Question

3.Rigid Body Systems. Acceleration: Consider the following diagram that shows three rigid-bodies simply connected by pins. Body AB is rotating about the pin at A and body C is confined to the horizontal slot. At the particular moment show body AB has a constant angular acceleration, au 0.8 rad/s', and an angular velocity. CAB - 4.0 rad/s. It is also known that the speed of pin B is, V8 - 12 m/s, the angular speed of body BC is OBC 1.789 rad/s, and the speed of body C is Vc= 8.683 m/s Determine the acceleration of pin B, äg, the angular acceleration of body BC, & pc, and the acceleration of pin C, ac *) AB, QAR 3 m 6 m 300 A

Answer 1

solution Given 30 AB iz 1 6 = WAB ö = LAB I B = WBC j = V 4 - - - - - - - WAB: 4 radlls LAB = 0.8 rady Was Vg= 12M/s A WBC = 1.789 rad/s Ve = 8.683m/s sms ZX x = 3 cose Z=3sine - 3 caso de - at = 38-node-0 Vax - 3x-Sinox4 DVBx = -12 sine - 3 Los Ox4 | Vay = 12 2039 differentiating for threr BER d2 x 12 = -3 ( cose do y los + sine do ) +968 -3 (cosex 42 + sinox0.80) asx --3(18 cose +0.80 sino) differentiating equ ☺ La 34 sine x cose

o aby = 3(-singx4² + cos oxo-so) =31-165in +0.80 LOS 9) .: Aueleration of pin'B' az = J ază + ac} =) 98=3* V ( 16 cos 0 +0.80 Sino)?+ (-16518 0+0.81019 = 33 ✓ 16 cos²o+sin² of +0.80²/sin²o+ws²) = 3x 16.02 = 148.06 m/s2/ Angular acceleration of bodly Bl BB'= 3 sing = 6 sing differentiating both sides worth 3 3 we de 6 cos de 2 3 cosex4 = 6 LOSBX 1.789 => Cose = 0.8945 LOSß differentiating further equo l-simox do y d y + ose do 2) = 2x 8-simBX da trosby off dez]

1-sinox 4?+ cosex 0.80 ) = 2x1 sinßx1.789?+ cosbx dip dt? 71-16 sin 58.25 +0.50x cos( 58.25) Tye 6 COSB - -6 Sava -8.68:-6 Simpr 1.789 .2117892 sin 53.97 +Cos S3 22 x 2 → dop=-15.6/ vad/s2 ARC = T15.61 rad/s27 And =B = 53.97 462 .: loso = 0.89952ses 0 = 58.25° | Acceleration of pin'c' () H2 6 wsp - - 6 Sim x R Bagais differentiating wat 'l ☺ = -6( cose red rø + Simßx B) -61 COS 53.97 x 1.789% + sin 53.97 8-15.00) = 64. 44 m/s2 .:: Aca K+ -311660558.25 +0.80 5ın 58. 25) +64.44 . .-24.71 +. 64. 4 4 2 / 39.66 m/s2) And