ezofT

by Tim C. Lueth, SG-Lib Toolbox: SolidGeometry 5.6 - Kinematics and Frames
Introduced first in SolidGeometry 5.2, Creation date: 2022-12-19, Last change: 2025-09-15

just returns the ez vector of an HT Matrix as row

See Also: ezofchar , ezof3P

Example Illustration

Syntax

ez=ezofT([T])

Input Parameter

T: DH Matrix 4x4

Output Parameter

ez: T(1:3,3)'

Examples


ezofT(TofR([0 pi/2 pi/4]))

Copyright 2022-2025 Tim C. Lueth. All rights reserved. The code is the property of Tim C. Lueth and may not be redistributed or modified without explicit written permission. This software may be used free of charge for academic research and teaching purposes only. Commercial use, redistribution, modification, or reverse engineering is strictly prohibited. Access to source code is restricted and granted only under specific agreements. For licensing inquiries or commercial use, please contact: Tim C. Lueth

Algorithm (Workflow)

This function, ezofT, is designed to extract the ez vector from a homogeneous transformation (HT) matrix, specifically a Denavit-Hartenberg (DH) matrix, and return it as a row vector.

Input Parameters

T: A 4x4 DH matrix. If not provided, the function defaults to the identity matrix eye(4).

Output Results

ez: The third column of the matrix T, specifically the first three elements, transposed into a row vector. This represents the z-axis direction of the transformation.

Algorithm Steps

Retrieve the input parameter T using the helper function getfuncparams. If no input is provided, use the identity matrix eye(4).
Extract the ez vector by taking the first three elements of the third column of T and transpose it to form a row vector.
If no output is requested (nargout==0), visualize the transformation:
- Call SGfigure to set up a figure with a range from -30 to 30.
- Use tplot to plot the transformation matrix T with a scale factor of 2 and label it as 'T'.
- Plot the ez vector using lplot, starting from the translation part of T and extending in the direction of ez, colored green, with a line width of 2, and label it as 'e_z'.

Algorithm explaination created using ChatGPT on 2025-08-18 22:07. (Please note: No guarantee for the correctness of this explanation)

Last html export of this page out of FM database by TL: 2025-09-21