Kinematics of General Spatial Mechanical Systems. M. Kemal Ozgoren

(3.227)

(3.228)

Note that, by referring to Figure 3.4, both Eqs. (3.227) and (3.228) can be verified by inspection, too. Moreover, Eq. (3.227) matches with Eq. (3.217), as it is supposed to do.

      As an additional manipulation with the homogeneous transformation matrices, the coordinates of the points A₂ and G₂ can also be obtained in as explained below.

      The HTM between and can be expressed as follows:

      (3.229)

Recall that has already been expressed by Eq. (3.220) as

      (3.230)

      On the other hand, Figure 3.4 implies that

      (3.231)

      Hence,

      (3.232)

      As for the coordinates of A₂ and G₂ in , they are obtained as follows with the help of Eqs. (3.227) and (3.228):

(3.233)

(3.234)

Note that, by referring to Figure 3.4, both Eqs. (3.233) and (3.234) can again be verified by inspection, too.