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**Mechanics of Machines Dr. Mohammad Kilani**

Class 9 DYNAMIC FORCE ANALYSIS

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Suggested Problems 11-(8,12)

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INTRODUCTION Kinematic analysis of mechanisms has been used to define the position, velocity and acceleration of the elements of a particular mechanism, Dynamic analysis, is concerned with the forces and torques in the system. We will take that approach in this chapter and concentrate on solving for the forces and torques that result from, and are required to drive, our kinematic system in such a way as to provide the required accelerations.

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**INTRODUCTION Determine the force acting on the table by: W = 50 N**

Taking a free body diagram around A and B together. Taking a free body diagram around A and another one around B. W = 50 N W = 100 N

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**Single Link in Pure Rotation**

Consider the single link in pure rotation shown. To carry out a dynamic analysis on the link, the kinematics of the problem must first be fully defined. That is, the angular speed and angular accelerations, and the linear accelerations of the CG must be found for the position of interest. The mass and the mass moment of inertia with respect to the CG must also be known. In addition there may be external forces or torques applied to any member of the system. These must be known as well. y P CG ω2 , α2 θ2 O2 x

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**Newtonian Solution Method**

Dynamic force analysis can be done by any of several methods. The one which gives the most information about forces internal to the mechanism requires only the use of Newton's law. These can be written as a summation of all forces and torques in the system. In two-dimensional problems, the above vector equations reduce to three independent scalar equations

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**Newtonian Solution Method**

These three equations must be written for each moving body in the system which will lead to a set of linear simultaneous equations for any system. If the kinematic accelerations are large compared to gravity, which is often the case, then the weight forces can be ignored in the dynamic analysis. If the machine members are very massive or moving slowly with small kinematic accelerations, or both, the weight of the members may need to be included in the analysis. The weight can be treated as an external force acting on the CG of the member at a constant angle.

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D’Alembert Principle Consider a moving rigid body of mass m acted upon by any system of forces, say F1, F2. and F3. Designate the center of mass of the body as point G, and find the resultant of the force system from the equation. D’Alemebr principle states that the inertia terms resulting from the linear acceleration of the center of mass, and the angular acceleration of the body can be treated as forces in the opposite direction to the inertia terms.

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D’Alembert Principle D’Alembert principle is summarized as follows. The vector sum of all the external forces and the inertia forces acting upon a rigid body is zero. The vector sum of all the external moments and the inertia torques acting upon a rigid body is also separately zero.

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D’Alembert Principle D’Alembert principle is summarized as follows. The vector sum of all the external forces and the inertia forces acting upon a rigid body is zero. The vector sum of all the external moments and the inertia torques acting upon a rigid body is also separately zero.

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Example 1 Determine the force F required to produce a velocity v = 1 m/s for the mechanism shown when θ3 = 120°. Assume that the linkage moves in a frictionless horizontal plane. Link 3 is 100 mm long, has a mass of 1 kg, and I3 = 2×10-3 kg.m.s2.

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Example 1 Determine the force F required to produce a velocity v = 1 m/s for the mechanism shown when θ3 = 120°. Assume that the linkage moves in a frictionless horizontal plane. Link 3 is 100 mm long, has a mass of 1 kg, and I3 = 2×10-3 kg.m.s2.

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Example 1 Determine the force F required to produce a velocity v = 1 m/s for the mechanism shown when θ3 = 120°. Assume that the linkage moves in a frictionless horizontal plane. Link 3 is 100 mm long, has a mass of 1 kg, and I3 = 2×10-3 kg.m.s2.

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Example 1 Determine the force F required to produce a velocity v = 1 m/s for the mechanism shown when θ3 = 120°. Assume that the linkage moves in a frictionless horizontal plane. Link 3 is 100 mm long, has a mass of 1 kg, and I3 = 2×10-3 kg.m.s2.

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Example 1 Determine the force F required to produce a velocity v = 1 m/s for the mechanism shown when θ3 = 120°. Assume that the linkage moves in a frictionless horizontal plane. Link 3 is 100 mm long, has a mass of 1 kg, and I3 = 2×10-3 kg.m.s2. maG= 40 N Iα = N.m C

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