Kinematics of General Spatial Mechanical Systems. M. Kemal Ozgoren
Чтение книги онлайн.
Читать онлайн книгу Kinematics of General Spatial Mechanical Systems - M. Kemal Ozgoren страница 50
![Kinematics of General Spatial Mechanical Systems - M. Kemal Ozgoren Kinematics of General Spatial Mechanical Systems - M. Kemal Ozgoren](/cover_pre848308.jpg)
(3.203)
In Eq. (3.203),
Note that Eq. (3.203) is actually valid for any pivot point whatsoever. Therefore, the HTM of a pure rotational displacement does not actually need a subscript and thus it may be denoted even in the following simplest form.
Note also that Eqs. (3.203) and (3.204) verify the well‐known fact that a rotation operator is indifferent to the location of the pivot point.
1 (e) HTM of a Pure Translation
A pure translational displacement of
(3.205)
(3.206)
1 (f) Observation in a Third Different Reference Frame
In general, the point P and the reference frames
(3.207)
The above affine relationship can be expressed in the following homogeneous form.
In Eq. (3.208), the coefficient matrix on the left‐hand side is the HTM of a pure rotation from
In case of a pure rotation with B = A, Eq. (3.209) takes the following form that involves two pure‐rotation HTMs.
(3.210)
In case of a pure translation with b = a, Eq. (3.209) takes the following form.
(3.211)
As another point of concern, note that Eq. (3.209) can also be written as
In Eq. (3.212),
(3.213)
When Eqs. (3.212) and (3.193) are compared, it is seen that
Equation (3.214) shows how an HTM