Читать книгу Kinematics of General Spatial Mechanical Systems - M. Kemal Ozgoren - Страница 63

In this case, rot(p, q) is expressed as a rotation matrix in one of the two relevant reference frames, i.e. either in the pre‐rotation frame or in the post‐rotation frame . Thus, the transformation matrix is related to rot(p, q) as follows according to Eq. (3.64):

(3.77)

Then, Eq. (3.76) gives with one of the following equivalent expressions.

(3.78)

(3.79)

On the other hand, is also equal to the overall rotation matrix expressed in either or . That is,

(3.80)

As noted above, in the rotated frame based (RFB) formulation, the rotation matrices are multiplied in the same order as the order of the rotation sequence indicated in Description (3.75).