Angular Displacement & Representation of Angular Displacement by a Vector

Theory of Machines – Angular Displacement

Angular displacement may be defined as the angle described by a particle from one position to another with respect to time. For example, let a line OB have an inclination θ radians to the fixed line OA.

If this line moves from OB to OC through an angle δθ during a short interval of time δt, then δθ is known as the angular displacement of the line OB.

Since angular displacement has both magnitude and direction, it is therefore a vector quantity.

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Representation of Angular Displacement as a Vector

In order to completely represent an angular displacement by a vector, the following three conditions must be satisfied:

1. Direction of the axis of rotation:
   It is fixed by drawing a line perpendicular to the plane of rotation in which the angular displacement takes place. In other words, it is fixed along the axis of rotation.


2. Magnitude of angular displacement:
   It is fixed by the length of the vector drawn along the axis of rotation to some suitable scale.


3. Sense of the angular displacement:
   It is fixed by the right-hand screw rule. This rule states that if a screw is rotated along a fixed nut in a clockwise direction, i.e., if the angular displacement is clockwise and an observer is looking along the axis of rotation, then the arrowhead will point away from the observer. Similarly, if the angular displacement is anticlockwise, then the arrowhead will point towards the observer.