Читать книгу Kinematics of General Spatial Mechanical Systems - M. Kemal Ozgoren - Страница 69

The comparison of Eqs. (3.95) and (3.102) shows that any transformation matrix obtained by an IFB sequence can also be obtained by an RFB sequence applied in the reversed order.

For example, the IFB 1‐2‐3 sequence (with the Euler angles φ₁, φ₂, and φ₃) and the RFB 3‐2‐1 sequence (with the Euler angles , , and ) give the same transformation matrix with the following relationships between the Euler angles.

The IFB and RFB sequences mentioned above can be described as shown below.

Both of the above sequences lead to the same transformation matrix, which is

(3.105)

Note that, although and are the same in the two sequences described above, the corresponding intermediate frames are obviously different. That is, and .