Euler angles: conversion of arbitrary rotation sequences to specific rotation sequence

摘要

Euler angles have been used to describe the orientation of objects in two-dimensional and three-dimensional spaces since its formulation by Leonhard Euler. Many applications intended to represent the rotation of a body have been developed on the basis of Euler angles. Two-dimensional rotations are combined in sequence to represent three-dimensional rotations. Because there are three axes in a three-dimensional Euclidean space (X, Y and Z), 12 rotation sequences in three dimensions are possible: XYZ, XZY, YXZ, YZX, ZXY, ZYX, XYX, ZYZ, ZXZ, YXY, XZX and YZY. Each rotation sequence yields different results, and different applications implement a different rotation sequence. Thus, conversion between different rotation sequences becomes essential to make applications developed in different rotation sequences compatible with each other. In this paper, a new method is introduced to convert arbitrary rotation sequences to a specific rotation sequence of choice. A sample program is also developed in a MATLAB-Simulink environment to demonstrate the use of the new method in converting an arbitrary Euler rotation sequence to the specific Euler rotation sequence of XYZ. A six-degrees-of-freedom animation block is used in the program to aid users to graphically see the rotation of a body in three-dimensional space. Copyright (c) 2013 John Wiley & Sons, Ltd.