RIGID BODY KINEMATICSRIGID BODY KINEMATICS

Instantaneous Center of Zero Velocity (IC)

(Ani Dönme Merkezi)

In relative velocity analysis, we determined

the velocity of a point on a rigid body in

plane motion by adding the relative

velocity due to rotation about a convenient

reference point to the velocity of the

reference point.

We are now going to solve the problem by

choosing a unique reference point which

momentarily has zero velocity.

Let’s assume that the body in the figure is in plane motion. As

far as velocities are concerned, the body may be considered to

be in pure rotation about an axis, normal to the plane of

motion, passing through this point. This axis is called the

instantaneous axis of zero velocity and the intersection of this

axis with the plane of motion is known as the instantaneous

center of zero velocity (point C). For this certain instant, the

velocity of point C is zero.

Locating the Instantaneous Center

For the body in the figure, let’s assume that the directions

of the absolute velocities of any two points A and B on the

body are known and are not parallel. If there is a point

about which A has absolute circular motion at the instant

considered, this point must lie on the normal to through

A.

Av

Similar reasoning applies to B, and the intersection of the two

perpendiculars will give point C, the instantaneous center of zero

velocity. Point C may lie on or off the body. If it lies off the body,

it may be visualized as lying on an imaginary extension of the

body. The instantaneous center need not be a fixed point in the

body or a fixed point in the plane.

If we know the magnitude of the velocity of one of the points,

say vA, we may easily obtain the angular velocity of the body and

the linear velocity of every point in the body.

BC

V

AC

V BA

Motion of the Instantaneous Center

As the body changes its position, the instantaneous

center C also changes its position in space and on

the body.

Although the velocity of the instantaneous center is

zero, its acceleration may not be equal to zero.

Thus, this point may not be used as an

instantaneous center of zero acceleration.

If two or more bodies are connected by pins, the

instantaneous center (IC) will be determined separately for

each body.

In a rotating disk the IC will be the point of contact of the

disk with the surface.

IC

IC for AB

IC for BCBC

AB

vB

Absolute IC

If the instantaneous center of velocity is fixed for a

certain motion of the body, it can be named as

“absolute IC”.

Point O absolute IC Point O absolute IC Points O1 and O2 absolute IC

Point C relative IC

If the instantaneous center of velocity changes

position for a certain motion of the body, it can be

named as “relative IC”.

Relative IC

Point P relative IC

Relative IC in infinity

For the position shown, rod AB translates, AB=0

PROBLEMS

1. Determine the angular velocity of link OB if the piston has a

velocity of 2 m/s to the right at the instant shown.

PROBLEMS

2. Vertical oscillation of the spring

loaded plunger F is controlled by a

periodic change in pressure in the

vertical hydraulic cylinder E. For the

position = 60°, determine the angular

velocity of AD and the velocity of the

roller A in its horizontal guide if the

plunger F has a downward velocity of 2

m/s.

PROBLEMS

3. The mechanism in the figure is used for riveting. If the velocity

of the piston A is vA = 20 m/s for the instant, determine the velocity

of D, which moves in the vertical slot.

PROBLEMS

4. The oil pumping unit consists of a walking beam AB, connecting

rod BC, and crank CD. If the crank rotates at a constant rate of 6

rad/s (counterclockwise), determine the speed of the rod hanger H

at the instant shown. Also find the angular velocities of members

BC and AB.

PROBLEMS

5. In relation to the elongation of the hydraulic piston AC, the

velocity of point A on the slider is v = 1.25 m/s for the instant when

=tan-1(3/4). At this moment BD is horizontal and DE is vertical.

Determine the angular velocities of arms BD and DE and the

hydraulic piston AC for this instant.

200 mm