Mathcad - P0740.xmcd - CBU

DESIGN OF MACHINERY SOLUTION MANUAL 7-40-1PROBLEM 7-40Statement:Figure P7-10 shows a linkage and its coupler curve. Write a computer program or use an equationsolver to calculate and plot the magnitude and direction of the acceleration of the coupler point Pat 2-deg increments of crank angle. Check your results with program FOURBAR.Units: rpm 2 radmin 1Given:Link lengths:Link 2 (O 2 to A) a 10mmLink 3 (A to B) b 20.6mmLink 4 (B to O 4 ) c 23.3mmLink 1 (O 2 to O 4 ) d 22.2mmCoupler point: R pa 30.6mm 31degCrank motion: 100rpm 0radsec 2Solution: See Figure P7-10 and Mathcad file P0740.1. Draw the linkage to scale and label it.2. Determine the values of the constants needed forfinding 4 from equations 4.8a and 4.10a.K 1dd K 2 acK 1 2.2200K 2 0.9528yb3BPa 2 b 2 c 2 d 2K 3 K 3 1.52652 a cA4p K 1A cos 2 B sin K 1 K 2 1C K 2 cos K 3 cos K 32 a2d1O 2cO 44x3. Use equation 4.10b to find values of 4for the open circuit. 2atan2 2A B B 2 4 A C 4. Determine the values of the constants needed for finding 3from equations 4.11b and 4.12.K 4dc 2 d 2 a 2 b 2 K 5 K 4 1.0777K 5 1.1512b2 a b K 1D cos 2E F sin K 1 K 4 15. Use equation 4.13 to find values of 3. K 4 cos K 5 cos K 5 2atan2 2D E E 26. Determine the angular velocity of links 3 and 4 using equations 6.18. 4 D F

DESIGN OF MACHINERY SOLUTION MANUAL 7-40-2 a sin b sin a sin c sin 7. Using the Euler identity to expand equation 7.13a for A A. 2A A a sin j cos a cos 8. Use equations 7.12 to determine the angular accelerations of link 3. A' c sin D' ccos B' b sin j sin E' bcos 2 2C' a sin a cos b cos 2F' a cos a sin b sin 2 C' D' A' F' A' E' B' D' 9. Use equations 7.32 to find the acceleration of the point P. A PA R pa sin A P A A A P R pa 2 cos A PA A P 2 c cos c j cos jsin 2 sin AP arg A P 10. Plot the magnitude and direction of the coupler point P. (See next page.) 0deg2deg360 deg6000MAGNITUDE OF COUPLER POINT ACCELERATIONAcceleration, mm/sec^2 sec24000A P mm200000 45 90 135 180 225 270 315 360 degCrank Angle, deg

DESIGN OF MACHINERY SOLUTION MANUAL 7-40-3200DIRECTION OF COUPLER POINT ACCELERATIONDirection Angle, deg AP deg10001002000 45 90 135 180 225 270 315 360 degCrank Angle, deg