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Unformatted text preview: of idle degrees of freedom associated with the mechanism. Show the equations used and identify any assumptions made when determining your answers. 2 3 4 2 3 4 1 n =4 j =4
j i =1 M = 3(n − j − 1) + ∑ fi = 3(4 − 4 − 1) + 4 = −3 + 4 = 1 Mobility = 1 Idle DOF = 1  13  Problem 1.12 Determine the mobility of each of the planar linkages shown below. Show the equations used to determine your answers. Hydraulic Cylinder Piston 1 Piston 2 Hydraulic Cylinder Bucket (a) 6 7 2 1 3 4 9 (a) 8 (b) 5 n =9 j = 11
j ∑ fi = 11 x 1 = 11
i =1 j i= 1 M = 3(n − j − 1) + ∑ fi = 3(9 − 11 − 1) + 11 = − 9 + 11 = 2 Mobility = 2 4 5 1 2 7 6 8 9 10 11 n = 11 j = 14
j ∑ fi = 14 x 1 = 14
i= 1 j i =1 3 M = 3(n − j − 1) + ∑ fi = 3(11 − 14 − 1) + 14 = −12 + 14 = 2 Mobility = 2 (b)  14  Problem 1.13 Determine the mobility and the number of idle degrees of freedom of each of the planar linkages shown below. Show the equations used to determine your answers. Pin in slot (a) (b) (c) 10 9 8 2 3 4 1 7 5 6 11 n = 11 j = 14
j i =1 M = 3(n − j − 1) + ∑ fi = 3(11 − 14 − 1) + 15 = − 12 + 15 = 3 Mobility = 3 Idle DOF = 0 (a)
4 3 7 5 2 1 6 N =7 j =9
j i =1 M = 3(n − j − 1) + ∑ fi = 3(7 − 9 − 1) + 9 = −9 + 9 = 0 Mobility = 0 Idle DOF = 0 n =8 j = 10
7 j i =1 (b)
5 3 4 2 1 6 8 M = 3(n − j − 1) + ∑ fi = 3(8 − 10 − 1) + 10 = −9 + 10 = 1 (c) Mobility = 1 Idle DOF = 0  15  Problem 1.14 Determine the mobility and the number of idle degrees of freedom of each of the planar linkages shown below. Show the equations used to determine your answers. (a) (b) (c) 1 2 4 3 5 n =5 j =6
j i =1 M = 3(n − j − 1) + ∑ fi = 3(5 − 6 − 1) + 7 = −6 + 7 = 1 Mobility = 1 Idle DOF = 0 n =7 (a) 2 3 4 5 7 6 1 j =9 j i =1 M = 3(n − j − 1) + ∑ fi = 3(7 − 9 − 1) + 9 = −9 + 9 = 0 Mobility = 0 Idle DOF = 0 n = 12
7 (b)
6 5 8 3 2 1 4 9 10 11 12 j = 15 j i =1 M = 3(n − j − 1) + ∑ fi = 3(12 − 15 − 1) + 15 = −12 + 15 = 3 Mobility = 3 Idle DOF = 0 (c)  16  Problem 1.15 Determine the mobility and the number of idle degrees of freedom of each of the planar linkages shown below. Show the equations used to determine your answers. (a) (b) (c) 4 3 5 2 6 1 7 8 9 10 11 12 n = 12 j = 15
j i =1 M = 3(n − j − 1) + ∑ fi = 3(12 − 15 − 1) + 15 = −12 + 15 = 3 Mobility = 3 Idle DOF = 0 n = 10 (a)
6 5 3 2 1 4 10 7 j = 11
8 9 j i =1 M = 3(n − j − 1) + ∑ fi = 3(10 − 11 − 1) + 11 = −6 + 11 = 5 Mobility = 5 Idle DOF = 0 n = 10 j = 13
9 10
j i =1 (b)
8 7 6 5 3 4 2 1 M = 3(n − j −...
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 Winter '11
 Shudong

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