Concept explainers
Solve Prob. 16.137 when
The forces exerted on the connecting rod at points B and D.
Explanation of Solution
Given information:
Connecting rod length,
Crank length
Rod mass,
Position vector,
Points D and A horizontal distance,
Position vector
Crank angular velocity in the form of vector,
Point B velocity,
Point B angular velocity in the form of vector is
Point D velocity is given by,
Compare j terms from equation A,
Compare i terms from equation A,
Crank AB angular acceleration is zero i.e.
Vector form of point B relative angular acceleration is
Vector form of point D acceleration is
Point B acceleration,
Point D acceleration,
Here,
Compare j terms in equation B,
Vector form of angular acceleration of connecting rod BD is
Compare i terms in equation B,
Vector form of acceleration of point D is
Pont G acceleration,
Here,
Point G inertial force,
Here,
Force horizontal component from figure 2,
Here,
Connected rod BD moment of inertia,
Moment at B from figure 2,
Here,
Compare K terms from equation C,
Force vertical component from figure 2,
Point B resultant reaction,
Here,
Resultant angle,
The force exerted at point B is
Forces along connecting rod from figure 3,
Hence, piston exerts force in rod which is
Point D resultant reaction,
Resultant angle,
The force exerted at point D is
Conclusion:
The force exerted at point B is
The force exerted at point D is
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Chapter 16 Solutions
Vector Mechanics For Engineers
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