Question

The mechanism in the figure is the slider-crank. Express the angular velocity WAB and angular acceleration & AB of the connecting rod AB in terms of the crank angle 0 for a given constant crank speed wo. Take WAB and QAB to be positive counterclockwise. Assume that r=0.2 m, 1=0.7 m, w, = 0.3 rad/s. Plot the position and velocity of point A with respect to . Using the parameters in part ii, plot was and AB with respect to 0. Find the maximum and minimum values of War and a AB 00

Answer 1

Given: 21 . letn 105.8 lousons from diagrain Sinø = sing cosø: Vn2-Sinzo :: o displacement function is written as x? OnCiscoso) +oren-Vo?-5w0) 0 -2 velocity function is calculated ses on diffrentialingi in sinzo 7-0 »Vs = Yes [sino + mnt-size : essor nosti zn -> Vs: reos | sin @ e Sipro for o acceleration function of slicker is calculated as 3) as a crocose + cosso a sinzo 7. Une sine ufoz sino } possi. as: row[coso e come] OSO

no ;) to find the anquloos acceleralion & angulos relocity of AB - connecting rod is as followos 3.co.k.t e sind = q sing 1 sing = sing - sing = sino : crisfeventing wirot + (sin ) = 1 storey >> cosøy deseas cosas 23. WABB Wolose coso ncoso 2) WersŻ Wo coso ie Wycoso DA Voz sin? o 20 I AB. Vn²-sino 2) angular acceleration is calculatedag xe dwab. diWAB do dobre AB ch. -w? nif) sino To? sino)? 1.731..

i) fet Y=0.2m; b=0.7m, W=0.3 rad/sec >> xin02=3.5 ; 20.30.3 radis 2) XS S 0.2(l-coso) +0oz (35- 3:52 Ng z o.14 0.3ſsinot Sinza a Vs: 0.06 I sino + siaze » as = 0.26637f cose + costa] >> ag = 0.018 [cose + costa] -> plots of velocits & position is as follows OS25 2) C 3-5 Joio position diagrams Unax = 0.06274 mis 0:76º relocits II Curve amar -> alleleration cuerlies uzo 'amin Velocity nay cur coso = -cosze as zo. 3 .T 2:0) 0:769

WAB Mar GWAB angular velocits ploof connait rod at 0:01 0=180° >> wrote: sus : i Max max (-Twar= 0.0857 rad/s priare der=o. w at o=90° [Wer=o] min I derzmas angular acceleratsion 09290° a) - . -ooz? . . er = mal :277 der = 0.0257 racl 1524 1 mar analo 0% 180° - to open to radis?