1. WEEKS 2 Dynamics of Machinery
References
Theory of Machines and Mechanisms, J.J. Uicker, G.R.Pennock ve J.E. Shigley, 2003
Makine Dinamiği, Prof. Dr. Eres SÖYLEMEZ, 2013
Uygulamalı Makine Dinamiği, Jeremy Hirschhorn, Çeviri: Prof.Dr. Mustafa SABUNCU, 2014
Prof.Dr.Hasan ÖZTÜRK
Dr.H.ÖZTÜRK-2010

2. Example:This slider-crank mechanism is in static equilibrium in the shown configuration. A known force F acts on the slider block in the direction shown. An unknown torque acts on the crank. Our objective is to determine the magnitude and the direction of this torque in order to keep the system in static equilibrium. 3 2 4
Prof.Dr.Hasan ÖZTÜRK

3. Simplified FBD method:
Numerical values for the link lengths are L2 = 2 m and L3 = 4 m. From the figures we extract the following measurements: a = 1.8 m , b = 1 m , c = 2 m , d = 3.6 m. Assume the applied force is given to be F = 10 N in the negative direction.
Simplified FBD method:
The connecting rod of this mechanism is a two-force member. The reaction forces at A and B must be equal but in opposite directions. These reaction forces are named F2 3 and F 43 , and given arbitrary directions
Prof.Dr.Hasan ÖZTÜRK

4. Graphical:
Prof.Dr.Hasan ÖZTÜRK

5. Coulomb Friction: Coulomb friction can be included between two contacting surfaces in a static force analysis. Given the static coefficient of friction, μ (s) , the friction force can be described as the product of the coefficient of friction and the reaction force normal to the contacting surfaces. The friction force must act in the opposite direction of the tendency of any motion.
Prof.Dr.Hasan ÖZTÜRK

6. Kinematics of meshing gears.
GEAR KINEMATICS
The kinematic function of gears is to transfer rotational motion from one shaft to another. Since these shafts may be parallel, perpendicular, or at any other angle with respect to each other, gears designed for any of these cases take different forms and have different names: spur, helical, bevel, worm, etc.
pitch diameter
number of teeth
module
tangential acceleration
Kinematics of meshing gears.
Prof.Dr.Hasan ÖZTÜRK

7. Spur Gear Force Analysis (Static):
The reaction forces between the teeth occur along the pressure line AB, tipped by the pressure angle, tipped by the pressure angle  from the common tangent to the pitch circles.
In applications involving gears, the power transmitted and the shaft speeds are often specified. remembering that power is the product of force times velocity or torque times angular velocity, we can find the relation between power and the transmitted force. Using the symbol P to denote power, we obtain

10. Spur Gear Force Analysis (Dynamic):
The reaction forces between the teeth occur along the pressure line AB, tipped by the pressure angle, tipped by the pressure angle  from the common tangent to the pitch circles.
Prof.Dr.Hasan ÖZTÜRK

11. Helical Gears Fa: axial, Fr: radial Ft: tangential
t: transverse pressure angle
: helix angle
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12. Straight Bevel Gears
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13. Dynamic Force Analysis

14. Sometimes it is convenient to arrange these mass moments of inertia and mass products of inertia into a symmetric square array or matrix format called the inertia tensor of the body:

15. Dynamic Force Analysis
D'Alembertls principle: The vector sum of all external forces and inertia forces acting upon a system of rigid bodies is zero. The vector sum of all external moments and inertia torques acting upon a system of rigid bodies is also separately zero.
inertia force
Fi has the same line of action of aG but is in opposite direction
inertia torque
Ti  is in opposite sense of the angular acceleration a
Prof.Dr.Hasan ÖZTÜRK

16. Slider –Crank Mechanism
external force and torque, F4 and T2
All frictions are neglected except for the friction at joint 14
Prof.Dr.Hasan ÖZTÜRK

17. EXAMPLE
We use the four-bar linkage of the below Figure. The required data, based on a complete kinematic analysis, are illustrated in the Figure and in the legend. At the crank angle shown and assuming that gravity and friction effects are negligible, determine all the constraint forces and the driving torque required to produce the acceleration conditions specifıed.
Prof.Dr.Hasan ÖZTÜRK

19. We start with the following kinematic information.
Next we calculate the inertia forces and inertia torques. Because the solution is analytical, we do not need to calculate offset distances nor do we replace the inertia torques by couples. The six equations are

20. Considering the free-body diagram of link 4 alone, we formulate the summation of moments about point 04:
Also, considering the free-body diagram of link 3 alone, we formulate the summation of moments about point A:
Prof.Dr.Hasan ÖZTÜRK

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27. PLANAR ROTATION ABOUT A FIXED CENTER
Application of the parallel-axis theorem for mass moments of inertia
For fixed-axis rotation, it is generally useful to apply a moment
equation directly about the rotation axis O.
Prof.Dr.Hasan ÖZTÜRK

28. Center of percussion P P P P
Prof.Dr.Hasan ÖZTÜRK

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