View Full Version : Euler angles

Herman J. Woltring
01-20-1992, 03:17 AM
Dear Biomch-L readers,

Further to my recent posting on Euler's angle and axis, I have obtained the
English translation of Liegeois' book:

Alain Liegeois, Performance and Computer-Aided Design
Vol. 7, Robot Technology Series
Hermes Publishing, London - Paris - Lausanne 1985

Following Section 1.4.4 on Euler's Angle and Axis, the next two sections
are concerned with Euler's Angles and Tate/Bryant (i.e., Cardanic) Angles,
i.e., those that describe three successive rotations about the axes of either
a fixed or moving, Cartesian co-ordinate system from a reference attitude (I)
to a current one (R).

Interestingly, the author states about *both* types of angles: "In general,
(these) angles are not easy to measure and it is better to limit their use to
the cases where the three rotations are actually carried out: for example when
the end effector of a Cartesian manipulator (ie an arm with three transla-
tions) is constructed such that the three successive rotations correspond to
linear functions of (these) angles." He does not motivate this preference,

While the calculus of Eulerian and Cardanic angles is relatively simple once
we have an attitude matrix via photogrammetric, ultrasonic, or electromagne-
tic means, human movement is fortunately not confined to actually carrying
out these successive rotations when getting from I to R, or worse, from R1
to R2 ...

Herman J. Woltring, Eindhoven/NL
are notorious for their perseverance! :-)