Читать книгу Kinematics of General Spatial Mechanical Systems - M. Kemal Ozgoren - Страница 57

The rotational deviation between two reference frames, e.g. and , can be represented by the direction angles as shown in Figure 3.2. In that figure, only six of the nine direction angles are illustrated for the sake of neatness. The direction angles between and are denoted and defined as follows for all i ∈ {1, 2, 3} and j ∈ {1, 2, 3}:

(3.49)

Figure 3.2 Direction angles between two reference frames.

Without any loss of generality, the direction angles can be defined to be positive angles that are confined to the range [0, π]. That is,

In a direct association with the direction angles, the direction cosines between and are denoted and defined as follows:

(3.50)