The fourbar linkage is a toggle mechanism 7 problem 16

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Unformatted text preview: r linkage is a toggle mechanism -7- Problem 1.6 Calculate the mobility, or number of degrees of freedom, of each of the mechanisms in Problem 1.3. A B n =4 j =4 2 3 j i =1 M = 3(n − j − 1) + ∑ fi = 3(4 − 4 − 1) + 4 = − 3 + 4 = 1 Mobility = 1 4 1 C Water Pump 1 2 pin-in-slot joint ( f i = 2) Arbitrarily pick link 1 as the frame 3 n =3 j =3 j i =1 M = 3( n − j − 1 ) + ∑ fi = 3(3 − 3 − 1) + 4 = 1 Mobility = 1 Folding Chair n =6 j=7 j i =1 M = 3(NL − N J − 1) + ∑ fi 4 3 5 2 1 = 3(6 − 7 − 1) + 7 = −6 + 7 = 1 Mobility = 1 6 Casement window mechanism -8- Problem 1.7 What is the number of members, number of joints, and mobility of each of the planar linkages shown below? (a) (b) n= 4 2 1 (a) 4 j=4 j (c) 3 ∑ fi = 4 i =1 x1= 4 j M = 3(n − j − 1) + ∑ f i = 3(4 − 4 − 1) + 4 = − 3 + 4 = 1 Mobility = 1 5 6 n =7 j =9 j i =1 4 3 2 1 (b) 7 ∑ fi i= 1 = 9 ×1= 9 j i =1 M = 3(n − j − 1) + ∑ fi = 3(7 − 9 − 1) + 9 = −9 + 9 = 0 Mobility = 0 n =5 j =6 2 3 1 (c) 5 4 j ∑ fi i= 1 = 5 × 1 +1× 2 = 7 j i =1 M = 3(n − j − 1) + ∑ fi = 3(5 − 6 − 1) + 7 = −6 + 7 = 1 Mobility = 1 -9- Problem 1.8 What are the number of members, number of joints, and mobility of each of the planar linkages shown below? (a) 4 (b) n=4 j =4 j (c) 2 3 ∑fi = 4 i =1 x1= 4 j i =1 1 M = 3( n − j − 1) + ∑ fi = 3(4 − 4 − 1) + 4 = − 3 + 4 = 1 Mobility = 1 n =7 5 j =8 j (a) 6 2 3 1 (b) 8 7 2 3 (c) 1 6 4 j 7 ∑ fi = 8 i= 1 x1= 8 j i= 1 4 M = 3( n − j − 1) + ∑ fi = 3(7 − 8 − 1) + 8 = −6 + 8 = 2 Mobility = 2 n=8 j = 10 5 ∑ fi = 10 x 1 = i= 1 10 j i= 1 M = 3( n − j − 1) + ∑ fi = 3(8 − 10 − 1) + 10 = −9 + 10 = 1 Mobility = 1 - 10 - Problem 1.9 Determine the mobility and the number of idle degrees of freedom of each of the planar linkages shown below. Show the equations used and identify the input and output links assumed when determining your answers. (a) (b) (c) 5 4 3 1 2 6 7 9 8 n =9 j = 12 j i =1 M = 3(n − j − 1) + ∑ fi = 3(9 − 12 − 1) + 12 = −12 + 12 = 0 Mobility = 0 Idle DOF = 0 n =7 (a) 4 6 3 7 2 1 5 j =9 j i =1 M = 3(n − j − 1) + ∑ fi = 3(7 − 9 − 1) + 9 = −9 + 9 = 0 Mobility = 0 Idle DOF = 0 (b) 8 9 7 3 4 2 1 5 6 n = 10 j = 12 10 j i =1 M = 3(n − j − 1) + ∑ fi = 3(10 − 12 − 1) + 12 = −9 + 12 = 3 Mobility = 3 Idle DOF = 0 (c) - 11 - Problem 1.10 Determine the mobility and the number of idle degrees of freedom of the linkages shown below. Show the equations used and identify any assumptions made when determining your answers. (a) (b) - 12 - Problem 1.11 Determine the mobility and the number...
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