Coriolis Component numerical
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1. The document discusses the velocity and acceleration analysis of a crank and slotted lever quick return motion mechanism. 2. It provides the given data of a crank angle of 60 degrees and crank speed of 100 rpm. 3. It then calculates the velocity and acceleration of the ram (J) as well as the angular acceleration of the slotted lever using graphical methods like velocity diagrams and acceleration diagrams.
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Coriolis Component numerical
- 1. Theory of Machines-I Velocity and Acceleration Analysis of Mechanisms Relative Velocity and Acceleration Method(Graphical Method) Quick Return Motion Mechanisms: Coriolis Component Prof. K N Wakchaure Department of Mechanical Engineering Sanjivani College of Engineering, Kopargaon
- 2. Theory of Machines-I Velocity and Acceleration Analysis of Mechanisms Part 2. Acceleration Analysis (Graphical Method) Quick Return Motion Mechanisms: Coriolis Component Prof. K N Wakchaure Department of Mechanical Engineering Sanjivani College of Engineering, Kopargaon
- 3. Given Data: Crank Angle θ=60° Crank speed 𝑵 𝒃/𝒂=100 rpm Find: 1. 𝒂𝒋 2. 𝜶 𝒐𝒄 A mechanism of a crank and slotted lever quick return motion is shown in Fig.. If the crank rotates counter clockwise at 100 r.p.m., determine for the configuration shown, the velocity and acceleration of the ram J. Also determine the angular acceleration of the slotted lever. Crank, AB = 150 mm ; Slotted arm, OD = 700 mm and link DJ = 200 mm, AW=300mm. Configuration Diagram
