INSTANTANEOUS CENTER OF ZERO VELOCITY

We were discussing the importance of friction i.e. positive and negative effects of friction, classifications of friction, coulomb's law of dry friction, some guidelines for solving frictional problems, concept of rolling resistance or rolling friction, wedge friction and concept of self- locking and the minimum stopping distance for a vehicle in engineering mechanics with the help of our previous posts. 

Now, we will be interested further to understand here a very important concept in engineering mechanics i.e. Instantaneous center of zero velocity with the help of this post.  

Instantaneous center of zero velocity 

Instantaneous center of zero velocity is basically defined as the point about which a body appears to be rotating at any given instantaneous or instant. It will have zero velocity and there will be only one instantaneous center per body per instant of time. 

Instantaneous center of zero velocity acts like absolute center of rotation at the instant considered. we must note it here that it will not be a fixed point in a body nor a fixed point in a plane. 

Let us consider a rigid body having a plane motion. There will be one linear component of translation motion and also rotary motion as displayed here in following figure. 

V_A is the absolute velocity of a point and ω is the rotational velocity of the body. We must note it here that these two quantities i.e. absolute velocity and rotational velocity will define the velocity of all other points in the body. 

Let us consider the two arbitrary points i.e. point A and point B and the absolute velocity V_A and V_B respectively. Now we will determine here the instantaneous center of zero velocity.  

Let us see here how we will determine the instantaneous center of zero velocity   

Instantaneous center of zero velocity could be found by drawing perpendiculars from these velocities. We have drawn the perpendiculars from these velocities and we can see in the following figure that these perpendiculars are meeting with each other at a point C. 

This point C will be known as instantaneous center of zero velocity.  

We can also determine the angular velocity from here with the help of following figure.

ω = V_A / r_A = V_B / r_B 

Let us see here how we will determine the instantaneous center of zero velocity when velocities are parallel, same in directions but not equal in magnitudes 

Let us consider the two arbitrary points i.e. point A and point B and their absolute velocity V_A and V_B respectively. Let us assume that these velocities are parallel, same in directions and not equal in magnitude as displayed here in following figure. 

Now we will determine here the instantaneous center of zero velocity for above mentioned case. 

Instantaneous center of zero velocity could be found by drawing the lines joining the tip and the base of these velocities. These lines will intersect or meet with each other at a point C which will be termed as instantaneous center of zero velocity.  

When the parallel velocities will become equal in magnitude, the instantaneous center will be pushed further and will approach to infinity and hence there will be a pure translation motion. 

Let us see here how we will determine the instantaneous center of zero velocity when velocities are parallel and opposite in directions 

Let us consider the two arbitrary points i.e. point A and point B and their absolute velocity V_A and V_B respectively. Let us assume that these velocities are parallel but opposite in directions as displayed here in following figure. 

Now we will determine here the instantaneous center of zero velocity for above mentioned case. 

Instantaneous center of zero velocity could be found by drawing the lines joining the tip and the base of these velocities. These lines will intersect or meet with each other at a point C which will be termed as instantaneous center of zero velocity. 

Therefore, we have seen here what is the basics of instantaneous center of zero velocity and we have also secured the information to determine the instantaneous center of zero velocity. 

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We will find out now the concept of in our next post.    

Reference:  

Engineering Mechanics, By Prof K. Ramesh  

Image courtesy: Google      

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Centrifugal pump working principle  

Minor head losses in pipe flow 

Hydraulic gradient and total energy line 

Working of syphon 

Flow through pipes in series  

Flow through pipes in parallel 

Flow through branched pipes 

Power transmission through pipes