Instant centre of rotation

In an instantaneous center is a label from the kinematics. By the determination of the roll center, it is possible to obtain a moving state of a moving body, which is a superposition of a translation and a rotation ( the instantaneous ) conceived so analytically treat a simple rotation in each moment as a pure rotation about a point. In a pure rotation is the speed of each point perpendicular to the connecting this point with the instantaneous center. This allows inversely determine the instantaneous when the speeds are known from two points that do not lie on a straight line.

Especially in the case of motion in the plane can determine its location by building the normal to the velocity directions of two body points. Your point of intersection is equal to the position of the instantaneous center. Are the normals parallel, is their point of intersection and thus the instantaneous center at infinity. In this case it is in the current state of motion to a pure translation that is perpendicular to the two parallel beams structure. Thus, the velocities have the same amounts and directions.

If the speeds of the two points on the body are parallel and perpendicular to the line connecting the two points, one can determine the instantaneous characterized in that it records the speed vectors of the points and a line through the tips of the vectors. This line intersects the straight line connecting the points of the body in the instantaneous center. Prerequisite for this method are different amounts of velocities. In a purely translational movement of the instantaneous center lies at infinity.

If one draws the line of instantaneous centers during a movement, then one obtains in the rest frame the Rastpolkurve and in the moving frame the moving centrode curve.

Example: Rolling wheel

The wheel on a vehicle shown in the picture has the view of the kinematics of multiple properties if you look at it along the dashed line through the center of rotation ( Z) and the contact point (A):

• Since it is attached to the vehicle, it shall participate in the translational motion. This portion is represented by the velocity arrows (T) along the line (L).
• An observer in the center ( Z) provides that the wheel (as opposed to the vehicle ) in addition to this center ( Z) turns. This portion (R) is represented by the arrows along the tangential line (L).
• As long as the wheel rolls, it has contact point (A ) is the velocity 0, because the road is and the wheel slip at this point, not across the street and does not slip in this idealized view also.

The superposition of the velocities ( R) and ( T), and the condition that the point on the wheel that is just the contact point (A ) on the stationary road itself also should be, makes the contact point (A) at the same time to the instantaneous center (M) wheel movement.

The right view shows how to determine the current speed with the instantaneous center (M) at four points by way of example selected AD: it is the product of the angular velocity ω about the instantaneous center (M, usually different from the angular velocity around Z) and the distance of each point (in the example A. .. D ) of the instantaneous center of rotation (M). If one looks, for example, the point is removed from the instantaneous most, so you have found the point with the highest speed.

The Rastpolkurve is the street in this example, because from the perspective of an observer on the street are all instantaneous centers on the roadway. The moving centrode curve is from the perspective of an observer on the wheel of the scope.