RIGID BODY KINEMATICS Instantaneous Center of Zero Velocity (IC) (Ani Dönme Merkezi)
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Transcript of RIGID BODY KINEMATICS Instantaneous Center of Zero Velocity (IC) (Ani Dönme Merkezi)
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