9.3 Absolute Motion
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Figure 9.7: Example 9.2 ([3], pp. 343)
9.3
Absolute Motion
An approach to kinematic analysis is the absolute motion method. The process is very straightforward. It starts with determining the geometric relations that define the configuration involved. Then, the time derivatives of the relations are perfomed to obtain velocities and accelerations. The sign consistency must be kept throughout the analysis. The crucial step, also the most difficult one, is to determine the geometric configuration. Consequently, some problems with complicated geometries are not suitable to analyze with this method as the constraints and the mathematics become increasingly involved. Instead, the principle of relative motion, introduced in section 9.4, is recommended. Example 9.3 ([3], SP. 5/4) A wheel of radius r rolls on a flat surface without slipping. Determine the angular motion of the wheel in terms of the linear motion of its center O. Also determine the acceleration of a point on the rim of the wheel as the point comes into contact with the surface on which the wheel rolls. Solution: The problem states the rolling without slipping condition of the wheel motion. This is in fact important which helps identifying the kinematic relationship. In the absolute motion approach, the kinematic relationship must first be determined. For this specific problem with the given condition, it can be concluded that the displacement of the center O must be equal to the arc length along the rim of the wheel that rolls over the flat surface. With the depicted ′ figure, fig. 9.8, the distance s is equal to the arc length C A. Mathematically, s = rθ Differentiating the above relationship, we have the velocity and the acceleration relations; vO = rω Chulalongkorn University
Phongsaen PITAKWATCHARA