- 4. Given Data: Crank Angle θ=60° Crank speed 𝑵 𝒃/𝒂=100 rpm o,a,k b c d j 𝐕𝐛/𝐚 𝐕𝐜/𝐛 𝐕𝐜/𝐨 𝐕𝐝/𝐨 𝐕𝐣/𝐝 𝐕𝐣/𝐤 B(C) Link Velocity Magnitude Direction Vector Scale(1:30) AB 𝑉𝑏/𝑎 𝜔 𝑏/𝑎 ∗ 𝐴𝐵 1571 𝒎𝒎 𝒔 Perpendicular to AB 𝑎𝑏 52.36 mm BC 𝑉𝑐/𝑏 − Along OD 𝑏𝑐 Unknown OC 𝑉𝑐/𝑜 𝜔 𝑐/𝑜 ∗ 𝑂𝐶 Perpendicular to OD 𝑜𝑐 Unknown Point D on OD 𝑉𝑑/𝑜 Velocity Image Principle 𝑜𝑑 𝑂𝐷 = 𝑜𝑐 𝑂𝐶 𝑜𝑑 52.59 mm DJ 𝑉𝑗/𝑑 𝜔𝑗/𝑑 ∗ 𝐽𝐷 Perpendicular to DJ 𝑑𝑗 Unknown Slider J 𝑉𝑗/𝑘 -- Along horizontal line 𝑘𝑗 Unknown Link Velocity Magnitude Vector Scale(1:30) From Velocity Diagram AB 𝑉𝑏/𝑎 𝜔 𝑏/𝑎 ∗ 𝐴𝐵 15708 𝒎𝒎 𝒔 𝑎𝑏 52.36 mm 1570.8 𝒎𝒎 𝒔 BC 𝑉𝑐/𝑏 − 𝑏𝑐 36.83mm 1105.0 𝒎𝒎 𝒔 OC 𝑉𝑐/𝑜 𝜔 𝑐/𝑜 ∗ 𝑂𝐶 𝑜𝑐 37.21mm 1116.420 𝒎𝒎 𝒔 Point D on OD 𝑉𝑑/𝑜 𝑜𝑑 52.59 mm 1587.0 𝒎𝒎 𝒔 DJ 𝑉𝑗/𝑑 𝜔𝑗/𝑑 ∗ 𝐽𝐷 𝑑𝑗 14.06 mm 421.890 𝒎𝒎 𝒔 Slider J 𝑉𝑗/𝑘 -- 𝑘𝑗 52.76 mm 1583.070 𝒎𝒎 𝒔 𝑉𝑐/𝑜 = 𝜔 𝑐/𝑜 ∗ 𝑂𝐶=1116.420 𝒎𝒎 𝒔 𝜔 𝑐/𝑜=1116.42/492.44= 2.27 rad/sec Velocity of Slider=𝑉𝑗/𝑘 = 𝑘𝑗*S.F =52.76*30 = 1583.070 𝒎𝒎 𝒔 Velocity Diagram Velocity Diagram
- 5. o,a,k b c d j 𝐕𝐛/𝐚 𝐕𝑪/𝐛 𝐕𝐜/𝐨 𝐕𝐝/𝐨 𝐕𝐣/𝐝 𝐕𝐣/𝐤 o1,a1,k1 b1 c1’ c1” d1 j1’ j1 c1 𝑎 𝑏/𝑎 𝑐 𝑎 𝑐/𝑏 𝑠𝑙𝑑 𝑎 𝑐/𝑜 𝑐 𝑎 𝑐/𝑜 𝑡 𝑎 𝑑/𝑗 𝑐 𝑎 𝑑/𝑗 𝑡 𝑎 𝑑/𝑗 . 𝑎𝑗/𝑘 . B(C)B(C) 𝑎 𝑐/𝑏 𝑐𝑜𝑟𝑟 𝑎 𝑐/𝑏 𝑠𝑙𝑑 Link Acceleration Magnitude Direction Vector Scale(1:200) AB 𝐚 𝐛/𝐨 𝐜 𝛚 𝐛/𝐚 𝟐 ∗ 𝐀𝐁 16449.34 𝐦𝐦 𝐬 𝟐 Along AB towards A 𝐚𝟏𝐛𝟏 82.24mm 𝐚 𝐛/𝐨 𝐭 -- -- -- - BC 𝐚 𝐜/𝐛 𝐜𝐨𝐫𝐫 𝟐 ∗ 𝛚 𝐜/𝐨 ∗ 𝐕𝐜 𝐛 5010.20 𝐦𝐦 𝐬 𝟐 Perpendicular to OC 𝐛𝟏𝐜𝟏′ 25.05mm 𝐚 𝐜/𝐛 𝐬𝐥𝐝 - Along OC 𝐜𝟏′ 𝐜𝟏 Unknown Acceleration of Slider 𝑎𝑗/𝑘 . J= 𝑘1𝑗1 8922.20 𝒎𝒎 𝒔 𝟐 Acceleration Diagram
