Mathcad - P0414.xmcd - CBU

DESIGN OF MACHINERY SOLUTION MANUAL 4-14-1PROBLEM 4-14Statement:Find the minimum and maximum values of the transmission angle for all the Grashof crank-rockerlinkages in Table P4-1.Given: Table P4-1 data: i 1 2 14Row id ia ib ic i"a""b""c""d""e""f""g""h""i""j""k""l""m""n"67388562042049992910558810510677773678881025101011119886699105107786Solution: See Table P4-1 and Mathcad file P0414.1. Determine which of the linkages in Table P4-1 are Grashof.Condition( a b c d ) S min( a b c d )Row aRow bL max( a b c d )SL S LPQ a bcdSLreturn "Grashof" if SL PQreturn "Special Grashof" if SL = PQreturn "non-Grashof"Condition( 6 2 7 9 ) "Grashof"Condition( 7 9 3 8 ) "Grashof"Row c Condition( 3106 8 ) "Grashof"Row dRow eRow fRow gotherwiseCondition( 8 5 7 6 ) "Special Grashof"Condition( 8 5 8 6 ) "Grashof"Condition( 5 8 8 9 ) "Grashof"Condition( 6 8 8 9 ) "Grashof"Row h Condition( 20101010) "non-Grashof"Row iCondition( 4 5 2 5 ) "Grashof"Row j Condition( 20105 10) "non-Grashof"Row k Condition( 4 6 107 ) "non-Grashof"Row l Condition( 9 7 107 ) "non-Grashof"

DESIGN OF MACHINERY SOLUTION MANUAL 4-14-2Row m Condition( 9 7 118 ) "non-Grashof"Row n Condition( 9 7 116 ) "non-Grashof"2. Determine which of the Grashof linkages are crank-rockers. To be a Grashof crank-rocker, the linkage must beGrashof and the shortest link is either 2 or 4. This is true of rows a, d, and e.3. Use equations 4.28 and 4.29 to calculate the maximum and minimum transmission angles.Row a i 1 acosb i 2 c 2 d a i i i2b c i i 2 if 58.412 deg2 Row d i 4 acos 2 2 2b c d a i i i i acos 25.209 deg2b c i ib i 2 c 2 d a i i i2b c i i 2 if 0.000deg2 2 2 2b c d a i i i i acos 25.209 deg2b c i iRow e i 5 acosb i 2 c 2 d a i i i2b c i i 2 if 44.049 deg2 2 2 2b c d a i i i i acos 18.573deg2b c i i