Question

*16–52. The crank AB has a constant angular velocity o. Determine the velocity and acceleration of the slider at C as a function of 0. Suggestion: Use the x coordinate to express the motion of C and the o coordinate for CB. x = 0 when 0 = 0° Prob. 16-52

Answer 1

soli B e a Top AB represent the crank and BC is the connecting rod of sliden erank mechanism used in engine. Point B denotes the position of piston When crank has rofected through angled from onder dead centre. At this Instant a denotes the distance of piston from crankshaft centre A. Let I-length of connecting god between centre r-radius of crank Ø -engle made by commecting red with lined stroke at e instant maraftoob length of connecting ood to radius ofesankaly S-Stooke of engine=28 from Figure, a=lcoso troso o esing- sino Sing Sino sino - Cost = (1-2 single = (1- Sin2012 from ego, and becomes x=l(1-28 in 202 + roso Lif( isimzo+colo = cose ++ (1-1281170) 2 & -c080 +1 -1 sin 2018 in 0-1 sin

Sno smo - elemente, (0920 = 104510 So, sin "O (60 gr #Ceket avis)_4 (8607229) 767 Sinyo = Cosuo_60920 +34 similarly, simbo = -52.0869 +26346 - 15, 49320 + 6 Pulting these value in equation , we get -6-osios g+680+ 0,30%y that -cosociation ) +0360 lasistow). Differentiating equalion wot time, weged $=0[sino-2sinnodu se s +usinyola ) Again, -tsinfo (tzt.)+. Differentiating eq wort time, weget - =84680 +A 26820-Ay co849 +48 60860-...) tö (sino+Azsino - Ay sinu Where ó = Angular velocity of crank (0) 6 = Angular Acceleration of crank (2) A2 = 1 + 2% + 15 16 Ay = 1² + 3 1 + Ant