Explanation Given information: Constant angular velocity of arm SE is 2 r a d / s counter clockwise. Constant angular velocity of forearm EW is 4 r a d / s clockwise. Plane motion of a particle relative to a rotating frame is defined as, v P = v P 1 + v P / F In the above equation, v P - Absolute velocity of particle P. v P 1 - Velocity of point P 1 of moving frame F Coinciding with P. v P / F - Velocity of P relative to moving frame F. The Coriolis acceleration is a combination of a P = a P 1 + a P / F + a C Where, a P - Absolute acceleration of particle P. a P 1 - Acceleration of point P 1 of moving frame F coinciding with P. a P / F - Acceleration of P relative to moving frame F. a C -The Coriolis acceleration. The Coriolis acceleration is defined as, a C = 2 Ω × v P / F Calculation: The relative position r W / S of point W with respect to S r W / S = r E / S + r W / E = ( 0.35 cos 30 ° ) i + ( 0.35 s i n 30 ° ) j − ( 0.3 cos 80 ° ) i + ( 0.3 s i n 80 ° ) j = 0.25101 i + 0.47044 j The angular velocity Ω of arm SE Ω = ( 2 r a d / s ) k The angular velocity ω of arm EW ω = − ( 4 r a d / s ) k The velocity v W 1 of coinciding point W 1 with point W v W 1 = Ω × r W / S = 2 k × ( 0.25101 i + 0.47044 j ) = − 0.94088 i + 0.50202 j The relative velocity v W / S E of point W relative to arm SE v W / S E = ω × r W / E = − ( 4 k ) × [ − ( 0.3 cos 80 ° ) i + ( 0.3 s i n 80 ° ) j ] = 1.18176 i + 0.2084 j Velocity v W of point W v W = v W 1 + v W / S E = − 0

12th Edition

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 15.5, Problem 15.170P

To determine

Velocity and acceleration of wrist W.

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Chapter 15.5, Problem 15.169P

Chapter 15.5, Problem 15.171P

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Chapter 15 Solutions

Vector Mechanics For Engineers

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Velocity and acceleration of wrist W.

Solution Summary: The author explains the velocity and acceleration of wrist W. The velocity of arm SE is 2rad/s counter clockwise.

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