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)
Find the angular acceleration of the bar DEF.
Answer to Problem 15.128P
The angular acceleration of the bar DEF is
Explanation of Solution
Given information:
Consider the angular acceleration of the bar DEF is denoted by
The constant angular acceleration of the flywheel AB is
The angular acceleration of the flywheel AB is
Consider the position of the point B with respect to point A is denoted by
Consider the position of the point D with respect to point B is denoted by
Consider the position of the point D with respect to point E is denoted by
The axis of rotation points A and E are fixed. Then,
The velocity at the point A and E are
Show the relation between the velocity of the point B and A as follows:
Show the relation between the velocity of the point B and D as follows:
Modify Equation (2) using Equation (1).
Show the relation between the velocity of the point E and D as follows:
Equate Equation (3) and (4).
Substitute
Equate j component of the Equation (5).
Equate i component of the Equation (5).
Substitute
Substitute
The axis of rotation points A and E are fixed. Then,
The acceleration at the point A and E are
Show the relation between the acceleration of the point B and A as follows:
Show the relation between the acceleration of the point B and D as follows:
Modify Equation (2) using Equation (1).
Show the relation between the acceleration of the point E and D as follows:
Equate Equation (9) and (10).
Substitute
Equate j component of the Equation (5).
Equate i component of the Equation (5).
Substitute
Thus, the angular acceleration of the rod DEF is
(b)
Find the acceleration at point F.
Answer to Problem 15.128P
The acceleration at F is
Explanation of Solution
Given information:
Calculation:
Consider the position of the point F with respect to the point E is
Calculate the acceleration at F using the relation:
Substitute
Calculate the magnitude of the acceleration at D as follows:
Calculate the direction of the acceleration at D as follows:
Thus, the acceleration at F is
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