Читать книгу Kinematics of General Spatial Mechanical Systems - M. Kemal Ozgoren - Страница 41

In this example, Eq. (2.87) will be verified for ijk = 123 as explained below. However, it can be verified similarly for any other distinct (unrepeated) triplet of indices as well.

For ijk = 123, Eq. (2.87) becomes

(2.110)

Let be the product of the three matrices on the left‐hand side of Eq. (2.110). It can be manipulated as follows:

(2.111)

According to the shifting formulas expressed by Eqs. (2.83)–(2.86), Eq. (2.111) can be manipulated further as shown below.

(2.112)

According to Eq. (2.68), . Therefore, Eq. (2.112) reduces to

(2.113)

Hence, it is seen that Eq. (2.110) is verified owing to Eq. (2.113).