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MIT2_007s09_sol_exam01 - MIT OpenCourseWare...

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MIT OpenCourseWare http://ocw.mit.edu 2.007 Design and Manufacturing I Spring 2009 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms .
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Page 1 of 8 2.007 Design and Manufacturing I Draft Exam on Drawing, CAD, Motors, Pneumatics, and Mechanisms You have 1.5 hours to answer the following 9 questions. Please show your work to the extent possible given the allotted time. Point allocations (out of 100 total) are listed for each question. 1. (10 points) What tension, T , must be applied to raise the 4 N weight at a constant rate? pulley 10 cm Going up! First, I deal with the right side which is a capstan and NOT a pulley Going down! 5N By the capstan equation F between =5N*e^(- * )=5N*e^(-0.3* /2)=3.12N NOTE the sign in the exponent. It is nagative because the 5N weight is going down and the frictional forces oppose the motion resulting in a lower tensile force in the rope in between the capstan and the pulley than was applied by gravity. Next, I deal with the left side which is a pulley and NOT a capstan Sum of moments about the pivot SM=4N*10cm-F between *10cm-T*5cm=0 T=1.76N 4N F between F between T
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Page 2 of 8 2. (5 points) How many degrees of freedom does this mechanism possess? 4 Bodies each with 3 DOF = 12 DOF 5 full pin joints eacg remove 2 DOF = -10 DOF Leaving 2 DOF of the mechanism One of the DOF is associated with the parallelogram linkage Comprised of the base, two links extending from the base, and the triangular piece near the top of the lamp. The other degree of freedom is associated with the lamp head itself which Is free to rotate about its pivot. Some students thought perhps some of the elements of the mechanism were Redundant, but none of them are.
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