The kinematics of all bodies is provided by the user through homogeneous transformation
matrices T function of the chosen configuration parameters as far as they are independent.
First, according to the joint angles measured by the absolute position sensor, the homogeneous transformation
matrix [sup.base][T.sub.end] between the end and the mounting base of the manipulator is calculated by the manipulator's forward kinematics.
Then the homogeneous transformation
matrix is applied for representing geometric relations between cameras from different coordinate system.
The mapping between configuration space and task space can be described by homogeneous transformation
matrix from the base to the end-effector.
In this paper, we present a novel design for small-size directional antenna using a linear homogeneous transformation
method whose transformation ratio is independent of the position.
Table 2 results in a 4 x 4 homogeneous transformation
matrix [sup.i-1][T.sub.i] representing each link's coordinate frame with respect to the previous link's coordinate frame.
We divide a polyhedron into many segments and apply linear homogeneous transformation
in each segment to get homogeneous constitutive parameters.
Suppose that homogeneous transformation
matrix T is one of these hypotheses, as show in Figure 5, the homogeneous transformation
matrix [T.sub.3] of the two robots' relative pose can be calculated with T, [T.sub.1], and [T.sub.2] as follows:
The kinematical deviation due to part locating and relocating is modelled by the Homogeneous Transformation
It is a nice illustration of a utilization of matrices in geometry, application of homogeneous coordinates, homogeneous transformation
matrices and matrix algebra (Many similar exercises can be found in [Cox, 1998], [Craig, 1986], [Tsai, 1999]).