Explanation Given: The angular velocity of the member A B is ω A B = 6 rad/s . Draw the free body diagram of the member A B and member C D as shown in Figure (1). Draw the free body diagram of the member B P D as shown in Figure (2). Write the relation between the linear velocity and angular velocity. ω = v r (I) v = ω r (II) Here, ω is the angular velocity, v is the linear velocity and r is the radial distance from the instantaneous center or permanent center to the point where the linear velocity acting on the object. Refer Figure (2) and Equation (I). Write the formula for the angular velocity ( ω B P D ) of the member B P D . ω B P D = v B r I C − B (III) ω B P D = v D r I C − D (IV) Here, v B is the velocity of the member A B and v D is the velocity of the member C D . Conclusion: Refer Figure (1) and Equation (II) to determine the velocities of the members A B and C D . Consider the member A B . Write the velocity of the member A B . v B = ω A B r A B Substitute 6 rad/s for ω A B and 200 mm for r A B . v B = 6 rad/s ( 200 mm × 1 m 1000 mm ) = 1.2 m/s Consider the member C D . Write the velocity of the member C D . v D = ω C D r C D Substitute 200 mm for r C D . v D = ω C D ( 200 mm × 1 m 1000 mm ) = 0.2 ω C D (V) The instantaneous center ( I C ) of the member B P D located as shown in Figure (2) by the effect of velocities of the members A B and C D

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Author: HIBBELER

Publisher: PEARSON

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Chapter 16, Problem 92P

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The velocity of the point D and the angular velocity of members BPD and CD .

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Chapter 16, Problem 91P

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The velocity of the point D and the angular velocity of members B P D and C D .

Solution Summary: The author illustrates the relationship between the linear velocity and angular velocity of the members AB and CD.

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The velocity of the point D and the angular velocity of members BPD and CD .

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