21 determine the mobility and the number of idle

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Unformatted text preview: 6 n = 12 8 4 3 2 1 5 9 10 7 11 12 j = 16 j i =1 M = 3( n − j − 1) + ∑ fi = 3(12 − 16 − 1) + 17 = − 15 + 17 = 2 Pin in slot (b) Mobility = 2 Idle DOF = 0 n =9 6 5 7 9 8 j = 12 j i =1 M = 3( n − j − 1) + ∑ fi = 3(9 − 12 − 1) + 13 = − 12 + 13 = 1 2 3 4 Pin in slot 1 Mobility = 1 Idle DOF = 0 (c) - 23 - Problem 1.21 Determine the mobility and the number of idle degrees of freedom for each of the mechanisms shown. Show the equations used and identify any assumptions made when determining your answers. Cam Contact Rolling Contact Cam Contact Pin in Slot Pin i Slot (c) (a) 1 2 3 4 7 5 6 8 11 9 10 (b) n = 11 j = 15 M = 3( − j− 1)+ n j f i = i1 11 = 3( − 15 − 1)+ 17 = −15 + 17 = 2 Mobility = 2 Idle DOF = 1 (a) 1 7 2 3 5 6 9 10 4 12 11 8 n = 12 j = 16 M = 3( − j− 1)+ n j = i1 f i 2) 1) = 3( −16− 1)+ 14( + 2 ( 12 = − 15+ 18 = 3 Mobility = 3 Idle DOF = 0 (b) 7 1 3 2 5 6 11 9 10 4 8 n = 11 j = 14 M = 3( − j− 1)+ n j f i = i1 (c) = 3( − 14 − 1)+ 16 = −12+ 16 = 4 11 Mobility = 4 Idle DOF = 1 - 24 - Problem 1.222 Determine the mobility and the number of idle degrees of freedom associated with the mechanism below. The figure is a schematic of the entire linkage for a large power shovel used in strip mining. It can cut into a bank 20 m high and can dump to a height of 14.5 m. Link 7 is connected to link 8 with a revolute joint. 11 7 8 16 10 12 14 15 17 9 2 18 13 5 3 4 6 n = 18 j = 24 11 7 8 16 10 12 14 15 17 9 2 18 13 N i =1 M = 3( n − j − 1) + ∑ fi = 3(18 − 24 − 1) + 24 = −21 + 24 = 3 6 Mobility = 3 Idle DOF = 0 5 3 4 2 Problem courtesy of Joseph Davidson, Arizona State University - 25 - Problem 1.23 In the figure is a portion of the support mechanism for the dipper on a large earth-moving machine used in removing overburden in strip mining operations. The fixed centers for the portion of the mechanism really move, but useful information can be obtained by observing the dipper motion relative to the "frame" as shown in the sketch. Both links 4 and 5 are mounted at O4 . Links 4 and 6 are parallel and of equal length. The dipper is moved by a hydraulic cylinder driving crank 5 about its fixed cylinder. Determine the number of degrees of freedom of the mechanism. O2 5 2 4 6 O4 Dipper 3 O2 5 O4 2 4 6 n =6 j =7 j i =1 M = 3(n − j − 1) + ∑ fi = 3(6 − 7 − 1) + 7 = − 6 + 7 = 1 Mobility = 1 Idle DOF = 0 Dipper 3 - 26 - Problem 1.24 What is the number of members, number of joints, mobility, and the number of idle degrees of freedom of each of the spatial linkages shown below? (a) (b) 5 3 n =5 j =6 j 2 4 ∑ fi = 3(3)...
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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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