Читать книгу Kinematics of General Spatial Mechanical Systems - M. Kemal Ozgoren - Страница 64

In this case, all the rotation operators are expressed as the following rotation matrices in the initial reference frame .

(3.81)

Of course, in such a formulation, except , none of the above rotation matrices is a transformation matrix. Therefore, the transformation matrices required in Eq. (3.76) can be obtained as shown below by means of Eq. (3.74).

(3.82)

(3.83)

(3.84)

(3.85)

(3.86)

The pattern observed in Eqs. (3.84) and (3.86) implies that

(3.87)

As noted above, in the initial frame based (IFB) formulation, the rotation matrices are multiplied in an order opposite to the order of the rotation sequence indicated in Description (3.75).

On the other hand, the rotation matrix (that describes the rotation of into ) is mathematically equivalent to the orientation matrix (that describes the orientation of with respect to ). Based on this equivalence, Eq. (3.87) can also be written as follows:

(3.88)