Explanation Given: The angular velocity and position vector are shown in Figure (1). The angular velocity of the gear S is ω S = 5 rad/s . From Figure (1): The radius r B / A for planetary gears is ( 80 mm ) . The radius r S for sun gear is 80 mm . Write the velocity υ A expression for point A . υ A = ω s × r s (I). The gear S is fixed the velocity of the gear S is zero v S = 0 From Figure (1): Write the equation for velocity vector v A for point A . v A = ( − υ A i ) (II). Write the angular velocity vector ω B . ω P = ω P k Write the expression for relative position vector from C to B . r B / A = ( 80 j ) Write the relative velocity equation for points B and A . v B = v A + ω P × r B / A (III). Write the equation for velocity vector v C for point C . v C = ( υ C j ) Write the angular velocity vector ω P . ω P = − ω P k (IV). Write the expression for relative position vector from C to B . r C / B = ( − 40 j ) Write the relative velocity equation for points C and B . v C = v B + ω P × r C / B (V). Write the angular velocity ω C expression for point C ω A = υ C r S + ( r B / A 2 ) (VI). Here, the angular velocity is for point A is ω A , the velocity for point C is υ C , radius of the planetary gears is r B / A and the radius of sun gear S is r S . Conclusion: Substitute 5 rad/s for ω S , and 80 mm for r S in Equation (I). υ A = ω s × r s = 5 ( 80 ) = 400 mm/s Substitute 400 mm/s for υ A in Equation (II). v A = ( − υ A i ) = − 400 i Substitute − ω P k for ω P , 0 for v B , − 400 i for v A and ( 80 j ) for r B / A in Equation (III)

Engineering Mechanics: Statics & Dynamics (14th Edition)

14th Edition

ISBN: 9780133915426

Author: Russell C. Hibbeler

Publisher: PEARSON

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Chapter 16.5, Problem 77P

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The angular velocity of the planet gears P and shaft A .

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Chapter 16.5, Problem 76P

Chapter 16.5, Problem 78P

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Chapter 16 Solutions

Engineering Mechanics: Statics & Dynamics (14th Edition)

Ch. 16.3 - When the gear rotates 20 revolutions, it achieves...Ch. 16.3 - The flywheel rotates with an angular velocity of ...Ch. 16.3 - The flywheel rotates with an angular velocity of (...Ch. 16.3 - The bucket is hoisted by the rope that wraps...Ch. 16.3 - A wheel has an angular acceleration of = (0.5 )...Ch. 16.3 - For a short period of time, the motor turns gear A...Ch. 16.3 - Prob. 1P Ch. 16.3 - The angular acceleration of the disk is defined by...Ch. 16.3 - The disk is originally rotating at 0 = 12 rad/s....Ch. 16.3 - Prob. 4P

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The angular velocity of the planet gears P and shaft A .

Solution Summary: The angular velocity of the planet gears P and shaft A is 5.67rad/s.

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The angular velocity of the planet gears P and shaft A .

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Chapter 16 Solutions