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Orientation Representation and the advantages of the tilt and torsion angles


Dr. Ilian Bonev < bonev@gmc.ulaval.ca >
Laval University

March 28, 2003 at  11:30 AM
357 Macdonald Eng.

Many challenging problems in spatial kinematics are related to orientation representation, typically based on Euler angles. Paradoxically, very little attention is paid to the parametrization of rotation in the literature. Few are aware of the existence of twelve different Euler-angle conventions and the multitude of interpretations of them. This often leads to poor understanding and incorrect visualization of motion in 3D. In response to this situation, the first goal of this presentation is to demystify the nature of Euler angles. An unorthodox variant of Euler Angles has recently been proposed. The second goal of this presentation is to shed light on the various advantages of these so-called Tilt and Torsion (T&T) angles.

The use of the new angles greatly facilitates the analysis of a special class of three-axis spatial parallel mechanisms with mi DOF: two rotations and one translation. It is shown that for this class, one of the angles is always zero. Hence, using the new angles leads to the simplest kinematic model and reveals the exact type of rotational DOFs. Thus, the common misconception that such mechanisms provide pure pitch and roll is refuted.