chapter4-D - MEEG439 MACHINE DYNAMICS SPRING2006 Limit...

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Unformatted text preview: MEEG439 MACHINE DYNAMICS SPRING2006 Limit Positions CrankRocker 1 b a d b a c 2 + c 2 - (d - a ) 2 b 1 = cos 2bc 2 = 0 -1 c a + b ) 2 + d 2 - c 2 ( 2 = cos 2 ( a + b) d -1 2 d b a 2 c d c 2 + c 2 - (d + a ) 2 b 2 = cos -1 2bc 2 = 180 b - a ) 2 + d 2 - c 2 ( 2 = cos 2( b - a) d -1 b a 2 d Transmission angle varies between 1 and 12 RockerCrank (a form of doublerocker) Toggle positions b a 2 c d 2 + d 2 - b 2 - c 2 bc a 2 = cos -1 - 2ad ad = 180 1 5f21a3fd37d893d68c70e19c83833021762bfea3.doc MEEG439 MACHINE DYNAMICS SPRING2006 a 2 b d c 2 + d 2 - b 2 - c 2 bc a 2 = cos + 2ad ad =0 -1 Grashof Double Rocker Coupler rotates 360 relative to the other links. min = 0 , max = 90 Toggle positions b a 2 c 2 + d 2 - b 2 - c 2 bc a 2 = cos - 2ad ad = 180 -1 d b a 2 c d 2 + d 2 - b 2 - c 2 bc a 2 = cos -1 + 2ad ad =0 NonGrashof Triple Rocker b a 2 c d b a d 2 + d 2 - b 2 - c 2 bc a 2 = cos -1 - 2ad ad = 180 c 2 + c 2 - (d - a ) 2 b = cos -1 2bc 2 = 0 2 5f21a3fd37d893d68c70e19c83833021762bfea3.doc MEEG439 MACHINE DYNAMICS SPRING2006 b a 2 c d 2 + d 2 - b 2 - c 2 bc a 2 = cos -1 + 2ad ad =0 b c 2 + c 2 - (d + a ) 2 b = cos -1 2bc 2 = 180 d a Example 1. What type of fourbar are the following linkages? a) b) c) d) a 1 3 1 2 b 4 1 2 3.5 c 3 4 4 2 d 3 3 2 4 Type 2. Find the minimum and maximum values of the transmission angle for a) 2 + c 2 - (d - a ) 2 b 1 = cos -1 2bc 2 + c 2 - (d + a ) 2 b 2 = cos -1 2bc 3 5f21a3fd37d893d68c70e19c83833021762bfea3.doc MEEG439 MACHINE DYNAMICS SPRING2006 3. Find the input angles corresponding to the toggle positions for b), c), d) Toggle is given by 2 + d 2 - b2 - c2 a 2 = cos-1 2ad (output link lines up with the coupler) Linkage b): bc ad Linkage c): Linkage d): 4. For linkage c) and d), find the extreme values of . For outward motion 2 + c 2 - (d + a ) 2 b = cos -1 2bc 4 5f21a3fd37d893d68c70e19c83833021762bfea3.doc MEEG439 For inward motion MACHINE DYNAMICS SPRING2006 2 + c 2 - (d - a ) 2 b = cos -1 2bc Linkage c): Linkage d): 5 5f21a3fd37d893d68c70e19c83833021762bfea3.doc ...
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This note was uploaded on 02/06/2012 for the course MEEG 439 taught by Professor Scf during the Spring '11 term at The Petroleum Institute.

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