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Mech220Tutorial7 - Copy (1)

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School
McGill University**We aren't endorsed by this school
Course
MECH 220
Subject
Mechanical Engineering
Date
Dec 17, 2024
Pages
10
Uploaded by MasterDragonMaster1133
MECH220-Tutorial 7:Planar Rigid Body Motion, Translation and Rotation, Absolute Motion Analysis and elative Motion AnalysisGuillaume Durandau - Fall 2024
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Question 1Determine the velocity and acceleration of the follower rod CD as a function of when the contact between the cam and follower is along the straight region AB on the face of the cam. The cam rotates with a constant counterclockwise angular velocity πœ”.
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Relation between OC and πœƒ? = 𝑂𝐢 cos πœƒπ‘‚πΆ =?cos πœƒVelocityαˆΆπ‘‚πΆ = 𝑣??=?αˆΆπœƒ tan πœƒcos πœƒAcceleration?π‘‚πΆπœƒ0αˆ·π‘‚πΆ = π‘Ž??=?αˆ·πœƒ tan πœƒcos πœƒ+?αˆΆπœƒ2tan2πœƒcos πœƒ+?αˆΆπœƒ2cos3πœƒ=?αˆΆπœƒ2tan2πœƒcos πœƒ+?αˆΆπœƒ2cos3πœƒ
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Question 2If the shaft and plate rotate with a constant angular velocity of πœ”=14 rad/s, determine the velocity and acceleration of point C located on the corner of the plate at the instant shown. Express the result in Cartesian vector form.
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Axe of rotation not normal to the plateAngular velocity to plate coordinate:𝝎 = πœ”?𝑂?𝝎 = πœ”π‘Άπ‘¨π‘‚π΄= 14(βˆ’0.3? + 0.2? + 0.6?βˆ’0.32+ 0.22+ 0.62)𝝎 = βˆ’6? + 4? + 12? ?π‘Žπ‘‘/???= 𝝎 Γ— 𝒓?0zxy0.3m0.6m0.2m
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𝒓?from 0:??= (βˆ’6? + 4? + 12?) Γ— (βˆ’0.3? + 0.4? + 0?)=40 βˆ’ 0.412? +βˆ’0.3 12 βˆ’βˆ’6 0 ?+βˆ’60.4 βˆ’βˆ’0.3 4 ?= βˆ’4.8? + 3.6? βˆ’ 1.2?
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Constant velocity so 𝛼 = 0𝒂 = 𝜢 Γ— 𝒓 + 𝝎 Γ— (𝝎 Γ— 𝒓)= 0 Γ—βˆ’0.3? + 0.4? + 0? +βˆ’6? + 4? + 12? Γ—βˆ’4.8? + 3.6? βˆ’ 1.2?=βˆ’6? + 4? + 12? Γ—βˆ’4.8? + 3.6? βˆ’ 1.2?=4βˆ’1.2 βˆ’3.6 12 ? +βˆ’4.8 12 βˆ’βˆ’6βˆ’1.2?+βˆ’63.6 βˆ’βˆ’4.8 4 𝐀= 48? βˆ’ 64.8? βˆ’ 2.4? m/s2
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Question 3If the motor turns gear A with an angular acceleration of 𝛼?= 2 ?π‘Žπ‘‘/?2when the angular velocity is πœ”?= 20 ?π‘Žπ‘‘/?. Determine the angular acceleration and angular velocity of gear D.
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Gear B:πœ”?=????πœ”?πœ”?=0.040.120= 8 ?π‘Žπ‘‘/?Gear C:πœ”?= πœ”?= 8 ?π‘Žπ‘‘/?Gear D:πœ”?=????πœ”?πœ”?=0.050.18 = 4 ?π‘Žπ‘‘/?
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Gear B:𝛼?= 𝛼?????𝛼?= 20.040.1= 0.8 ?π‘Žπ‘‘/?2Gear C:𝛼?= 𝛼?Gear D:𝛼?= 𝛼?????𝛼?= 0.80.050.1= 0.4 ?π‘Žπ‘‘/?2
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