- 6. o,a,k b c d j 𝐕𝐛/𝐚 𝐕𝐜/𝐛 𝐕𝐜/𝐨 𝐕𝐝/𝐨 𝐕𝐣/𝐝 𝐕𝐣/𝐤 o1,a1,k1 b1 c1’ c1 𝑎 𝑏/𝑎 𝑐 𝑎 𝑐/𝑏 𝑐𝑜𝑟𝑟 𝑎 𝑐/𝑜 𝑐 𝑎 𝑐/𝑜 𝑡 B(C)B(C) D B(C) O D 𝐕𝑪/𝐛 𝐕𝐜/𝐨 ω 𝐜/𝐨 𝑎 𝑐/𝑏 𝑐𝑜𝑟𝑟 𝑉𝑐/𝑜 = 𝜔 𝑐/𝑜 ∗ 𝑂𝐶=1116.420 𝒎𝒎 𝒔 𝜔 𝑐/𝑜=1116.42/492.44= 2.27 rad/sec 𝑎 𝑐/𝑏 𝑐𝑜𝑟𝑟 2 ∗ 𝜔 𝑐/𝑜 ∗ 𝑉𝑐 𝑏 𝑎 𝑐/𝑏 𝑐𝑜𝑟𝑟 =2 ∗ 𝜔 𝑐/𝑜 ∗ 𝑉𝑐 𝑏 Coriolis Acceleration
- 7. o,a,k b c d j 𝐕𝐛/𝐚 𝐕𝑪/𝐛 𝐕𝐜/𝐨 𝐕𝐝/𝐨 𝐕𝐣/𝐝 𝐕𝐣/𝐤 o1,a1,k1 b1 c1’ c1” d1 j1’ j1 c1 𝑎 𝑏/𝑎 𝑐 𝑎 𝑐/𝑏 𝑠𝑙𝑑 𝑎 𝑐/𝑜 𝑐 𝑎 𝑐/𝑜 𝑡 𝑎 𝑑/𝑗 𝑐 𝑎 𝑑/𝑗 𝑡 𝑎 𝑑/𝑗 . 𝑎𝑗/𝑘 . B(C)B(C) 𝑎 𝑐/𝑏 𝑐𝑜𝑟𝑟 𝑎 𝑐/𝑏 𝑠𝑙𝑑 Link Acceleration Magnitude Direction Vector Scale(1:200) AB 𝐚 𝐛/𝐨 𝐜 𝛚 𝐛/𝐚 𝟐 ∗ 𝐀𝐁 16449.34 𝐦𝐦 𝐬 𝟐 Along AB towards A 𝐚𝟏𝐛𝟏 82.24mm 𝐚 𝐛/𝐨 𝐭 -- -- -- - BC 𝐚 𝐜/𝐛 𝐜𝐨𝐫𝐫 𝟐 ∗ 𝛚 𝐜/𝐨 ∗ 𝐕𝐜 𝐛 5010.20 𝐦𝐦 𝐬 𝟐 Perpendicular to OC 𝐛𝟏𝐜𝟏′ 25.05mm 𝐚 𝐜/𝐛 𝐬𝐥𝐝 - Along OC 𝐜𝟏′ 𝐜𝟏 Unknown OC 𝐚 𝐜/𝐨 𝐜 𝐕𝐜/𝐨 𝟐 𝐎𝐂 =2531.0 𝐦𝐦 𝐬 𝟐 Along OC towards O 𝐨𝟏𝐜𝟏" 12.65mm 𝐚 𝐜/𝐨 𝐭 𝛂 𝐜/𝐨 ∗ 𝐎𝐂 Perpendicular to OC 𝐜𝟏"𝐜𝟏 Unknown Point D on OD 𝐚 𝐝/𝐨 . Acceleration Image Principle 𝑜1𝑑1 𝑂𝐷 = 𝑜1𝑐1 𝑂𝐶 9814.20 𝐦𝐦 𝐬 𝟐 𝐨𝟏𝐝𝟏 49.98mm DJ 𝐚 𝐝/𝐣 𝐜 𝐕 𝐝/𝐣 𝟐 𝐉𝐃 =890 𝐦𝐦 𝐬 𝟐 Along DJ towards D 𝐝𝟏𝐣𝟏′ 4.45mm 𝐚 𝐝/𝐣 𝐭 𝛂 𝐝/𝐣 ∗ 𝐉𝐃 Perpendicular to DJ 𝐣𝟏′ 𝐣𝟏 Unknown Slider J 𝐚𝐣/𝐤 -- Along horizontal line 𝐤𝟏𝐣𝟏 Unknown Link Acceleration Magnitude Vector Scale(1:200) From Acceleration Diagram AB 𝑎 𝑏/𝑜 𝑐 𝜔 𝑏/𝑎 2 ∗ 𝐴𝐵 16449.34 𝒎𝒎 𝒔2 𝑎1𝑏1 82.24mm 16449.34 𝒎𝒎 𝒔 𝟐 𝒂 𝒃/𝒐 𝒕 -- -- - -- BC 𝑎 𝑐/𝑏 𝑐𝑜𝑟𝑟 2 ∗ 𝜔 𝑐/𝑜 ∗ 𝑉𝑐 𝑏 𝑏1𝑐1′ 25.05mm 5010.20 𝒎𝒎 𝒔 𝟐 𝑎 𝑐/𝑏 𝑠𝑙𝑑 - 𝑐1′ 𝑐1 455.80mm 9160.2 𝒎𝒎 𝒔 𝟐 OC 𝑎 𝑐/𝑜 𝑐 𝑉𝑐/𝑜 2 𝑂𝐶 𝑜1𝑐1" 12.65mm 2531.0 𝒎𝒎 𝒔 𝟐 𝑎 𝑐/𝑜 𝑡 𝛼 𝑐/𝑜 ∗ 𝑂𝐶 𝑐1"𝑐1 32.80mm 6561.0 𝒎𝒎 𝒔 𝟐 Point D on OD 𝑎 𝑑/𝑜 . Acceleration Image Principle 𝑜1𝑑1 49.98mm 9814.20 𝒎𝒎 𝒔 𝟐 DJ 𝑎 𝑑/𝑗 𝑐 𝑉𝑑/𝑗 2 𝐽𝐷 𝑑1𝑗1′ 4.45mm 890 𝒎𝒎 𝒔 𝟐 𝑎 𝑑/𝑗 𝑡 𝛼 𝑑/𝑗 ∗ 𝐽𝐷 𝑗1′ 𝑗1 5.64mm 1129.20 𝒎𝒎 𝒔 𝟐 Slider J 𝑎𝑗/𝑘 -- 𝑘1𝑗1 44.61mm 8922.20 𝒎𝒎 𝒔 𝟐 Acceleration of Slider 𝑎𝑗/𝑘 . J= 𝑘1𝑗1 8922.20 𝒎𝒎 𝒔 𝟐 Acceleration Diagram
