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Chapter 16: Problem 81

In each case show graphically how to locate the instantaneous center of zero velocity of link \(A B\). Assume the geometry is known.

Short Answer

Expert verified
The Instantaneous center of zero velocity or link AB can be found graphically by identifying two points on the link, drawing their velocity vectors and erecting perpendiculars to these vectors from points of application. The point of intersection of these perpendiculars will be the ICR at that instant.

Step by step solution

01

Identify Known Parameters

Given in the problem is a link AB. Its geometric measurements, placements and movement are known.
02

Understanding Instantaneous Center of Zero Velocity

Instantaneous center of zero velocity (also known as Instantaneous Center of Rotation - ICR) is a point at which the velocity of any body is zero at a particular instant. For a rotating link AB this point will be some point in space at which the velocity of the entire link will be zero, while the link itself moves around this point. Essentially, the ICR makes the general motion of any rigid body momentarily appear as purely rotational.
03

Determine ICR Graphically

To figure out the ICR graphically, we need to draw velocity vectors of two chosen points on the link (not necessarily at A and B, but these can typically be easier). Since the velocity in a rigid body moves perpendicular to the direction of the link, we can draw perpendiculars to the velocity vectors at their points of application which will intersect at the ICR. This method is well applicable as long as both points have non-zero velocities.
04

Complete the Exercise

If all steps have been followed accurately, the ICR for link AB should be located graphically. Always remember, the point of ICR keeps shifting as the link changes its position, thus 'instantaneous center'. It should be borne in mind that this is a graphical method 鈥� precisions depend much on drawing skills and scaling.

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Most popular questions from this chapter

A wheel has an initial clockwise angular velocity of \(10 \mathrm{rad} / \mathrm{s}\) and a constant angular acceleration of \(3 \mathrm{rad} / \mathrm{s}^{2}\). Determine the number of revolutions it must undergo to acquire a clockwise angular velocity of \(15 \mathrm{rad} / \mathrm{s}\). What time is required?

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