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a = tan-1 = 18.435° 300/ 02 Link length: 30° a 11.565° (input angle) ⚫ a = OA= 100 mm ⚫ c = CB = 200 mm b=AB 300 mm d=0C= √300² + 100² = 316.228 mm Then, calculate the following constants needed for finding the output angle 03 and 04. ⚫ K₁ = 3.1623 ⚫ K₂ = 1.5811 • K₁ = 1.5 Using the formula of 04.12. you obtain 04.1 = 83.4699° (rejected) ⚫ 04.2 = -93.9662° or 266.0338° (Accepted) A = -2.2316 B = -0.4010 C = 2.1335 And using the following equation, you obtain directly the angle of 03, b sin 03 = -a sin 0₂+c sin 04.2 => sin 03 = -a sin ₂+c sin 04.2 then, 03 = -47.0456° or 63 = 312.954° For the slider-crank mechanism CDE. Determine the input angle and link length 11 Angle: • 6 = 360 - (042 - a) = 360-(93.9662° -18.435°) = 284.4688° (input angle for the crank) Link length ⚫ a = CD = 200 mm, b=ED = 250 mm, c=-150 mm (offset) Then, calculate the output angle and distance sin(i)=-10.057° (rejected) 02=sin(in)+x=190.057° (Accepted) c) Velocity analysis For the pin jointed linkage (OABC), -100x2m Input velocity: W₂ = =-10.472 rad/s d = 296.129 mm (Accepted) then, the angular velocity of BCD (W4) is a cose₂ W₁ =WBCD = cos W₂ = 6.2772 rad/s The angular velocity (w) is used as input for slider crank CDE => (w₂ = w₁ = 6.2772 rad/s). For the slider crank linkage (CDE), The angular velocity of ED is w₁ = WED= a cose₂ b cose w2 -1.2743 rad/s and the velocity of the slider Eis daw sino₂+ bw'sin03 = -0.2 x 6.27 x sin-75° + 0.25 x (-1.27) x sin 190° = -1.271 m/s

a = tan-1 = 18.435° 300/ 02 Link length: 30° a 11.565° (input angle) ⚫ a = OA= 100 mm ⚫ c = CB = 200 mm b=AB 300 mm d=0C= √300² + 100² = 316.228 mm Then, calculate the following constants needed for finding the output angle 03 and 04. ⚫ K₁ = 3.1623 ⚫ K₂ = 1.5811 • K₁ = 1.5 Using the formula of 04.12. you obtain 04.1 = 83.4699° (rejected) ⚫ 04.2 = -93.9662° or 266.0338° (Accepted) A = -2.2316 B = -0.4010 C = 2.1335 And using the following equation, you obtain directly the angle of 03, b sin 03 = -a sin 0₂+c sin 04.2 => sin 03 = -a sin ₂+c sin 04.2 then, 03 = -47.0456° or 63 = 312.954° For the slider-crank mechanism CDE. Determine the input angle and link length 11 Angle: • 6 = 360 - (042 - a) = 360-(93.9662° -18.435°) = 284.4688° (input angle for the crank) Link length ⚫ a = CD = 200 mm, b=ED = 250 mm, c=-150 mm (offset) Then, calculate the output angle and distance sin(i)=-10.057° (rejected) 02=sin(in)+x=190.057° (Accepted) c) Velocity analysis For the pin jointed linkage (OABC), -100x2m Input velocity: W₂ = =-10.472 rad/s d = 296.129 mm (Accepted) then, the angular velocity of BCD (W4) is a cose₂ W₁ =WBCD = cos W₂ = 6.2772 rad/s The angular velocity (w) is used as input for slider crank CDE => (w₂ = w₁ = 6.2772 rad/s). For the slider crank linkage (CDE), The angular velocity of ED is w₁ = WED= a cose₂ b cose w2 -1.2743 rad/s and the velocity of the slider Eis daw sino₂+ bw'sin03 = -0.2 x 6.27 x sin-75° + 0.25 x (-1.27) x sin 190° = -1.271 m/s

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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I want to explain where the numbers 6.2772 and -1.274 come from(are marked in red) just calculation for the two nb
