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

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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.

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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.

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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.

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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.

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If we know the magnitude of the velocity of one of the points, say v A, we may easily obtain the angular velocity of the body and the linear velocity of every point in the body.

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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.

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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 vBvB

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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 Points O 1 and O 2 absolute IC

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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

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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.

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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.

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PROBLEMS 3. The mechanism in the figure is used for riveting. If the velocity of the piston A is v A = 20 m/s for the instant, determine the velocity of D, which moves in the vertical slot.

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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.

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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

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