Mid-term Part II Solutions

Mid-term Part II Solutions - Mid-Term L62A Spring ZOLL PART...

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Mid-Term L62A Spring ZOLL PART ll- solve the following problems as instructed. open text book and open lecture notes. (35 points total) Problem 1: The figure below shows a mechanism used in production line to turn overcartons. ThedriverarmisL5in. longand,attheinstantshown,itisinclinedat60oasshown. The follower arm is 16 in. long. The distance between the pins on the carriage is 7 in, and pins are currently in verticalalignment. Cnrriarc L + \. ..- '7tt 1 'h \ I I ii o 15" lfi'' Follower arm \: l' 't- I ljrr\''ur - \, an]l \ NOT TO SCALE Using complex algebra method and applying the conventions covered in the class to the mechanism shown in the current orientation, solve for the rotational position of the follower arm and the distance between the pin joints that ground the driver and the follower arms in the following steps: (a) (4 points) ln the space below, draw the R vectors corresponding to the configuration in the figure above. (Vectors need not beto exactscale). Clearly indicate rotationalangles (0,s) following the convention discussed in class. r! \..,-,; . - V g_Oa Rv+:ci;t-,*tt,?"irlii j '\\ t';rb #, 5tl A ,,Y+ 2fr I Fln "6
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w[,\r,il* (c) (b) (3 points) Write the loop closure equation first in vector form and then in complex polar form. Leave the equations in the generalform in terms of 0r,02,03 and 0a and lengths t1, t2,r3and ra. E*+ila'=Fo* + K"p ,f'rt'*r'fiii:i *4 R=*Fu'= -Fu-Ht li' :1i.:,r1"ri;r Pl,}fii' -} frgio' * q€Je+ = \",g\'r+,.f,* eleq t0 i0 i j giir 6, (10 points) Separate out the real and imaginary parts. Now substitute the actual values of knownrotationalanglesandlengthsandsolvefortheunknowns,i.e.,rotationalpositionofthe
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Mid-term Part II Solutions - Mid-Term L62A Spring ZOLL PART...

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