Concept explainers
(a)
Find the angular velocity of the member ABD.
(a)
Answer to Problem 15.92P
The angular velocity of the member ABD is
Explanation of Solution
Given information:
The angular velocity of the arm DE is
Calculation:
Show the member ABD as shown in Figure 1.
Refer to Figure 1.
Calculate the velocity at D as follows:
Substitute
Consider the velocity of the point B as follows:
Consider the velocity at point B and D are denoted by
The perpendiculars to
The perpendicular BC and DC intersect at C. Then,
The point C is the instantaneous centre of ABD.
Refer to Figure 1.
Calculate the distances BD and DK as follows:
Calculate the value of the angle
Substitute
Calculate the value of the angle
Consider the triangle BCD.
Apply law of sine.
Calculate the distance BC and CD as follows:
Consider the triangle ABC.
Apply law of cosine.
Substitute
Apply law of sine.
Substitute
Calculate the angular velocity of the member ABD as follows:
Substitute
Thus, the angular velocity of the member ABD is
(b)
Find the velocity of A.
(b)
Answer to Problem 15.92P
The velocity at A is
Explanation of Solution
Given information:
Calculation:
Refer to Part (a).
Calculate the velocity of A using the relation:
Substitute
The velocity
Thus, the velocity at A is
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Chapter 15 Solutions
Vector Mechanics for Engineers: Statics and Dynamics
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