Читать книгу Kinematics of General Spatial Mechanical Systems - M. Kemal Ozgoren - Страница 43

Note that , i.e.

(2.128)

Therefore, the side‐by‐side addition of Eqs. (2.116)–(2.118) leads to the following equation.

(2.129)

Hence, cos θ and sin θ are found as follows:

(2.130)

(2.131)

In Eq. (2.131), σ is an arbitrary sign variable, i.e.

(2.132)

With the availability of sin θ and cos θ, θ can be found by means of the double argument arctangent function. That is,

(2.133)

The definition and the properties of the atan₂ function can be seen in Section 2.10.