Instantaneous Center of rotation

The instantaneous center of rotation (CIR) is a term used in traditional Mécanique and more particularly in Cinématique to indicate the point around whose a solid turns at one moment given compared to a reference mark of reference.

Definition

When a solid isolated with the mechanical direction from the term, moves according to a trajectory included/understood in a plan, the CIR is defined as the point where the Flight Path Vector is null.

The CIR is located on the perpendicular at each Vecteur speed of the solid isolated passing by the point from application from this last.

When the isolated solid moves only in translation in a plan, the CIR is projected ad infinitum.

The kinematic Torseur of the CIR is:

$\ {\ mathcal {V} (S/R) \} _ {CIR/R} =

\begin{Bmatrix}
\ \ vec \ Omega (S/R) \ \
\ \ vec 0
\end{Bmatrix}_{CIR/R}$

Example of the dancers of Cancan

The illustration represents dancers of Cancan seen of top. If it is considered that all five dancer is a solid isolated with the mechanical direction from the term, one can say that the Instantaneous Center of Rotation is the central dancer, since it not speed relative contrary to his/her partners who have a speed proportional to their distance of the center.

Example of use of the CIR in a problem of plane kinematics

That is to say a car in turn, which one knows the direction, the direction, the point of application and intensity (5 m/s) of the Flight Path Vector of the nose gear wheel. One also knows the direction, the point of application and the direction of the aft wheel. The points has and B are the centers of the wheels and respectively the points of application of their Flight Path Vector.

The objective is to determine the intensity of the Flight Path Vector of the aft wheel.

Graphic resolution thanks to the CIR:

One chooses a scale speeds here 10mm = 1 m/s

One places the Flight Path Vector of the nose gear wheel at point A.

One traces (in red) the direction of the Flight Path Vector of the aft wheel at the point B.

the CIR is located on a line passing by the point of application of the Flight Path Vectors and perpendicular to the latter: the green features are thus traced, and the CIR is deduced.

One measures the segment B and one defers measurement on the segment milked blue.

One plots a straight line passing by the CIR and the end of the Flight Path Vector associated with point A.

One traces a segment perpendicular to has passing by the measurement deferred on has and cutting the segment passing by CIR and the end of $\ vec V A$ .

One measures this last segment and according to the scale one finds the intensity of the Flight Path Vector $\ vec V B$ .

See too

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