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CSU MECH 324 - Slider-crank Analysis

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0 90 180 270 36000.51dlcθ2()θ2deg0 90 180 270 36000.51d θ2()θ2degθ20 deg⋅ 1 deg⋅, 360 deg⋅..:=error θ2()dappθ2()dlcθ2()−:=dappθ2()a cos θ2()⋅ b+a24b⋅1 cos 2 θ2⋅()−()⋅−:=Error in approximation:Approximation:d θ2()a cos θ2()⋅ b cos θ3θ2()()⋅−:=dlcθ2()a cos θ2()ba2sin θ2()2−+⋅:=θ3θ2()180deg asinabsin θ2()⋅−:=Law of cosines approach:Vector loop approach:b20in⋅:=a10in⋅:=Crank and coupler dimensions:Slider-crank Analysisd_dot θ2ω2,()if θ2180 deg⋅> v4_geoθ2ω2,(), v4_geoθ2ω2,()−,():=v4_geoθ2ω2,()a ω2⋅()2b ω3θ2ω2,()⋅()2+2a⋅ b⋅ω2⋅ω3θ2ω2,()⋅ cos θ3θ2()θ2−()⋅−:=Geometric Solution Result:0 90 180 270 3600.500.5v4θ2ω2,()θ2deg0 90 180 270 3600.500.5ω3θ2ω2,()θ2degθ20 deg⋅ 1 deg⋅, 360 deg⋅..:=v4θ2ω2,()9.744−insec=ω3θ2ω2,()0.378−radsec=θ3θ2()159.295 deg=ω21radsec⋅:=θ245 deg⋅:=v4θ2ω2,()a−ω2⋅ sin θ2()⋅ b ω3θ2ω2,()⋅ sin θ3θ2()()⋅+:=ω3θ2ω2,()abcos θ2()cos θ3θ2()()⋅ω2⋅:=Velocity Analysis:0 90 180 270 3600123error θ2()θ2deg0 90 180 270 36000.51dappθ2()θ2deg0 90 180 270 3600.500.5d_dot θ2ω2,()θ2degAcceleration Analysis:ω21radsec⋅:= α21radsec2⋅:=α3θ2ω2,α2,()1b cos θ3θ2()()⋅a α2⋅ cos θ2()⋅ a ω22⋅ sin θ2()⋅− b ω3θ2ω2,()2⋅ sin θ3θ2()()⋅+⋅:=a4θ2ω2,α2,()a− cos θ2()ω22⋅ sin θ2()α2⋅+⋅ b cos θ3θ2()()ω3θ2ω2,()2⋅ sin θ3θ2()()α3θ2ω2,(⋅+⋅+:=θ20 deg⋅ 1 deg⋅, 360 deg⋅..:=0 90 180 270 360101α3θ2ω2,α2,()θ2deg0 90 180 270 3600.500.5a4θ2ω2,α2,()θ2degSlider Block Kinematics Summary:α21radsec2⋅:= ω2t() α2t⋅:= θ2t()12α2⋅ t2⋅:=θ3t( ) 180deg asinabsin θ2t()()⋅−:= d t( ) a cos θ2t()()⋅ b cos θ3t()()⋅−:=ω3t()abcos θ2t()()cos θ3t()()⋅ω2t()⋅:= v4t() a−ω2t()⋅ sin θ2t()()⋅ b ω3t()⋅ sin θ3t()()⋅+:=α3t()1b cos θ3t()()⋅a α2⋅ cos θ2t()()⋅ a ω2t()2⋅ sin θ2t()()⋅− b ω3t()2⋅ sin θ3t()()⋅+⋅:=a4t() a− cos θ2t()()ω2t()2⋅ sin θ2t()()α2⋅+⋅ b cos θ3t()()ω3t()2⋅ sin θ3t()()α3t()⋅+⋅+:=∆θ 22π⋅()⋅:= T2 ∆θ()⋅α2:= t 0 sec⋅ 0.01 sec⋅, T..:=0 1.25 2.5 3.76 5.010180360540720θ2t()degt0 1.25 2.5 3.76 5.0100.51dt()t0 1.25 2.5 3.76 5.012.533.54θ3t()t0 1.25 2.5 3.76 5.0121012v4t()t0 1.25 2.5 3.76 5.0142024ω3t()t0 1.25 2.5 3.76 5.0110010a4t()t0 1.25 2.5 3.76


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CSU MECH 324 - Slider-crank Analysis

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