Show the equations used to determine your answers a b

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Unformatted text preview: + 3(1) = 12 i =1 j M = 6(n − j − 1) + ∑ fi i =1 1 = 6(5 − 6 − 1) + 12 = − 12 + 12 = 0 Mobility = 0 Idle DOF = 0 (a) 1 2 4 3 n =5 j =5 j ∑ fi = 4(1) + 1( 3) = 7 i =1 j i =1 5 M = 6(n − j − 1) + ∑ fi = 6(5 − 5 − 1) + 7 = − 6 + 7 = 1 (b) Mobility = 1 Idle DOF = 0 - 27 - Problem 1.25 Determine the mobility and the number of idle degrees of freedom of the spatial linkages shown below. Show the equations used to determine your answers. (a) (b) (c) 3 2 4 n =4 j =4 j M = 6(n − j − 1) + ∑ fi = 6(4 − 4 − 1) + (3 + 3 + 2 + 1) = −6 + 9 = 3 Mobility = 3 Idle DOF = 2 n =5 j =5 j M = 6(n − j − 1) + ∑ fi i =1 i =1 1 (a) 3 2 4 5 1 (b) 6(5 − 5 − 1) + (3 + 3 + 3 + 1 + 2 ) = − 6 + 12 = 6 Mobility = 6 Idle DOF = 3 = 4 5 6 n =7 j =9 j M = 6(n − j − 1) + ∑ fi = 6(7 − 9 − 1) + 5(3) + 2(2) + 2(1) = − 18 + 21 = 3 Mobility = 3 Idle DOF = 1 i =1 3 2 1 7 (c) - 28 - Problem 1.26 Determine the mobility and the number of idle degrees of freedom of the spatial linkages shown below. Show the equations used to determine your answers. (a) (b) (c) 3 4 5 2 1 n =5 j =6 j M = 6(n − j − 1) + ∑ fi i =1 (a) = 6(5 − 6 − 1) + (3 + 3 + 3 + 1 +2 + 2 ) = −12 + 14 = 2 Mobility = 2 Idle DOF = 2 3 2 4 5 n =5 j =5 j M = 6(n − j − 1) + ∑ fi i =1 1 (b) = 6(5 − 5 − 1) + (3 + 3 + 3 + 1 + 2 ) = − 6 + 12 = 6 Mobility = 6 Idle DOF = 2 3 2 4 8 6 7 n =8 j = 10 j M = 6(n − j − 1) + ∑ fi i =1 5 = 6( 8 − 10 − 1) + 6(3) + 2(1) + 2(2) = − 18 + 24 = 6 Mobility = 6 Idle DOF = 1 (c) 1 - 29 - Problem 1.27 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. (a) (b) (c) 2 1 5 4 3 n =5 j j=6 M = 6(n − j − 1) + ∑ fi i =1 = 6(5 − 6 − 1) + 4(3) + 2 + 1 = −12 + 15 = 3 Mobility = 3 Idle DOF = 1 n =4 j j =5 M = 6(n − j − 1) + ∑ fi 3 4 i =1 (a) 2 1 (b) 2 1 3 6 (4 − 5 − 1) + (3 + 3 + 3 + 1 + 1) = − 12 + 11 = − 1 Mobility = -1 Idle DOF = 0 = n =4 j j=5 M = 6(n − j − 1) + ∑ fi i =1 4 (c) = 6(4 − 5 − 1) + 3(3) + 2 + 1 = − 12 + 12 = 0 Mobility = 0 Idle DOF = 1 - 30 - Problem 1.28 Determine the mobility and the number of idle degrees of freedom associated with each mechanism.3 Show the equations used to determine your answers. C C C C R H C C C C C P (a) (b) (c) P H P S H P S H S C C C (d) (e) C (f) S C S S C R R P H R R (g) ( h) (i) 3 C C 2 R 1 4 C (a) n =4 j =4 j M = 6(n − j − 1) + ∑ fi i =1 = 6(4 − 4 − 1) + 3(2) + 1 = −6 + 7 = 1 Mobility = 1 Idle DOF = 0 3 Problem based on paper entitled "A Number Synthesis Survey of Three-Dimensional Mechanisms" by L. Harrisberger, Trans. ASME, J. of Eng. for Ind., May, 1965, pp. 213-220. - 31 - C 3 C 4 C n =4 j =4 j 6(n − j − 1) + ∑ fi M= i =1 (b) H 1 2 = 6(4 − 4 − 1) + 3(2) + 1 = −6 + 7 = 1 Mobility = 1 Idle DOF = 0 n =4 j =4 j M = 6(n − j − 1) + ∑ fi = 6(4 − 4 − 1) + 3(2) + 1 = 6 + 7 = 1 Mobility = 1 Idle DOF = 0 P i =1 3 C C 4 C P 2 1 (c) 3 P (d) 4 2 n =...
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This note was uploaded on 02/20/2011 for the course MEC 411 taught by Professor Shudong during the Winter '11 term at Ryerson.

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