4 3 5 6 n 7 j8 j 3n j 1 f m i i 1 37 8

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Unformatted text preview: 1) + ∑ fi = 3(10 − 13 − 1) + 13 = − 12 + 13 = 1 Mobility = 1 Idle DOF = 0 (c) - 17 - Problem 1.16 If position information is available for all points in the planar linkage shown below, can all of the velocities be determined uniquely if the value of is given? Explain your answer. ω 4 3 5 6 n =7 j=8 j = 3(n − j − 1) + f M ∑i i =1 = 3(7 − 8 − 1) + 8 = − 6 + 8 = 2 2 ω Mobility = 2 7 Therefore, the answer to the problem is no. The mechanism has two degrees of freedom, and two independent input variables must be specified before all of the velocities must be determined. - 18 - Problem 1.17 Determine the mobility and the number of idle degrees of freedom associated with each mechanism. Show the equations used and identify any assumptions made when determining your answers. Rolling joints Cam joint Pin in Slot Sliders (b) (c) Pin-in-Slot Joint Slider (a) (d) (e) - 19 - - 20 - Problem 1.181 Determine the mobility and the number of idle degrees of freedom associated with the mechanism shown below. The mechanism is a side-dumping car that consists of body 2 and truck 3 connected together by two six-bar linkages, ABCDEF and AGHKLMN. Link NM is designed as a latch on its free end (see left drawing). When jack 1 is operated, body 3 is lifted to the dumping position shown in the right-hand drawing. Simultaneously, the six-bar linkage AGHKLMN opens the latch on link N M and raises link G H . Linkage ABCDEF swings open side BC and the load can be dumped at some distance from the car (see right-hand drawing). Show the equations used to determine your answers. H G N L 3 A 1 2 K E F D B C 1 2 F K E L D C B H M 3 N M G G N 11 3 4 1 2 A F H 12 M 10 L D 7 8 6 9 B C n = 12 j = 16 N i =1 M = 3(n − j − 1) + ∑ fi = 3(12 − 16 − 1) + 16 = − 15 + 16 = 1 Mobility = 1 Idle DOF = 0 K 5 E 1 Problem courtesy of Joseph Davidson, Arizona State University - 21 - Problem 1.19 Determine the mobility and the number of idle degrees of freedom associated with the mechanism below. The round part rolls without slipping on the pieces in contact with it. n 4 =4 =4 −j j j DF = 3(n 3 2 − 1) + ∑ fi i =1 = 3(4 − 4 − 1) + 4 = − 3 + 4 = 1 Mobility = 1 Idle DOF = 0 1 - 22 - Problem 1.20 Determine the mobility and the number of idle degrees of freedom for each of the mechanisms shown. Show the equations used to determine your answers. Cam Contact Pin in Slot (a) 1 2 3 4 6 8 12 5 11 9 7 10 Pin in Slot (b) n = 12 j = 15 j i =1 Pin in Slot (c) M = 3( n − j − 1) + ∑ fi = 3(12 − 15 − 1) + 17 = − 12 + 17 = 5 Mobility = 5 Idle DOF = 2 Cam Contact Pin in slot (a)...
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