Читать книгу Kinematics of General Spatial Mechanical Systems - M. Kemal Ozgoren - Страница 54

The basis vector triad associated with is not only orthonormal but also right‐handed. Therefore, one of the columns of can be obtained from its other two columns by using the cross product operation. For example, and hence can be obtained as follows by using the matrix equivalent of the cross product operation:

(3.34)

Note that Eq. (3.34) gives three elements of readily in terms of its other six elements. In other words, it already provides three independent constraint equations on the nine elements of . Therefore, in the presence of Eq. (3.34), only three additional independent constraint equations can be posed on the elements of . These three additional constraint equations are written as follows involving the first two columns of :

(3.35)

(3.36)

(3.37)