Theoryof Machines

Chapter (2)

Velocity,

Acceleration in

Mechanisms

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In the mechanism shorvn in Fig., OB rotates at a uniform rate of litrad-,s. Determine the

velocity and acceleration of D, the angular acceleration of AC; find aiso the torque requiredat the driving shaft through O if the slider D has a mass of I C I{g. a-nd the coefficieat offriction between the slider and the horizontal guides is 0. I OA = I -i0mm. OB : 75mm,AC:300 mm. CD - .250 mm

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In the mechanisrn shown in Fig., the fi>red bearings A and B are 30 mm apart. lle crank ACof length 60 mm rotates at a uniform speed of 60iev/min aboutA, and carries a slitjercwhich moves elong BC, causing cBDio rotate about B. BD is 45 mm and drives the head Ethrough the iink DE rvhich is 180 mm long- BE is perpendicular to BA. Find the velocity andacceleration of E when the angre BAC:45c; the ungurm accereration of cD; find arso thetorque required at the ciriving shaft through A if the ior"" opporing the rnotion of E is 320 N.

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A quick return rnechanism is illusrrateti in Irig l- The disrance bet$,een the fi;<eci centersis I 5 cm' rhe dri'ing crank Ac is r cir, ioug, Hn; i.. tr-,. srorted link w,irh BD = lthe connecting link -DE

rs l3 crn long. rhe slicier E has a irass ol 2 Kg Fcr theco,fisuration, (anvle FAC:145", arid A(l :orares at-l,lC r,r,-,,. clcck.,vise), ilncI -l-he

ratic ol'trre rirrre orcutting'to rhe trrne oIrerurn2 T'e 'elocity and are celerarion of ,n. slider ij

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:1.:-,.,'isc ;rbout O a'r a !-orlstartI li':c. i;ivci ai C and ile siidiig'.r'lrcir fJ.,\ makcs an anqlc 60o

S..a(L\in the incclt,j n;i!r show,n irr Fig l, the crar)k DC is trrrninq clockrvise at 100 r,p rn $/hen Lhemechanisnl is rn the posit;on shown' tlre cl3ckrvis^e rorquc appried to DC resisrs a verticar rorce o[ I00N l'' icrional eil-ects arrd deter nrinc, [or tlre qir.en posit;on oI the rrrechanisnt(a) ti''-. \r' 'j'-':' "rocit)' and acccieratio. oIEIr (b) the ,riign;,..,a. and direction of the [orce at DAB = 5 cn-i, BC: lB cm, CD = I crn

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end (hc d.i'ing lor-que *rll,i.h is..,;,,i,'",i ,;;r'.';."..,c a !-'si-sri.g i,rcc oi I00 N acting on

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