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KINEMATICS OF RIGID BODY

DYNAMICS - Lecture Notes / Mehmet Zor

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23 Agust, 2024

(Calculations of Velocity and Acceleration in Mechanisms)

3.

Attention: At the end of the chapter, in section 3.4, there are Exam Questions with Answers related to all chapter topics.

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DYNAMICS - Lecture Notes / Mehmet Zor

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23 Agust, 2024

2- Our goal: is to calculate the velocity and acceleration of any point on the rigid body (or rigid body system) at a time t.

3. Kinematics of Rigid Body

  • In order for an object to be examined within the scope of a rigid body, it must have a rotational motion at the moment of examination. Since all points of objects with only translational motion will have the same speed and acceleration at a time t, such objects can be examined as particles.
  • The difference in speed and acceleration between points of small rolling objects such as billiard balls is negligible. Therefore, such small objects are thought to have only translational motion of the center of gravity and can be examined as particles.

General Explanations on Rigid Body Kinematics

1- Rigid Body in terms of Dynamics: They are bodies whose points on them have different speeds and accelerations at a time t during motion and this difference cannot be neglected.

Figure 3.1

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DYNAMICS - Lecture Notes / Mehmet Zor

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23 Agust, 2024

Case 1 : Calculations of velocity and acceleration between two points of same object (done with absolute equations of motion)

3. Kinematics of Rigid Body

  • Known: The velocity and acceleration of a point on the object or system, the angular velocity and angular acceleration of the object at that moment, and the dimensions of the object.
  • Desired: The velocity and acceleration of another point on the object or system.

3- Solution Methods: Rigid body kinematics solutions are made with the appropriate one of the following two cases:

2. Durum: Velocity and acceleration calculations between the points of two different objects in contact (made with the equations of relative motion)

Note: It is important to see whether the problem is in absolute or relative motion at the beginning and to determine the solution method. Some sources use definitions such as fixed axis set - movable axis set for this. However, these are more difficult for students to understand. In order to overcome this difficulty, the above two situations unique to these notes have been presented.

In general, we can summarize what are knowns and what we want to calculate as follows:

Figure 3.2