Explanation Given information: θ = 75 ° Angular velocity of shank AK is 1 r a d / s counter clockwise. Angular acceleration of shank AK is 1.5 r a d / s 2 counter clockwise. The absolute acceleration of point B is defined as: a B = a A + a B / A a B = a A + ( a B / A ) t + ( a B / A ) n The tangential acceleration is defined as: ( a B / A ) t = r α The normal acceleration is defined as: ( a B / A ) n = r ω 2 In above equations α - Angular acceleration ω - Angular velocity r - Distance from A to B Calculation: According to above diagram: sin ϕ = 375 sin 75 ° − 310 442 = 0.118 ϕ = 6.785 ° Therefore: ϕ + β = 15 ° β = 8.215 ° For Δ C H K : α = 180 ° − ( ( 90 ° − ϕ ) + ( 90 ° − β ) ) α = 15 ° For shank AK: Velocity of point K: v K = ( A K ) ( ω A K ) = ( 375 m m ) ( 1 r a d / s ) = 375 m m / s Apply sine rule for: C K sin ( 90 ° − ϕ ) = 442 sin α Rearrange: C K = 442 sin α cos ϕ = 442 sin 15 ° cos ( 6.785 ) = 1695.8 m m For link KH: ω H K = v K C K = 375 m m / s 1695.8 m m = 0.221 r a d / s Velocity of hip H: v H = v K + v H / K Substitute: [ ← v H ] = [ 375 m m / s ↙ 75 ° ] + [ ( H K ) ω H K ↖ 6.785 ° ] Equate components: ← : v H = 375 sin 75 ° + ( 442 ) ( 0.221 ) sin 6.785 ° Therefore: v H = 373.76 m m / s ← Acceleration of point K: a K = ( A K ) ( α A K ) + ( A K ) ( ω A K ) 2 a K = [ ( 375 m m ) ( 1.5 r a d / s 2 ) ↙ 75 ° ] + [ ( 375 m m ) ( 1 r a d / s ) 2 ↘ 75 ° ] a K = [ 562.5 m m / s 2 ↙ 75 ° ] + [ 375 m m / s 2 ↘ 75 ° ] Position vector of H relative to K: r H / K = − ( 442 cos 6

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ISBN: 9781259977305

Author: BEER, Ferdinand P. (ferdinand Pierre), Johnston, E. Russell (elwood Russell), Cornwell, Phillip J., SELF, Brian P.

Publisher: Mcgraw-hill Education,

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Chapter 15.4, Problem 15.123P

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Velocity an acceleration of tip H.

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Chapter 15.4, Problem 15.122P

Chapter 15.4, Problem 15.124P

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Chapter 15 Solutions

Vector Mechanics For Engineers

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Velocity an acceleration of tip H.

Solution Summary: The author explains the velocity and acceleration of tip H. The angular velocity of shank AK is 1rad/s counter clockwise.

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