RIGID 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 BC BC

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 q =

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 q=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