I have been trying to close the loop on the concept of instantaneous axis of rotation ISA, also called screw axis. I see how this axis, both in 2D and 3D, is a unique axis (locus of points having the same velocity parallel to the axis itself) at each different instant in time $t$ (see [Centre of instantaneous rotation problem ). In 2D rigid motion, we talk about center of instantaneous rotation since the screw axis is perpendicular to the plane of motion...

However, the velocity $v_P(t)$ of any arbitrary point $P$ on the moving rigid body can be expressed as $v_P(t) = v_O(t) + \omega(t) \times (P-O)$, i.e. as the vector sum of the velocity $v_O(t)$ of an arbitrary point $O$ on the rigid body and the velocity of $P$ about the point $O$ expressed by the term $\omega(t) \times (P-O)$. Saying "the velocity of $P$ about the point $O$" means, to me at least, that point $P$ rotates about $O$ and there is an axis of rotation (not the ISA) passing through point $O$. What is then the difference between the axis passing through $O$ (or any other arbitrary point $Q\neq O$ on the obdy) and the unique instantaneous axis of rotation ISA (screw axis)? Are they both axis of rotations? Aren't they both instantaneous since they are parallel to the vector $\omega(t)$ which can change in time in direction and/or magnitude? Thanks!!


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