
Concept explainers
(a)
The common angular acceleration of unit AB.
(a)

Answer to Problem 15.200P
The common angular acceleration of unit AB
Explanation of Solution
Given information:
The constant angular velocities of gears C and D is 30 rad/s and 20 rad/s respectively.
Calculation:
Draw the free body diagram of the planetary gear system as in Figure (1).
Place origin at F.
Write the relative position vector
Write the relative position vector
Determine the velocity value
Here,
Substitute
Determine the velocity value
Here,
Substitute
The motion of gear unit AB is
Determine the velocity vector
Substitute
Substitute 0 for
Equate the k component in Equation (1).
Determine the velocity vector
Substitute
Equate the k component.
Add the Equation (2) and (3).
Determine the value of
Substitute
Determine the common angular velocity of gears A and B
Substitute
Draw the free body diagram of the shaft system with FH as in Figure (2).
The point N is at nut, which is a part of unit AB and also is a part of shaft GH.
Write the distance of point N along x axis.
Write the relative position vector
Substitute
The nut N as a part of unit AB.
Determine the velocity vector
Substitute
The nut N as a part of shaft FH.
Determine the velocity vector
Substitute
Equate the Equations (4) and (5).
The angular velocity vector
Determine the common angular acceleration of unit AB.
Substitute
Therefore, the common angular acceleration of unit AB
(b)
The acceleration of the tooth of gear A which is in contact with gear C at point 1.
(b)

Answer to Problem 15.200P
The acceleration of the tooth of gear A which is in contact with gear C at point 1
Explanation of Solution
Given information:
The constant angular velocities of gears C and D is 30 rad/s and 20 rad/s respectively.
Calculation:
Determine the acceleration of the tooth of gear A which is in contact with gear C at point 1.
Substitute
Therefore, the acceleration of the tooth of gear A which is in contact with gear C at point 1
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Chapter 15 Solutions
Vector Mechanics for Engineers: Statics and Dynamics
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