Consider a rigid body B with a fixed point O. Rotation about the fixed point O is the only possible motion of the body. We represent the rigid body by a body coordinate frame \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$B\left ( O,x,y,z \right ) $$ \end{document}, which rotates in another coordinate frame \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$G\left ( O,X,Y,Z\right ) $$ \end{document}. In this chapter, we develop the rotation calculus based on transformation matrices to determine the orientation of B in G and relate the coordinates of a body point P in both frames.
Two Cartesian coordinate frames B and G with a common origin are related by nine directional cosines of a frame in the other. The conversion of coordinates in the two frames can be casted in a matrix transformation. Any relative orientation of B in G can be achieved by three consecutive principal rotations about the coordinate axes in either frames, B or G.
This chapter is about Rotation Kinematics in which we learn the following two objectives:
To learn how to determine the transformation matrix between two Cartesian coordinate frames B and G with a common origin by applying rotations about principal axes of either frames.
To decompose a given transformation matrix to a series of principal rotations.
Rotation Kinematics
Theory of Applied Robotics ; Kapitel : 2 ; 37-89
2021-12-08
53 pages
Aufsatz/Kapitel (Buch)
Elektronische Ressource
Englisch
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