Question

4 4 or 04 3. Make a complete kinematic and dynamic analysis of the four-bar linkage of Problem 2 using the given data but in the posture when 2170°. The constant angular velocity of the input link 2 is 2 12 rad/s ccw, and the external force at point is FD8.95 kN 464.3°.

Answer 1

Kinematic analysis

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ku ㄑㄚ 115 tan() 2 A

Eq. 1 has two solutions, obtained from the ± conditions on the redical. If the redical is negative, then the solution is complex conjugate, which simply means that the link lengths chosen are not suitable to make connection for the given value of the input angle (crank angle) θ2. This can be possible either when the length of links is completely incapable to make connection in any position or, in a non-Grashof mechanism, when the crank angle is beyond a toggle limit position. Thus, there is no real solution for that value of crank angle θ2. These are considered as crossed and open configurations of mechanism and also as the two branches of the mechanism. The positive value gives θ4 for the crossed and minus value gives θ4 for the opened configuration in case of Grashof four bar planar mechanism as shown in Fig. 2

Similar to the angle θ4, the angle θ3 has two values, corresponding to the crossed and open configurations of mechanism.

es is E2x sine

Dynamic analysis

Dynamic force analysis involves the application of Newton’s three laws of motion. The second law is expressed in terms of rate of change of momentum.

M = m × v

F = m × a

We can differentiate between two subclasses of dynamics analysis depending upon which quantities are known and which are to be found. The “forward dynamics analysis” is the one in which we know everything about the forces and/or torques being exerted on the system, and we wish to determine the accelerations, velocities, and displacements which result from the application of those forces and torques. Given ‘F’ and ‘m’, solve for ‘a’. The second subclass of dynamics analysis, called the “inverse dynamics analysis” is one in which we know the (desired) accelerations, velocities, and displacements to be imposed upon our system and wish to solve for the magnitudes and directions of the forces and torques which are necessary to provide the desired motions and which result from them. This inverse dynamics case is sometimes also called kinetostatics. Given ‘a’ and ‘m’, solve for ‘F’ .

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Fn Fi2y 12× O 6
This kinematic analysis is useful to find the velocity and acceleration of the mechanisms at the different position of the links.