PROBLEM 4-18b Statement: Scale Figure P4-5b to obtain dimensions for the problem. Find and plot the...

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PROBLEM 4-18b Statement: Scale Figure P4-5b to obtain dimensions for the problem. Find and plot the angular position of links BC and CD and the transmission angle as a function of the angle of wheel Was it rotates through one revolution. Given: Measured link lengths: Wheel W (AB) Rocker (CD) Two argument inverse tangent a = 10.7-mm c = 19.2 mm Coupler (BC) Ground link (AD) b=24.5-mm d=41.8-mm atan2 (x, y) return 0.5x if x=0 2 return atan if x>0 B4 | 3 W Solution: atan + otherwise See Figure P4-5b and Mathcad file P0418b. 1. Check the Grashof condition of the linkage. Condition( S, L,P,Q) = |SLS+L PQ-P+Q return "Grashof" if SL sPQ return "non-Grashof" otherwise Condition(a, d,b,c) = "non-Grashof" D 2. Using the geometry defined in Figure 3-1a in the text, determine the wheel angles (relative to the line AD) at which links 3 and 4 are in toggle. -acos 21 [a+d (b+c)] 2.a.d 822-360-deg-8 21 21 = 93.073-deg 822 = 266.927 .deg 3. Define one cycle of the input crank: 82-93-deg,-91 deg. 93-deg 4. Use equations 4.8a and 4.10 to calculate 4 as a function of (for the crossed circuit). a K = K =3.9065 d K2 K = 2.1771 A(2):=cos(82)-K1-K2. cos(2)+K 3 B(02)=-2-sin(02) 2.(atan2 a = b +c +d K3= (2-a-c) K3=3.9674 C(2)=1-(2+1) cos(82)+K3 41(2):-2 atan2 (2-A(82)--B (02) + B(e 2)-4-A(82) C(02)) 2nd Edition, 1999 DESIGN OF MACHINERY 5. SOLUTION MANUAL 4-18b-2 If the calculated value of 04 is greater than 2, subtract 2 from it. If it is negative, make it positive. 42 (2)if( 41 (02)>2.8 41(2)-2-0 41(2)) 84( 2)if( 42(2) <0,8 42 (82) + 2,8 42 (62)) 6. Determine the values of the constants needed for finding 0; from equations 4.11b and 4.12. K4: K5: (2-a-b) K 4=1.7061 K5=-3.9926 De 2) = cos(2)-K+K 4.cos (62)+K5 E(2):=-2.sin(2) F(82) K1+(K4-1).cos(82)+K5 7. Use equation 4.13 to find values of 63 for the crossed circuit. 8. 8 31 (82) :=-2-(aran2(2-D(82).-E(82) + F(82)-4D82F92))) If the calculated value of 8, is greater than 2, subtract 2 from it. If it is negative, make it positive. 832(02)if( 31 (2)>2-0 31 (2)-2,0 31 (2)) 83(02) 32 (2) <0, 32(82)-2-1.8 32(82)) 9. Plote, and as functions of the crank angle 02 (measured from the ground link). 400 300 32) deg 200 deg 100 Angular Displacement of Coupler & Rocker 100 -75 -50 -25 0 25 50 75 100 2 deg Crank angle, deg ( ) = ( )- 11 10. Use equations 4.28 to find the transmission angle. Tran(2) 03 (2)-04(02) | 2nd Edition, 1999 DESIGN OF MACHINERY Trans (2): if(Tran (2)>-Tran (2) | Tran ( 2)) 11. Plot the transmission angle. SOLUTION MANUAL 4-18b-3 100 80 Trans (e deg Bap ay uoss 60 60 40 20 20 100 Transmission Angle deg Wheel angle, deg le 100 PROBLEM 4-18b Statement: Scale Figure P4-5b to obtain dimensions for the problem. Find and plot the angular position of links BC and CD and the transmission angle as a function of the angle of wheel Was it rotates through one revolution. Given: Measured link lengths: Wheel W (AB) Rocker (CD) Two argument inverse tangent a = 10.7-mm c = 19.2 mm Coupler (BC) Ground link (AD) b=24.5-mm d=41.8-mm atan2 (x, y) return 0.5x if x=0 2 return atan if x>0 B4 | 3 W Solution: atan + otherwise See Figure P4-5b and Mathcad file P0418b. 1. Check the Grashof condition of the linkage. Condition( S, L,P,Q) = |SLS+L PQ-P+Q return "Grashof" if SL sPQ return "non-Grashof" otherwise Condition(a, d,b,c) = "non-Grashof" D 2. Using the geometry defined in Figure 3-1a in the text, determine the wheel angles (relative to the line AD) at which links 3 and 4 are in toggle. -acos 21 [a+d (b+c)] 2.a.d 822-360-deg-8 21 21 = 93.073-deg 822 = 266.927 .deg 3. Define one cycle of the input crank: 82-93-deg,-91 deg. 93-deg 4. Use equations 4.8a and 4.10 to calculate 4 as a function of (for the crossed circuit). a K = K =3.9065 d K2 K = 2.1771 A(2):=cos(82)-K1-K2. cos(2)+K 3 B(02)=-2-sin(02) 2.(atan2 a = b +c +d K3= (2-a-c) K3=3.9674 C(2)=1-(2+1) cos(82)+K3 41(2):-2 atan2 (2-A(82)--B (02) + B(e 2)-4-A(82) C(02)) 2nd Edition, 1999 DESIGN OF MACHINERY 5. SOLUTION MANUAL 4-18b-2 If the calculated value of 04 is greater than 2, subtract 2 from it. If it is negative, make it positive. 42 (2)if( 41 (02)>2.8 41(2)-2-0 41(2)) 84( 2)if( 42(2) <0,8 42 (82) + 2,8 42 (62)) 6. Determine the values of the constants needed for finding 0; from equations 4.11b and 4.12. K4: K5: (2-a-b) K 4=1.7061 K5=-3.9926 De 2) = cos(2)-K+K 4.cos (62)+K5 E(2):=-2.sin(2) F(82) K1+(K4-1).cos(82)+K5 7. Use equation 4.13 to find values of 63 for the crossed circuit. 8. 8 31 (82) :=-2-(aran2(2-D(82).-E(82) + F(82)-4D82F92))) If the calculated value of 8, is greater than 2, subtract 2 from it. If it is negative, make it positive. 832(02)if( 31 (2)>2-0 31 (2)-2,0 31 (2)) 83(02) 32 (2) <0, 32(82)-2-1.8 32(82)) 9. Plote, and as functions of the crank angle 02 (measured from the ground link). 400 300 32) deg 200 deg 100 Angular Displacement of Coupler & Rocker 100 -75 -50 -25 0 25 50 75 100 2 deg Crank angle, deg ( ) = ( )- 11 10. Use equations 4.28 to find the transmission angle. Tran(2) 03 (2)-04(02) | 2nd Edition, 1999 DESIGN OF MACHINERY Trans (2): if(Tran (2)>-Tran (2) | Tran ( 2)) 11. Plot the transmission angle. SOLUTION MANUAL 4-18b-3 100 80 Trans (e deg Bap ay uoss 60 60 40 20 20 100 Transmission Angle deg Wheel angle, deg le 100