Difference between revisions of "Template:Important topics"
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'''[[Matrices]]'''<br> | '''[[Matrices]]'''<br> | ||
− | This article gives a brief explanation of matrices and basic arithmetic algebra. | + | This article gives a brief explanation of matrices and basic arithmetic algebra. After a brief introduction [[Multiplication with a scalar|multiplication with a scalar]] and computing the [[The transpose of a matrix|transpose]] is described. Then the approaches for [[Addition of matrices|addition]] and [[Multiplication of matrices|multiplication]] of matrices to each other are presented. Conclusively the [[Minors and cofactors|minors and cofactors]] and the [[Determinant of a 4-by-4 matrix|determinant]] of a matrix are described. |
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+ | <td align="center" valign="middle" width="100px"> | ||
+ | [[File:Matrixinversion.png|75px]] | ||
+ | </td> | ||
+ | <td valign="top"> | ||
+ | '''[[Matrix inversion]]'''<br> | ||
+ | After describing the preconditions for the existence of an inverse and its definition, two procedures to determine the inverse of a matrix, the [[Gauß-Jordan-Algorithm]] and the [[Adjugate Formula]], are introduced and clarified by examples. | ||
+ | </td> | ||
+ | </tr> | ||
+ | </table> | ||
+ | ---- | ||
+ | <table style="border-spacing:5px;"> | ||
+ | <tr> | ||
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+ | [[File:Transformationen.png|100px]] | ||
+ | </td> | ||
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+ | '''[[Transformations]]'''<br> | ||
+ | In this article general transformations used in the context of robotics and the underlying mathematics are described. The two basic types of transformation are [[Translation|translation]] and [[Rotation|rotation]]. To be able to apply all types of transformations by matrix multiplication, [[Homogeneous coordinates|homogeneous coordinates]] are introduced. Based on the two basic transformations, [[Combinations of transformations|combinations of transformations]] are possible. Additionaly a special matrix inversion method is presented for [[Inverse transformation|inverse transformation]]. | ||
+ | </td> | ||
+ | </tr> | ||
+ | </table> | ||
+ | ---- | ||
+ | <table style="border-spacing:5px;"> | ||
+ | <tr> | ||
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+ | [[File:ThreeAngle.png|100px]] | ||
+ | </td> | ||
+ | <td valign="top"> | ||
+ | '''[[Three-Angle Representations]]'''<br> | ||
+ | Three angles are enough to describe the orientation of an object in three-dimensional space. But there are two different ways to define these angles, the notation of [[Roll-Pitch-Yaw|Roll-Pitch-Yaw]] and of [[Euler angles]]. | ||
+ | </td> | ||
+ | </tr> | ||
+ | </table> | ||
+ | ---- | ||
+ | <table style="border-spacing:5px;"> | ||
+ | <tr> | ||
+ | <td> | ||
+ | [[File:Quaternion.png|100px]] | ||
+ | </td> | ||
+ | <td valign="top"> | ||
+ | '''[[Quaternions]]'''<br> | ||
+ | In this chapter [[Quaternions|quaternions]] are introduced, with which rotations can be represented. First, the [[basic properties of quaternions|basic properties]] of a quaternion are presented. Then [[Pure and unit quaternions|pure and unit quaternions]] followed by the rules for [[Addition of quaternions|addition]] and [[Multiplication of quaternions|multiplication]] are explained. Quaternions are usually used to represent [[Rotations using quaternions|rotations]] but can also be used for the [[Realization of transformations|realization of transformations]] in general. | ||
+ | </td> | ||
+ | </tr> | ||
+ | </table> | ||
+ | ---- | ||
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− | [[File: | + | [[File:dh-convention-logo.png|100px]] |
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− | '''[[ | + | '''[[Denavit-Hartenberg Convention]]'''<br> |
− | + | The Denavit-Hartenberg convention covers methods to [[Assigning coordinate frames|assign coordinate frames]] to the links of serial link manipulators and to describe the spatial relationship between them by the four [[Denavit-Hartenberg parameters]]. Based on the [[A-matrices]], the transformation of the end-effector with respect to the manipulators base frame can easily be determined and used for further computations. [[Typical link examples|Typical examples]] for links are presented to illustrate the usage of the convention. | |
+ | </td> | ||
+ | </tr> | ||
+ | </table> | ||
+ | ---- | ||
+ | <table style="border-spacing:5px;"> | ||
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+ | [[File:kinematics-logo.png|100px]] | ||
+ | </td> | ||
+ | <td valign="top"> | ||
+ | '''[[Kinematics]]'''<br> | ||
+ | |||
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Latest revision as of 15:54, 29 October 2015
Vector algebra |
Matrices |
Matrix inversion |
Transformations |
Three-Angle Representations |
Quaternions |
Denavit-Hartenberg Convention |