Question

Problem 3: Crank arm OB rotates about point with a constant clockwise angular velocity of 990 rpm. TE connecting link AB drives the piston A. Ifr = 5 inches and I = 12 inches, determine the following when 0 = 60°: (a) the angular velocity and the angular acceleration of the connecting link. (6) the velocity and the acceleration of the piston.

please explain your work

Answer 1

G - wo B T Los COB rotates about point o with woga 990rpm (clockwise) N=5inches & l= 12 inches, O = 60 angular acceleration of the connecting rod, = a) angular relocity of & CA rsino = I sinB = BD sinp = sino sino differentiating both sides cosp d e cose Cosp. WAB = Coso x WoB WAB = cos o x WOB Sin²ßt cos?p=1 Cosp -(i-Sinºp ) n cosp sinß= sino XWX - COAB W coso . (1-sing) e (1-sipo y la = w.coso.ro po ?sidog's AB (connecting rod) = woso (n? Sio?0) 2 = 2/7 = 12 = 2-4 490% cos Go - 990x V2 495 (WAR)= 221-15 rpg V (1/2) = (sin 68 5.76 -0.75 √5.00 (clockwise) Los = d (WAB) (WAB do d (wcaso dondt - do 2 in ) xw w Copen)'=sino wo) – w cosOxy (0?_S1030) -15h06aso - nesino a tao sino (o sintol + cocoso Chasin 30jts sino caso 12 smºo rev/min 2 & -w²sino. | o²sino caso 2 sin 2021 mesmo LAB = wing tsin 20) - cos wasino [²1] - (22 sin 02 (masing) 3/2 – (1990) Sinbo (2-4)= 1) - 920900 W/2) X4.56 404024753 - 36025 (2.4) - sinh66) (976 – 0.75)3 = 360289-563 LAB LAB - = 0.21399 revo Ben min?

*) piston velocity and acceleration. de planet e = v(C-60)+ a sindo Chinelily taken) [st Oy the 2 show.so- ( 10 4 Si, 0) 2n Si020 , da da do at - do dt N. sw(smo+ Sinzo 2n Sin2o 2n Sin Up = ro (Sing A SM20 ) = 5x 999 (sin båt sin 126 ) = 49500-266+0.866 1 - 4998 (0.36670.12) - 4956x1.046 ap - date de velocity station for Piste 15 8 7 8 8.7 inch laten cox do te vas vw (cos 0 + 8670). a piston ou ( casot casso Qp = 5x920x970 ( cassó + Cos120) = 21900307 (0.5+ (0:) = 4990005440-16.00 = 4900800 (0.5-0.20033 Jap= 1455.439.49 fach/amina q=1489312-5 inchy a acceleration of piston angular angular velocity of connecting rod wc = WARZ 221.15 rpm acceleration of connecting rod L=LAB = 360-289 x103 revo velocity of piston up=5179.87 inch /min acceleration of piston ap= 1429.3125 X109 inch) mine min min
I have derived the formula for all. If any calculation error is there please ignore.