# Difference between rotation and pure rotation

Hi i am trying to understand my teacher's assignment. I have 2 write 2 Matlab functions

R = rot(k,fi)       - Rotation matrix (rotation about unit vector k by angle fi in
degrees)


and

T = Rot(k,fi)  - Homogeneous transform (pure rotation)


After along time have i finally gotten the rot(k,fi) down, but i am having some problems finding out what the difference is between the 2 functions.

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Rotation :- A circular movement.

There is a central point that stays fixed and everything else moves around that point in a circle.

A "Full Rotation" is 360°

Pure Rotation : (quote from imechanica.org)

The concept of axis of of pure rotation ( or instantatious center of rotation) is a bit confusing. The text books in engineering mechanics( Irvin shames , Beer & Johnston etc) tells that the locus of points in a body, which is (are) having zero veloity. This fits well in case of a 2D motion. As a limiting case of this we are assuming the center of rotation is at inifinity for a rigid body moving in a straight line

But in case of a 3D motion, there are every chance is there that such a locus may not exist. For example,take a case of a nut which is going in a helical thread. In that we know that the traslationary motion and the rotation are in the same direction, and there will not be any point where velocity is zero.

In such cases how we can define axis of pure roration. I feel that the locus of points in which the linear velocity in the plane perpendicular to the axis of rotation is zero can be considered as the axis ofpure rotation.

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For future reference, we request that if you quote a web resource, that you use the "quote" environment and provide a link to the original. – Willie Wong Oct 25 '12 at 7:14