Читать книгу Kinematics of General Spatial Mechanical Systems - M. Kemal Ozgoren - Страница 47

As mentioned in Chapter 1, the vectors are independent of the reference frames in which they are observed. However, their components are naturally dependent on the selected observation frames. In other words, they have different components and matrix representations in different reference frames. Their matrix representations in different reference frames are related to each other by means of the transformation matrices. The transformation matrix between two reference frames can be expressed in various ways. It can be expressed as a rotation matrix, or as a direction cosine matrix, or as a function of the Euler angles of a selected sequence, or as a function of the basis vectors of the relevant reference frames. All these expressions are studied in this chapter together with several examples. Moreover, the matrix representations of the position vectors of a point in differently oriented and/or located reference frames can be related by means of either affine or homogeneous transformations. So, the affine and homogeneous transformations together with the 4 × 4 homogeneous transformation matrices are also studied in this chapter.