Explanation Given: The angular velocity of input A B , ω A B = 2.5 rad / s . The position vector directed from B to C , r B / C = ( 150 mm ) or 0 .15 m . The angle formed by link C , θ C = 30 ° . The angle formed by link A , θ A = 45 ° . Show the free body diagram of the system as in Figure (1). Show the free body diagram of angles formed by link A B C in the two link mechanism as in Figure (2). Conclusion: Express the radius of link B A . r B A sin ( θ + θ C ) = r B / C sin θ A (I) Substitute 0 .15 m for r B / C , 90 ° for θ , 30 ° for θ C and 45 ° for θ A in Equation (I). r B A sin ( 90 ° + 30 ° ) = 0.15 sin 45 ° r B A = 0.15 ( 0.8660 ) 0.7071 = 0.1837 m As the link C is fixed, take its linear velocity and acceleration vector as zero. v C = 0 a C = 0 Express the position vectors of link C D . Ω = − ω C D k Ω ˙ = − α C D k Here, angular velocity is Ω , angular acceleration is Ω ˙ , angular velocity of link C D is ω C D and angular acceleration of link C D is α C D . Write the motion of link C B with respect to moving reference. r B / C = { − 0.15 i } m ( v B / C ) x y z = ( υ B / C ) x y z i ( a B / C ) x y z = ( a B / C ) x y z i Here, absolute velocity and velocity of B along C with reference to x y z frame is ( v B / C ) x y z and ( υ B / C ) x y z respectively, acceleration vector of B along with C with reference to x y z frame is ( a C / A ) x y z , and acceleration of B along with C with reference to x y z frame is ( a C / A ) x y z . Express the the position vector directed from B to A . r B / A = − r B A cos ( θ A − θ C ) i + r B A sin ( θ A − θ C ) j (II) Substitute 0 .1837 m for r B A , 45 ° for θ A and 30 ° for θ C in Equation (II)

Engineering Mechanics: Statics & Dynamics (14th Edition)

14th Edition

ISBN: 9780133915426

Author: Russell C. Hibbeler

Publisher: PEARSON

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Chapter 16.8, Problem 150P

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The angular velocity ωCD of link CD .

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Chapter 16.8, Problem 149P

Chapter 16.8, Problem 151P

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Chapter 16 Solutions

Engineering Mechanics: Statics & Dynamics (14th Edition)

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The angular velocity ω C D of link C D .

Solution Summary: The author explains the angular velocity of input AB and the free body diagram of angles formed by link ABC in the two link mechanism.

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The angular velocity ωCD of link CD .

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Chapter 16 Solutions