Читать книгу Kinematics of General Spatial Mechanical Systems - M. Kemal Ozgoren - Страница 52

Alternatively, Eq. (3.28) can also be written as follows by interchanging a and b:

(3.30)

Recalling that , Eq. (3.30) leads to the following equation when it is transposed on both sides.

(3.31)

Note that picks up the kth row of the matrix, by which it is premultiplied. Thus, in Eq. (3.31), happens to be the kth row of . Therefore, as an alternative to Eq. (3.29), can also be expressed row by row as shown below.

(3.32)

Here, it is worth paying attention that the column‐by‐column expression of requires the column matrix expressions of the basis vectors of in , whereas the row‐by‐row expression of the same requires the row matrix expressions of the basis vectors of in .