fourbar mathcad - Slider-crank Analysis Crank and coupler...

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0 90 180 270 360 0 0.5 1 d lc θ 2 () θ 2 deg 0 90 180 270 360 0 0.5 1 d θ 2 θ 2 deg θ 2 0 deg 1 deg , 360 deg .. := error θ 2 d app θ 2 d lc θ 2 := d app θ 2 a cos θ 2 b + a 2 4b 1 cos 2 θ 2 := Error in approximation: Approximation: d θ 2 a cos θ 2 b cos θ 3 θ 2 := d lc θ 2 a cos θ 2 b a 2 sin θ 2 2 + := θ 3 θ 2 180deg asin a b sin θ 2 := Law of cosines approach: Vector loop approach: b2 0 i n := a1 0 i n := Crank and coupler dimensions: Slider-crank Analysis

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d_dot θ 2 ω 2 , () if θ 2 180 deg > v 4_geo θ 2 ω 2 , , v 4_geo θ 2 ω 2 , , := v 4_geo θ 2 ω 2 , a ω 2 2 b ω 3 θ 2 ω 2 , 2 + 2a b ⋅ω 2 3 θ 2 ω 2 , cos θ 3 θ 2 θ 2 := Geometric Solution Result: 0 90 180 270 360 0.5 0 0.5 v 4 θ 2 ω 2 , θ 2 deg 0 90 180 270 360 0.5 0 0.5 ω 3 θ 2 ω 2 , θ 2 deg θ 2 0 deg 1 deg , 360 deg .. := v 4 θ 2 ω 2 , 9.744 in sec = ω 3 θ 2 ω 2 , 0.378 rad sec = θ 3 θ 2 159.295 deg = ω 2 1 rad sec := θ 2 45 deg := v 4 θ 2 ω 2 , a
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fourbar mathcad - Slider-crank Analysis Crank and coupler...

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