Question

Knowing that at the instant shown ter AB has a constant angular velocity of 4 radis clockwise, determine the angular acceleration of bar BD and bar DE (Round the final answers to two decimal places 175 B Th15 The angular acceleration of bat eos The angular acceperation of har DES rady Clockwise radis? clockwise

Answer 1

The angular acceleration of bar BD and DE is calculated using the angular velocities of bar BD and DE .

100 mm 175mm A 200mm A TX(0) CL Solution: Given: Angular velocity of bar AB, WAB = 4 radls. (CW) - 4K To calculate angular Tomin D acceleration of bar BD and DE, we have to calculate angular velocities of bar Bo P DE first. Velocity of B with respect to A (Bar AB), USA - JA ve-o = (-4E) x (-0.175?) { v=0} Y = (0.7m/s) ; Now, Velocity of D with respect to B (B0BD), Joe - Joue WBOX roe WBD - Wook and ROB WABY IBA -0.2 so, Vot ū + Web X 8DB 0,75 + (WBD Å ) x (0.25) to = 0.7 +0.2 Wao i O velocity of Dworto E Voe u ve u = 0 and Wor work WOE Х ProE A

IDE we get, j-components, position vector of o with respect to E (-0.275 ? +0.0757) = (WOBŘx ( - 6.2758 +0.0757) -0.275 WDE 0.075 UDE Equating equation and 0.7 = – 0.2750DE CODE = -2.545 hadis T (CW) ¡- components = – 0.075 UDE - 0.075 (-2.545) WBD = 0.954 rad)s The total acceleration comprises of tangential and radial acceleration, a point, So, Accelerations of s with respet to A, (BOY AB) + ayardal 0.2 WBD 0.2 WBD of BRA - Iyong. W ABRBA az - DA LAB X IBA since, A=0 TAB OXEBA B ((.) ² (-0.1758) 2.8 m/s2 î Siasi lasly, Acceleration of D with sepat to Be (Don Bo), a oe arong. 7 a radial & BD XRDB 2 IDB BD ao - 2-8 i EBDK) X(-0.2)) - (0.954) €0.27)

+0.2 BD 8 (LDEX.roe a = 28 +0.182 (2 8 + 0.2&BD) ? + 0.1823 Acceleration of D with respect to E, (Bar DE), Ditang + radial - worthor IDE ao-a Since, a and Rof a - 0 = a=0 Loe- & DE (-0.275 +0 6. 0757) = (DER DX(-0.27570-0459) - (-2.545 1-0-2752 +0.0758) = -0.275 4DE 5- 60754plt 1.781 - 0.4053 a = (-0.075 &0E +1-78) i -(0.27500E to. 485 +0.485); _4 Equating equation ③ & 6 get, j-components, 0.182= -10.275_DE +0:485) ODE = -2.425 radys 1-components 2.8 to. 2280 -0.075 IDE + 1.78 2.8 +0.2 BD = -0.075(-2.495) +1-78 OBD = -4.19 rad's Solving, Angular Acceleration of bar BD, RBD = 4,19 %ads? clockwise Acceleration of bar DE, XE = 2.425 ralls Clockwise Angular