We have discussed in the previous topics the velocities of various points in the mechanisms. Now we shall discuss the acceleration of points in the mechanisms. The acceleration analysis plays a very important role in the development of machines and mechanisms.

Acceleration diagram for a link

Consider two points *A* and *B* on a rigid link as shown in Fig. (*a*). Let the point *B* moves with respect to *A*, with an angular velocity of ω rad/s and let α rad/s^{2} be the angular acceleration of the link *AB*.

We have already discussed that acceleration of a particle whose velocity changes both in magnitude and direction at any instant has the following two components:

1. The *centripetal or radial component,* which is perpendicular to the velocity of the particle at the given instant.

2. The *tangential component,* which is parallel to the velocity of the particle at the given instant. Thus for a link *AB*, the velocity of point *B* with respect to *A* (*i.e. v*BA) is perpendicular to the link *AB *as shown in Fig.(*a*). Since the point* B *moves with respect to* A *with an angular velocity ofωrad/s, therefore centripetal or radial component of the acceleration of *B* with respect to *A*,

This radial component of acceleration acts perpendicular to the velocity *v*BA, In other words, it acts *parallel* to the link *AB.*

We know that tangential component of the acceleration of *B* with respect to *A*,

This tangential component of acceleration acts parallel to the velocity *v*BA. In other words, it acts *perpendicular *to the link* AB*.

In order to draw the acceleration diagram for a link *AB*, as shown in Fig. (*b*), from any point *b’*, draw vector *b’x parallel to BA* to represent the radial component of acceleration of *B* with respect

to *A i.e. * from point *x* draw vector *xa’* perpendicular to *B A* to represent the tangential component of acceleration of *B* with respect to *A i.e. *. *Join b’ a’.* The vector *b’ a’* (known as *acceleration image *of the link* AB*) represents the total acceleration of* B *with respect to* A *(*i.e. a*BA) and it is the vector sum of radial component and tangential component of acceleration.

**Exercise Problems:**

1. In a four bar chain ABCD link AD is fixed and in 15 cm long. The crank AB is 4 cm long rotates at 180 rpm (cw) while link CD rotates about D is 8 cm long BC = AD and | BAD = 60^{o}. Find angular velocity of link CD.

2. In a crank and slotted lever mechanism crank rotates of 300 rpm in a counter clockwise direction. Find

(i) Angular velocity of connecting rod and

(ii) Velocity of slider.

A

60 mm 150 mm

45^{o}

B

**Configuration diagram**

Step 1: Determine the magnitude and velocity of point A with respect to 0,

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