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Exam1-2007-solutions

Exam1-2007-solutions - ME3212 Mechanisms Exam 1 Fall 2007...

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Unformatted text preview: ME3212: Mechanisms Exam 1: Fall 2007 all/($1043 Name 1. (20 pts) Calculate the number of degrees of freedom for each of the following mechanisms. Number the links on each mechanism and indicate the degrees of freedom of each joint with a “(1)” °“‘<2>-”dojc; m: 36w) 15,437. Page 1 of4 ME3212: Mechanisms Exam 1: Fall 2007 6a ‘om Name 2. (25 pts) Consider the mechanism with the configuration shown below and the given dimensions. a1 =35 mm a2 = 25 mm a3 = 10 mm a4 = 40 mm as = 45 mm (1) = 30 deg 92 = 100 deg 63 = 13.4 deg 64 = 140.8 deg 51 (02 = 20 rad/s ccw 033 = -4l.12 rad/s cw (D4 = 15.7 rad/s ccw a) Determine whether or not link 02A can make a complete revolution with respect to the other links. mo/ be COVWSL an Jr‘rz 7 013 l‘c‘ui 'fo23' > IO H10 b)What kind of mechanisms is this? X double rocker, double crank, crank-rocker c) Write down expressions for the x and y positions of point P in the x—y system shown above. 7<> PX: Ot‘ + POH Cog <94~Y3 W») ': POL‘ sin (@q-‘VU _ 5929mm WW POL : .. 22, I C) 7‘ : 77.3% { Oqtivétuil —a;z> _ a a C05 ( p 1PM "-1 d) Write expressions for the x and y components of :Ielocity of point P. VYP:hP0H SM (94 “‘0 9L, : “Ziqwm/j Vgp: my, Cos (éq away : 21! MW; e) Determine the magnitude and direction of the velocity vector of point P. K ME3212: Mechanisms Exam 1: Fall 2007 j 3. (30 pts) Consider the multi—loop mechanism shown below. A a) Write the loop closure equations. w)" ,0“ + 6t: C03 (.963 ’ r “05 (a!) :0 50 -M +61: smtféé) - F sm(92>/ :0 “‘0 '14) 4: 001,92) 1- 013 “’5 (e3) ‘4‘! C03 (6% ~ 9’5 N ~47.) 42 swiiéel ~93 g xlmfjéj) '”‘ 441 3171(6115 ‘0 b) Identify the unknown variables and the number of degrees of freedom. V‘) 9” @214 9’3, 69% / gawk) Liam 33> c) Can link 02A or link 04B make a complete revolution with respect to the other links? , / W) I 6 he épflg 6mg hag flaw / 20 +70 ft/ZOMO mot angflxwfl \ r d) What is the maximum value of r? (Hint: this happens in adead— enter configuration)< &Z_ [5’ m’”""”“““, ’7’“ a 92m 2 4 C65 i. all + as} 4qu : 44,5? v _ 2a a; ' e) What is he value of 92 when r = 45 inches? | at W = m + «1 ea»; + e: M Z @:a(pg w 3-“ 37%” L561; 9;:l%0‘¢”/3 ‘ f) What is the value of 64 when r = 45 inches? L}. {biz 5N3 m a,%‘l 6W0 7k : OLSIVL > m ' -~ _ El 1 *z z 2 W67 ~ 45"? (,9) “ a COS < d #Qq wq3> Page3of4 2,04 014 ME3212: Mechanisms Exam 1: Fall 2007 36L: Hang Name 4. (20 pts) Determine the angle 92 to the nearest 0.5 degree of the slider crank in the position sketched (not to scale) below. NONE ‘l’lAlS Lamlo’l mléo lee LEE/ha Miwlvm’lZaWL‘Sm Page 4 of4 ...
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