Читать книгу Kinematics of General Spatial Mechanical Systems - M. Kemal Ozgoren - Страница 26

As a typical problem involving the singularity of , consider the following equation, from which is to be found for given and .

(1.74)

Due to Eqs. (1.68) and (1.69), cannot be found uniquely from Eq. (1.74). However, it can be found with the following expression that contains an arbitrary parameter λ.

(1.75)

In Eq. (1.75), is the part of that is orthogonal to . So, it can be expressed as

(1.76)

The coefficient γ is to be determined so as to satisfy Eq. (1.74). That is,

Since and are orthogonal, . Therefore, Eq. (1.77) gives γ as

(1.78)

Hence, and are obtained as shown below.

(1.79)

(1.80)