Concept explainers
The elliptical exercise machine has fixed axes of rotation at points A and E. Knowing that at the instant shown the flywheel AB has a constant angular velocity of 6 rad/s clockwise, determine (a) the angular acceleration of bar DEF, (b) the acceleration of point F.
Fig. P15.127 and P15.128
(a)
Angular acceleration of bar DEF.
Answer to Problem 15.128P
The angular acceleration of bar DEF is
Explanation of Solution
Given information:
Constant angular velocity of AB is
Point A and E are fixed.
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:
Position vector of B relative to A:
Position vector of D relative to B:
Position vector of D relative to E:
Absolute velocity of point B:
Absolute velocity of point D:
We know that:
Substitute equation 1 into 2 and equate with 3:
Substitute:
Equate components:
Therefore:
Similarly:
But we know that:
Therefore, substitute equation 4 into 5 and equate with 6:
Substitute:
Solve further:
Equate components:
Solve above equations:
Conclusion:
The angular acceleration of bar DEF is
(b)
Acceleration of point F
Answer to Problem 15.128P
The acceleration of point F is
Explanation of Solution
Given information:
Constant angular velocity of AB is
Point A and E are fixed.
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
Absolute acceleration of point F
We know that
Therefore
Substitute
Then
Find the magnitude and the angle
Conclusion:
The acceleration of point F is
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Chapter 15 Solutions
Vector Mechanics For Engineers
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