DESIGN OF MACHINERY SOLUTION MANUAL 4-7a-1θ42θ2()deg=θ42θ42θ2():=Crossed:θ41θ2()deg=θ41θ41θ2():=Open:Output link angle (1:open, 2:crossed) from Equation 4.10b:Constants from Equations 4.8a and 4.10a:θ265 deg⋅:=input link angle:c 9:=Link 4:a 3:=Link 2:b 6:=Link 3:d 10:=Link 1:Given:David G. Alciatore, PhD, PEFourbar position analysis2nd Edition, 1999DESIGN OF MACHINERY SOLUTION MANUAL 4-7a-2Constants from equations 4.11b and 4.12:Coupler link angle (1:open, 2:crossed) from Equation 4.13:Open:θ31θ2():=θ31θ2()deg=θ31Crossed:θ32θ2():=θ32θ2()deg=θ322nd Edition, 1999DESIGN OF MACHINERY SOLUTION MANUAL 4-7a-3Linkage positions:xjointθ2θ3,θ4,()0a cosθ2()⋅a cosθ2()⋅ b cosθ3()⋅+d:=yjointθ2θ3,θ4,()0a sinθ2()⋅a sinθ2()⋅ b sinθ3()⋅+0:=open:7.4530.000yjointθ2θ31θ2(),θ41θ2(),()10.0000.000 xjointθ2θ31θ2(),θ41θ2(),()θ41crossed:2.7193.271−yjointθ2θ32θ2(),θ42θ2(),()10.0000.000 xjointθ2θ32θ2(),θ42θ2(),()θ42Transmission angle:µA1θ41θ2()θ31θ2()−:=θ31µA1ifµA1180 deg⋅> 360 deg⋅µA1−,µA1,():=µA1µA1deg=µA1µA2θ42θ2()θ32θ2()−:=θ32µA2ifµA2180 deg⋅> 360 deg⋅µA2−,µA2,():=µA2µA2deg=µA22nd Edition, 1999DESIGN OF MACHINERY SOLUTION MANUAL 4-7a-4Coupler point:p 6:=δ45 deg⋅:=xpθ2()a cosθ2()⋅ p cosθ31θ2()δ+()⋅+:=θ31xpθ2()=xpypθ2()a sinθ2()⋅ p sinθ31θ2()δ+()⋅+:=θ31ypθ2()=ypCoupler Path:θ20 deg⋅ 1 deg⋅, 360 deg⋅..:=8.9951.758ypθ2()0.5283.187− xpθ2()yp2nd Edition,
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