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CSU MECH 324 - DESIGN OF MACHINERY

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DESIGN OF MACHINERY SOLUTION MANUAL 6-31-1! PROBLEM 6-31Statement:The linkage in Figure P6-8b has the dimensions and crank angle given below. Find and plot ω4, VB, VC, and VD in the local coordinate system for the maximum range of motion that this linkage allows if ω2 = 20 rad/sec counterclockwise (CCW).Given:Link lengths:Link 2 (A to B)a 40 mm.Distance from D to VDe 36 mm.Link 3 (B to C) b 96 mm.Link 4 (C to D) c 75 mm.Link 1 (A to D) d 162 mm.Input crank angular velocityω220 rad.sec1.CCWTwo argument inverse tangentatan2 x y,( ) 0.5π.return x 0ifatanyxreturn x 0>ifatanyxπotherwiseSolution:See Figure P6-8b and Mathcad file P0631.1. Draw the linkage to scale and label it.CWω2fABY83.000° 150.959°xDVD43Xy2. Determine the range of motion for this non-Grashof triple rocker using equations 4.33.arg1a()2d()2b()2c()22 a.d.()bc.ad.()arg12.114=arg2a()2d()2b()2c()22 a.d.()bc.ad.()arg20.108=θ2toggleacos arg2θ2toggle96.2 deg=The other toggle angle is the negative of this. Thus,θ2θ2toggleθ2toggle1 deg.,θ2toggle..2nd Edition, 1999DESIGN OF MACHINERY SOLUTION MANUAL 6-31-23. Determine the values of the constants needed for finding θ4 from equations 4.8a and 4.10a.K1daK2dcK14.0500=K22.1600=K3a2b2c2d22 a.c.()K34.0422=Aθ2cosθ2K1K2cosθ2.K3Bθ22 sinθ2.Cθ2K1K21 cosθ2.K34. Use equation 4.10b to find values of θ4 for the crossed circuit.θ42θ22 atan2 2 Aθ2.Bθ2Bθ224 Aθ2.Cθ2.,.5. Determine the values of the constants needed for finding θ3 from equations 4.11b and 4.12.K4dbK5c2d2a2b22 a.b.()K41.6875=K54.0931=Dθ2cosθ2K1K4cosθ2.K5Eθ22 sinθ2.Fθ2K1K41 cosθ2.K56. Use equation 4.13 to find values of θ3 for the crossed circuit.θ32θ22 atan2 2 Dθ2.Eθ2Eθ224 Dθ2.Fθ2.,.7. Determine the angular velocity of links 3 and 4 for the crossed circuit using equations 6.18.ω32θ2aω2.bsinθ42θ2θ2sinθ32θ2θ42θ2.ω42θ2aω2.csinθ2θ32θ2sinθ42θ2θ32θ2.8. Determine the velocity of points B, C and D for the crossed circuit using equations 6.19.VBθ2aω2.sinθ2j cosθ2..VBxθ2ReVBθ2VByθ2ImVBθ2VCθ2cω42θ2.sinθ42θ2j cosθ42θ2..VCxθ2ReVCθ2VCyθ2ImVCθ2Angle from link 4 to VD:δ4150.959 deg.2nd Edition, 1999DESIGN OF MACHINERY SOLUTION MANUAL 6-31-3VDθ2eω42θ2.sinθ42θ2δ4j cosθ42θ2δ4..VDxθ2ReVDθ2VDyθ2ImVDθ29. Plot the angular velocity of the output link, ω4, and the magnitudes of the velocities at points B and C.100 75 50 25 0 25 50 75 100100806040200204060ANGULAR VELOCITY OF LINK 4Crank Angle, deg.Angular Velocity, rad/secω42θ2secrad.θ2deg100 75 50 25 0 25 50 75 100100050005001000VELOCITY COMPONENTS, POINT BCrank Angle, degJoint Velocity, mm/secVBxθ2secmm.VByθ2secmm.θ2deg2nd Edition, 1999DESIGN OF MACHINERY SOLUTION MANUAL 6-31-4100 75 50 25 0 25 50 75 10030002000100001000200030004000VELOCITY COMPONENTS, POINT CCrank Angle, degJoint Velocity, mm/secVCxθ2secmm.VCyθ2secmm.θ2deg100 75 50 25 0 25 50 75 100300020001000010002000VELOCITY COMPONENTS, POINT DCrank Angle, degJoint Velocity, mm/secVDxθ2secmm.VDyθ2secmm.θ2deg2nd Edition,


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CSU MECH 324 - DESIGN OF MACHINERY

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