Читать книгу Kinematics of General Spatial Mechanical Systems - M. Kemal Ozgoren - Страница 67

In an RFB sequence, e.g. the RFB i‐j‐k sequence, each of the unit vectors of the rotation axes is specified as one of the basis vectors of the reference frames , , and , respectively. That is,

(3.96)

The specified unit vectors must be such that j ≠ i and j ≠ k. However, since the rotation axes between the pre‐rotation and post‐rotation frames are common, the following equations can also be written for the unit vectors of the rotation axes.

(3.97)

Such a rotation sequence can be described as shown below.

(3.98)

In a sequence that has the axis unit vectors specified as shown above, i.e. as the basis vectors of the pre‐rotation frames, the matrix representations of the rotation operators are also expressed naturally in the pre‐rotation frames. In other words,

(3.99)

(3.100)

(3.101)

Hence, according to the RFB formulation explained in Section 3.7, is obtained as follows:

(3.102)