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30b. Joint Kinematical Description-Mechanism Soln

30b. Joint Kinematical Description-Mechanism Soln - ME 270...

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Unformatted text preview: ME 270 —- Basic Mechanics l — Group Quiz Your Name: Group Members: 1) Date: ' Period: 2) 3) 4) Given: Arm AB rotates clockwise at the constant rate of 5 rad/s. Find: Determine the velocity and acceleration of pin P when (3 = 90° in cylindrical coordinates. Solution: Step 4 5 = REE + Rq55¢ = vé", 2 a x (R _ R¢2)ER + (qu + 2qu. m :35, + ”$22,, Step 5 Matching the two kinematical descriptions requires expressions for t] unit vectors of one description with respect to the other. Thus "(5, = —-cos GER - sin 95¢ = “0-5051: - 0.866023}, 5,, = “sin 9203K + cos 65¢, == «0.8660221R + 0.5064, Substitution of ‘67,, R, and 4) into the velocity equations, followed by equating 1i} components, yields '5 = R5,. + 6.928(-— 5m = zip-0.5022}. — 0866054,) "éR component: R = —0.50v "e11, component: —— 34.64 = -—0.86600 e=mmn, R=mmmn B = -20"éR -— 34.654, = 405, in./s ' 4 The same procedure is now applied to the acceleration. The results for v and , as well as the other parameters, are substituted into the acceleration formulas. Th 5 = [R — 6.928(w5)2]ER + [0 + 2(—20)(—5)]a¢ (40)2 8 = 13(——0.50€_R - 0.8660§¢) + (—-O.8660ER + 0.5054,) 2",. component: it —— 173.20 a: $0.51) — 173.20 54, component: 200 = ——0.866013 + 100 :3 = —115.47 in./sz, R = 57.74 in./s2 it" =2 —115.5é"R + 200?}, = ——115.5E, + 2002",, in./S2 4 ...
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