a = tan-1 = 18.435° 300/ 02 Link length: 30° a 11.565° (input angle) ⚫ a = OA= 100 mm ⚫ c = CB = 200 mm b=AB 300 mm d=0C= √300² + 100² = 316.228 mm Then, calculate the following constants needed for finding the output angle 03 and 04. ⚫ K₁ = 3.1623 ⚫ K₂ = 1.5811 • K₁ = 1.5 Using the formula of 04.12. you obtain 04.1 = 83.4699° (rejected) ⚫ 04.2 = -93.9662° or 266.0338° (Accepted) A = -2.2316 B = -0.4010 C = 2.1335 And using the following equation, you obtain directly the angle of 03, b sin 03 = -a sin 0₂+c sin 04.2 => sin 03 = -a sin ₂+c sin 04.2 then, 03 = -47.0456° or 63 = 312.954° For the slider-crank mechanism CDE. Determine the input angle and link length 11 Angle: • 6 = 360 - (042 - a) = 360-(93.9662° -18.435°) = 284.4688° (input angle for the crank) Link length ⚫ a = CD = 200 mm, b=ED = 250 mm, c=-150 mm (offset) Then, calculate the output angle and distance sin(i)=-10.057° (rejected) 02=sin(in)+x=190.057° (Accepted) c) Velocity analysis For the pin jointed linkage (OABC), -100x2m Input velocity: W₂ = =-10.472 rad/s d = 296.129 mm (Accepted) then, the angular velocity of BCD (W4) is a cose₂ W₁ =WBCD = cos W₂ = 6.2772 rad/s The angular velocity (w) is used as input for slider crank CDE => (w₂ = w₁ = 6.2772 rad/s). For the slider crank linkage (CDE), The angular velocity of ED is w₁ = WED= a cose₂ b cose w2 -1.2743 rad/s and the velocity of the slider Eis daw sino₂+ bw'sin03 = -0.2 x 6.27 x sin-75° + 0.25 x (-1.27) x sin 190° = -1.271 m/s
Transcribed Image Text:a = tan-1 = 18.435° 300/ 02 Link length: 30° a 11.565° (input angle) ⚫ a = OA= 100 mm ⚫ c = CB = 200 mm b=AB 300 mm d=0C= √300² + 100² = 316.228 mm Then, calculate the following constants needed for finding the output angle 03 and 04. ⚫ K₁ = 3.1623 ⚫ K₂ = 1.5811 • K₁ = 1.5 Using the formula of 04.12. you obtain 04.1 = 83.4699° (rejected) ⚫ 04.2 = -93.9662° or 266.0338° (Accepted) A = -2.2316 B = -0.4010 C = 2.1335 And using the following equation, you obtain directly the angle of 03, b sin 03 = -a sin 0₂+c sin 04.2 => sin 03 = -a sin ₂+c sin 04.2 then, 03 = -47.0456° or 63 = 312.954° For the slider-crank mechanism CDE. Determine the input angle and link length 11 Angle: • 6 = 360 - (042 - a) = 360-(93.9662° -18.435°) = 284.4688° (input angle for the crank) Link length ⚫ a = CD = 200 mm, b=ED = 250 mm, c=-150 mm (offset) Then, calculate the output angle and distance sin(i)=-10.057° (rejected) 02=sin(in)+x=190.057° (Accepted) c) Velocity analysis For the pin jointed linkage (OABC), -100x2m Input velocity: W₂ = =-10.472 rad/s d = 296.129 mm (Accepted) then, the angular velocity of BCD (W4) is a cose₂ W₁ =WBCD = cos W₂ = 6.2772 rad/s The angular velocity (w) is used as input for slider crank CDE => (w₂ = w₁ = 6.2772 rad/s). For the slider crank linkage (CDE), The angular velocity of ED is w₁ = WED= a cose₂ b cose w2 -1.2743 rad/s and the velocity of the slider Eis daw sino₂+ bw'sin03 = -0.2 x 6.27 x sin-75° + 0.25 x (-1.27) x sin 190° = -1.271 m/s
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