# homogeneous transformation

## homogeneous transformation

[‚hä·mə′jē·nē·əs ‚tranz·fər′mā·shən]
(mathematics)
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
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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.
In this investigation, the homogeneous transformation is utilized to develop the kinematics and dynamics of steering tires.
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 Method.
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]).

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