429_Dynamics 11ed Manual

429_Dynamics 11ed Manual - Engineering Mechanics - Dynamics...

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Unformatted text preview: Engineering Mechanics - Dynamics Chapter 16 L r cos ( θ ) ω v= 2 2 d +r a= 2 2 d +r 2 + 2r d cos ( θ ) −L r sin ( θ ) ω d L r sin ( θ ) ω + (d2 + r2 + 2r d cos (θ))3 3d L r sin ( θ ) cos ( θ ) ω 2 + 2r d cos ( θ ) 2 + (d 2 2 + r + 2r d cos ( θ ) 2 ) 3d L r sin ( θ ) ω 2 + 3 3 2 (d2 + r2 + 2r d cos (θ))5 Problem 16-49 The Geneva wheel A provides intermittent rotary motion ωA for continuous motion ωD of disk D. By choosing d = 2 r, the wheel has zero angular velocity at the instant pin B enters or leaves one of the four slots. Determine the magnitude of the angular velocity ωΑ of the Geneva wheel when θ = θ1 so that pin B is in contact with the slot. Given: ωD = 2 rad s r = 100 mm θ 1 = 30 deg Solution: θ = θ1 Guesses φ = 10 deg ωA = 1 rad s sBA = 10 mm s'BA = 10 Given r cos ( θ ) + sBA cos ( φ ) = mm s 2r −r sin ( θ ) ωD + s'BA cos ( φ ) − sBA sin ( φ ) ωA = 0 r sin ( θ ) = sBA sin ( φ ) r cos ( θ ) ωD = s'BA sin ( φ ) + sBA cos ( φ ) ωA 427 ...
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