Question

100 mm А 75 mm С 100 mm X mm At the instant shown, bar BC has a constant angular velocity of 6.8 rad/s counter clockwise. Given x 182 mm. Using relative velocity and acceleration analysis, determine: (a) the angular velocity (magnitude and direction of the plate. rad/s Check (b) the velocity (magnitude) of point relative to the plate. m/s Check c) the angular acceleration (magnitude and direction of the plate. rad/s2 Check (d) the acceleration magnitude) of point relative to the plate, m/s2 X @ w

Answer 1

Giren ! ehoose a at the Solution 6.8 raolls. coordinate system with the origin o lowey left pin and the x aois parallel to the plate Surface. The Unit vector parallel AB is exs=1 The unit vector tangent to the slot at B is enab=j- The velocity of the pin in terms of the motion of be - WBC X 8Bico to is NB 2. k s WBC -182 75 0 WBC (-759 - 1827). 6.8(-751 - 1821) - 5101 - 1237.63 cmmis), -(i) The velocity of pin in teams of the plate is, j k VB - Vorel j + WAB XT BIA WAB 100 75 a - V Brel j + WAB (-75i+100i) (mm/s) ciju Equate the equation and Separate components to obtain -- 510 75WAB. WAB 6.8 radis - 1237-6 Vorel + loow AB. .: Vorel -1917.6) (mm/s) => 1.9176jfmis). WEB 6.8 radls.ccountem clockwise). of the aum BC is. the acceleration of the pin in teams XBC XYBIC W?BC NB1c. 0 - 46,24 (-1821+ 75;) dB 10 8416.68 i - 3468; (mm/s2).

the acceleration of the pin in teams of the plate AB 91B abrel +6.8 WABX UBrel ENAB + XAB X BIO WAB Blo docpand term by teum : abrel a 6 Brel CNAB a Brel @was - (voorlog CAB . Aliorel j 36771.89 1 (mm15), 6.8wABX Ubrl ENAB 88669.824 i comis2). 88.66 i (m/s2). LAB x Yв (о j k 0 XAB 100 75 0 LBA (-751+ 100j) immis), ..-W?AB (looit 75;) - 4624 1 - 3468 ; cmm/s2). collect teums and Sepauating them. for i: 8415.68 - 36771.89 t 88669.82 75LBA - 4624. - 3468 a orel + 100XBA 3468, solving! 29. Abrel. - 51000 mm 152 => -51.800 (mis?) (downucund) LAB 518 rad Is? 2 Cetork Ccounter clockwise ),