Explanation Given: The angular velocity and position vector of link A B are shown in Figure (1). The angular velocity, position vector and angle of link B C are shown in Figure (2). The angular velocity of link A B is ω A B = 5 rad/s . Angle ϕ = 45 ° . Angle θ = 30 ° . The radius of the link A B is r A B = 3 m . The radius of the link B C is r B C = 2 m . Consider link A B from Figure (1) and write the velocity vector v B equation for rotation about fixed axis link A B . v B = ω A B × r A B (I). Refer Figure (1) and Write the angular velocity vector ω A B . ω A B = ω A B k (II). Refer Figure (1) and Write the expression for position vector for A B . r A B = [ ( − 3 cos 45 ° ) i − ( 3 sin 45 ° ) j ] Write the relative velocity equation to points B and C . v C = v B + ω B C × r C / B (III). Refer Figure (2) and Write the equation for velocity vector v B for point C . v C = ( υ C i ) Refer Figure (2) and Write the angular velocity vector ω A B . ω B C = ω B C k Refer Figure (2) and Write the expression for position vector from C to B . r C / B = [ ( 2 sin 30 ° ) i − ( 2 cos 30 ° ) j ] Conclusion: Since, ω A B = 5 rad/s . Substitute 5 rad/s for ω A B in Equation (II). ω A B = ω A B k = 5 k Substitute 5 k for ω A B , and [ ( − 3 cos 45 ° ) i − ( 3 sin 45 ° ) j ] for r A B in Equation (I)

Engineering Mechanics: Statics & Dynamics (14th Edition)

14th Edition

ISBN: 9780133915426

Author: Russell C. Hibbeler

Publisher: PEARSON

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Chapter 16.5, Problem 70P

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The velocity of block C , the angular velocity of link BC and draw the position of link BC when θ=45° , 60° and 75° .

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Chapter 16.5, Problem 69P

Chapter 16.5, Problem 71P

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Engineering Mechanics: Statics & Dynamics (14th Edition)

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The velocity of block C , the angular velocity of link B C and draw the position of link B C when θ = 45 ° , 60 ° and 75 ° .

Solution Summary: The author illustrates the angular velocity and position vector of link AB, and the angle of the link.

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The velocity of block C , the angular velocity of link BC and draw the position of link BC when θ=45° , 60° and 75° .

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Chapter 16 Solutions