Abstract
This article presents the cross-motion invariant group—CMI(3)—whose group operation is defined over unit dual quaternions such that rigid motions are cross-motion invariant; that is, the resultant translation does not depend on rotation and vice-versa. We present the main properties of CMI(3) and the differences between this group and the standard group Spin(3)⋉ℝ3 of unit dual quaternions, as well as the kinematic equations under a sequence of CMI(3) operations. Two numerical examples are presented in order to illustrate the main characteristics of CMI(3).
| Original language | English |
|---|---|
| Pages (from-to) | 1359-1378 |
| Number of pages | 20 |
| Journal | IMA Journal of Mathematical Control and Information |
| Volume | 34 |
| Issue number | 4 |
| Early online date | 11 Jul 2016 |
| DOIs | |
| Publication status | Published - 1 Dec 2017 |
Keywords
- cross-motion invariance
- kinematics
- rigid motion
- unit dual quaternion