Question

Please explain how to solve using vector algebra and explain why V_AB = W_AB x BA and not V_AB = W_AB x AB.

P 5/82 TO 900 mm 300 mm In the design of a produce-processing plant, roller trays of produce are to be oscillated under water spray by the action of the connecting link AB and crank OB. For the instant when e = 15°, the an- gular velocity of AB is 0.086 rad/s clockwise. Find the corresponding angular velocity of the crank and the velocity va of the tray. Solve the relative- velocity equation by either vector algebra or vector geometry.

Answer 1

VVVY = 30mm comm =15 e-gcomm 75 a 9 da et WAB = at K KAH is de do We do From geometry, we can write and dea BC = AB sin ß = OB sind e sing = r sind 0.086 rad/s gov sin 8= 300 Sin 750 / ((w) sin B=0.3215 WAB= -0,086 » [B= 18.78° 1 rades Differentiating equation wort. time (t)! e of (sing) = de a (sind) e cosß dp = r cosa da 900 cos (18.78) WAR = 300 cos 750 (-w) We = -10,974 WAB We = - 10.974 (- 0.086) rad/s Wc = 0.9437 rad/s | (cow).

Again from geometry , we can write. NA = (2+2) - (a cosa + 2 copp) de la no-as cosa) + l da Comb)} = - 2(-samned) se te (sup) deny A = reind dat te simpatte A = & sin a (We) t l auß (CAR) VAE - 0.3 S 750X0.9437 +0.9 Sm(18.78') (-0.08) VA= -0.2984 m/sec) Negative sign in relocity says that the velocity is in negative a direction in the given (assumed) co-ordinate system. Now, to - whox BA radial distance Velocity of Angular of A wirit B. point & wirtB velocity Calways points away (Hore B is centre) of line AB toward centre, since we are looking to velocity of A wint B, the radial vector will be pointing outward away from Centre Bele. T Taking magnitude VA = Wall BA sim 90° Since Angle ble way and B Ã is go. VAB = 0.086 80.941=0.0774 mis Relative velocity of A Wort B is 0.0774 mes to the direction " from normal to link AB.