Concept explainers
Roberts linkage is named after Richard Roberts (1789-1864) and can be used to draw a close approximation to a straight line by locating a pen at point F. The distance AB is the same as BF, DF, and DE. Knowing that at the instant shown bar AB has a constant angular velocity of 4 rad/s clockwise, determine (a) the angular acceleration of bar DE, (b) the acceleration of point F.
Fig. P 15.135
(a)
Angular acceleration of bar DE.
Answer to Problem 15.135P
The angular acceleration
Explanation of Solution
Given information:
Constant angular velocity of link AB is
The absolute value of point A:
The relative velocity of A with respect to B is defined as:
The absolute acceleration of point B is defined as:
The tangential acceleration is defined as:
The normal acceleration is defined as:
In above equations:
Calculation:
The position vector
The velocity
Substitute:
The position vector
The velocity
Substitute
For bar DE
The position vector
The velocity
Equate components in equation 1 and 2:
Therefore
Bar AB has constant angular velocity. Therefore angular acceleration
Acceleration
For object BDF:
Acceleration
Substitute:
For bar DE
Acceleration
Substitute
Equate components
Therefore
Conclusion:
The angular acceleration
(b)
Acceleration of point F.
Answer to Problem 15.135P
The acceleration
Explanation of Solution
Given information:
Constant angular velocity of link AB is
The absolute acceleration of point B is defined as:
The tangential acceleration is defined as:
The normal acceleration is defined as:
In above equations
Calculation:
According to sub part a:
The acceleration
Angular acceleration
Angular velocity
Position vector
Acceleration
Substitute
Solve
The magnitude and angle of acceleration
Conclusion:
The acceleration
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Chapter 15 Solutions
Vector Mechanics For Engineers
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