- 8. o,a,k b c d j 𝐕𝐛/𝐚 𝐕𝑪/𝐛 𝐕𝐜/𝐨 𝐕𝐝/𝐨 𝐕𝐣/𝐝 𝐕𝐣/𝐤 o1,a1,k1 b1 c1’ c1” d1 j1’ j1 c1 𝑎 𝑏/𝑎 𝑐 𝑎 𝑐/𝑏 𝑠𝑙𝑑 𝑎 𝑐/𝑜 𝑐 𝑎 𝑐/𝑜 𝑡 𝑎 𝑑/𝑗 𝑐 𝑎 𝑑/𝑗 𝑡 𝑎 𝑑/𝑗 . 𝑎𝑗/𝑘 . B(C)B(C) 𝑎 𝑐/𝑏 𝑐𝑜𝑟𝑟 𝑎 𝑐/𝑏 𝑠𝑙𝑑 Link Acceleration Magnitude Vector Scale(1:200) From Acceleration Diagram AB 𝑎 𝑏/𝑜 𝑐 𝜔 𝑏/𝑎 2 ∗ 𝐴𝐵 𝑎1𝑏1 82.24mm 16449.34 𝒎𝒎 𝒔 𝟐 𝒂 𝒃/𝒐 𝒕 -- -- - -- BC 𝑎 𝑐/𝑏 𝑐𝑜𝑟𝑟 2 ∗ 𝜔 𝑐/𝑜 ∗ 𝑉𝑐 𝑏 𝑏1𝑐1′ 25.05mm 5010.20 𝒎𝒎 𝒔 𝟐 𝑎 𝑐/𝑏 𝑠𝑙𝑑 - 𝑐1′ 𝑐1 455.80mm 9160.2 𝒎𝒎 𝒔 𝟐 OC 𝑎 𝑐/𝑜 𝑐 𝑉𝑐/𝑜 2 𝑂𝐶 𝑜1𝑐1" 12.65mm 2531.0 𝒎𝒎 𝒔 𝟐 𝑎 𝑐/𝑜 𝑡 𝛼 𝑐/𝑜 ∗ 𝑂𝐶 𝑐1"𝑐1 32.80mm 6561.0 𝒎𝒎 𝒔 𝟐 Point D on OD 𝑎 𝑑/𝑜 . Acceleration Image Principle 𝑜1𝑑1 49.98mm 9814.20 𝒎𝒎 𝒔 𝟐 DJ 𝑎 𝑑/𝑗 𝑐 𝑉𝑑/𝑗 2 𝐽𝐷 𝑑1𝑗1′ 4.45mm 890 𝒎𝒎 𝒔 𝟐 𝑎 𝑑/𝑗 𝑡 𝛼 𝑑/𝑗 ∗ 𝐽𝐷 𝑗1′ 𝑗1 5.64mm 1129.20 𝒎𝒎 𝒔 𝟐 Slider J 𝑎𝑗/𝑘 -- 𝑘1𝑗1 44.61mm 8922.20 𝒎𝒎 𝒔 𝟐 Acceleration of Slider 𝑎𝑗/𝑘 . J= 𝑘1𝑗1 8922.20 𝒎𝒎 𝒔 𝟐 𝑎 𝑐/𝑜 𝑡 𝑎 𝑐/𝑜 𝑡 = 𝛼 𝑐/𝑜 ∗ 𝑂𝐶 𝛼 𝑐/𝑜 = 𝑎 𝑐/𝑜 𝑡 /𝑂𝐶 𝛼 𝑐/𝑜=6551/492.44= 13.32 RAD/SEC2 𝛼 𝑐/𝑜 Solution
- 9. D 𝑎 𝑐/𝑏 𝑐𝑜𝑟𝑟 2 ∗ 𝜔 𝑐/𝑜 ∗ 𝑉𝑐 𝑏 𝑎 𝑐/𝑏 𝑐𝑜𝑟𝑟 =2 ∗ 𝜔 𝑐/𝑜 ∗ 𝑉𝑐 𝑏 B(C) O D 𝐕𝑪/𝐛 ω 𝐜/𝐨 𝑎 𝑐/𝑏 𝑐𝑜𝑟𝑟 B(C) O ω 𝐜/𝐨 𝑎 𝑐/𝑏 𝑐𝑜𝑟𝑟 B(C) ω 𝐜/𝐨 𝑎 𝑐/𝑏 𝑐𝑜𝑟𝑟 Direction of Coriolis Component 𝐕𝑪/𝐛 𝐕𝑪/𝐛 B(C) 𝐕𝑪/𝐛 ω 𝐜/𝐨 clockwise +ve ω 𝐜/𝐨 Counter clockwise -ve Case ω 𝐜/𝐨 𝐕𝑪/𝐛 𝑎 𝑐/𝑏 𝑐𝑜𝑟𝑟 1 CCW (-) UP (+) (-) towards left 2 CW (+) Down (-) (-) towards left 3 CW (+) UP (+) (+) towards Right 4 CCW (-) Down (-) (+) towards Right 𝐕𝑪/𝐛 upward +ve 𝐕𝑪/𝐛 Downward -ve D O ω 𝐜/𝐨 𝑎 𝑐/𝑏 𝑐𝑜𝑟𝑟 1 2 3 4 D D O
- 10. 10Prof. K NWakchaureTheory of Machines-I Simulation using GeoGebra Software
- 11. •THANKYOU… 11Prof. K NWakchaureTheory of Machines-I