to a non-Grashof mechanism. 1. Draw the four bar in both positions 2. Select any point C on link 2. 3. 4. Connect C 1 to C 2 and extend. Select any location on this line for third fixed pivot, O 6. 5. Draw a circle with radius C 1 C 2 / 2. The radius is the length of the sixth link. 6. Measure O 6 D = link 6, DC = link 5 Ken Youssefi B 1 3 A 1 O 6 A 2 B 2 2 6 D 2 5 C 1 C 2 4 O 2 O 4 Mechanical & Aerospace Engineering Dept. SJSU 13

Graphical Synthesis – Motion Generation Mechanism 6 -Bar Grashof mechanism B 1 A A 1 2 O 2 3 D 5 B 4 C O 4 6 O 6 Ken Youssefi Mechanical & Aerospace Engineering Dept. SJSU 14

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

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

Graphical Synthesis – Motion Generation Mechanism Two positions Grashof 4 -Bar mechanism with rocker as the output 1. 2. 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 3. The intersection of the two midnormals is the fixed pivot point O 4. Select point B 1 anywhere on link O 4 C 1 and locate B 2 so O 4 B 1= O 4 B 2 5. Connect B 1 to B 2 and extend. Select any location on this line for fixed pivot point O 2. 6. 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. Ken Youssefi D 1 C 2 C 1 O 2 A 2 B 1 O 4 7. D 2 B 2 O 2 A = B 1 B 2 / 2 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 Mechanical & Aerospace Engineering Dept. SJSU 17

Graphical Synthesis – Motion Generation Mechanism Two positions Grashof 4 -Bar mechanism with rocker as the output D 1 C 2 C 1 O 2 B 2 A 2 D 2 O 4 Ken Youssefi Mechanical & Aerospace Engineering Dept. SJSU 18

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

Graphical Synthesis – Motion Generation Mechanism Three positions with specified fixed pivot points, coupler as the output O’ 4 1. 2. 3. 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 C 2 D 1 D 3 C 1 C 3 O 2 O’ 4 O 4 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. Ken Youssefi Mechanical & Aerospace Engineering Dept. SJSU 20

Graphical Synthesis – Motion Generation Mechanism Three positions with specified fixed pivot points, coupler as the output 4. 5. 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. Ken Youssefi O” 4 C 2 D 1 O” 2 D 3 C 1 C 3 O” 2 O” 4 O’ 2 Mechanical & Aerospace Engineering Dept. SJSU O’ 4 O 4 21

Graphical Synthesis – Motion Generation Mechanism Three positions with specified fixed pivot points, coupler as the output O” 4 6. 7. O” 2 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. 8. O 2 G is link 2 and O 4 H is link 4. 9. Construct a link (3) containing GH and CD. O’ 4 C 2 D 1 O’ 2 C 1 H D 3 G O 2 C 3 O 4 10. Verify the solution by constructing the mechanism in three position Ken Youssefi D 2 Mechanical & Aerospace Engineering Dept. SJSU 22

Graphical Synthesis – Motion Generation Mechanism C 2 D 1 C 1 D 2 H D 3 G O 2 C 3 O 4 Ken Youssefi Mechanical & Aerospace Engineering Dept. SJSU 23

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

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 1. Draw the three desired points, P 1, P 2, and P 3. 2. Select the location of the fixed pivot points, O 2 and O 4. 3. Select the length of the crank O 2 A and the coupler side AP. P 2 P 3 4. With A 1 P 1 established, locate A 2 and A 3, A 1 P 1 = A 2 P 2 = A 3 P 3. 5. Measure angles α 1 (O 2 A 1 P 1), α 2 and α 3. Ken Youssefi P 1 A 1 α 1 A 2 α 3 A 3 O 2 Mechanical & Aerospace Engineering Dept. SJSU O 4 25

Graphical Synthesis – Path Generation Mechanism Three prescribed points. Locate moving pivot B by means of kinematic inversion. Fix coupler AP in O” 4 position 1 and rotate O 2 O 4. 6. Rotate A 1 O 2 about A 1 by (α 2 – α 1) to O’ 2. O’ 4 P 1 7. 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. 8. Rotate A 1 O 2 about A 1 by (α 3 – α 1) to O” 2. 9. 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. 10. Connect O 4 to O’ 4 and O’ 4 to O” 4 and draw the midnormals. Locate the intersection, B. P 2 P 3 A 1 B O” 2 O 4 O’ 2 11. Verify the mechanism. Ken Youssefi Mechanical & Aerospace Engineering Dept. SJSU 26

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 1. Select location of the fixed pivot point O 2. Rotate O 2 P 2 , in the opposite direction of motion, through angle α, P’ 2. 3. Rotate O 2 P 3 , in the opposite direction of motion, through angle β, P’ 3. P 1 P 2 P 3 P’ 3 A α β 4. Draw midnormals to P 1 P’ 2 and P 1 P’ 3. and locate the intersection A. 5. Measure O 2 A = link 2 and AP. 6. Follow the same procedure as before , for without timing, to locate the moving pivot point B. Ken Youssefi P’ 2 O 2 Note: timing takes away the free choices of the crank length and coupler length AP. Mechanical & Aerospace Engineering Dept. SJSU 27

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

Quick – Return Mechanism Consider the two toggle positions of a crank-rocker mechanism. C B 1 B 2 r 3– 4 3 2 A 1 O 4 O 2 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 Ken Youssefi B 2 C = r 2 +r 3 - (r 3 – r 2) = 2 r 2 Mechanical & Aerospace Engineering Dept. SJSU 29

Quick – Return Mechanism C B 1 B 2 α 2 A 2 4 3 A 1 O 2 180 – α, Return stroke O 4 Q = advance / Return = (180 + α) / (180 – α), Time Ratio Ken Youssefi Mechanical & Aerospace Engineering Dept. SJSU 30

Synthesis of a Quick – Return Mechanism Known or selected; Determine; r 1, r 2, r 3 Rocker angle, φ Rocker length, r 4 Time ratio, Q 1. Select the location for the fixed pivot point, O 4. 2. Draw the two toggle positions, knowing r 4 and φ. Calculate the angle α from known time ratio Q = (180 + α) / (180 – α) 3. 4. Construct an arbitrary line XX’ through point B 1. 5. Construct the line YY’ through point B 2 making an angle α with XX’. The intersection of XX’ and YY’ is the other fixed pivot, O 2 6. Ken Youssefi Y’ B 1 B 2 α O 2 X’ φ O 4 X Y Mechanical & Aerospace Engineering Dept. SJSU 31

Synthesis of a Quick – Return Mechanism C 7. Locate point C on YY’ so O 2 C = O 2 B 1. 8. Measure length B 2 C, Link 2 = r 2 = (B 2 C) /2 9. Y’ 2 r 2 Calculate the length of link 3, AB = r 3 = O 2 B 1 – r 2 B 2 X’ B A 1 O 2 B 1 O 4 X A A 2 O 4 O 2 r 2 Y 10. Verify the motion of the mechanism and check the minimum transmission angle. Ken Youssefi Mechanical & Aerospace Engineering Dept. SJSU 32