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For motion about a fixed point, Į must account for a change in
both the magnitude and direction of Ȧ, so that, in general, Į is not
directed along the instantaneous axis of rotation, Fig. 2-35.

Fig. 2-35.
As the direction of the instantaneous axis of rotation (or the line
of action of Ȧ) changes in space, the locus of the axis generates a
fixed space cone, Fig. 2-36. If the change in the direction of this axis
is viewed with respect to the rotating body, the locus of the axis
generates a body cone.

Fig. 2-36
At any given instant, these cones meet along the instantaneous
axis of rotation, and when the body is in motion, the body cone
appears to roll either on the inside or the outside surface of the fixed
space cone. Provided the paths defined by the open ends of the cones
are described by the head of the Ȧ vector, then must act tangent to
these paths at any given instant, since the time rate of change of Ȧ is
equal to Į, Fig. 2-36.

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