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For numerical orientation workspace analysis, a finite partition of the orientation workspace in its parametric domain is necessary. Among various parameterization methods for rigid-body rotations, it has been realized that the Euler angles, the tilting-and-torsion (T&T) angles, and the exponential coordinates are appropriate for finite partition. With these three parameterization methods, the...
Orientation workspace analysis is a critical issue in the design of robot manipulators, especially the spherical manipulators. However, there is a lack of effective methods for such analysis, because the orientation workspace of a robot manipulator is normally a subset of SO(3) (the special orthogonal group) with a complex boundary. Numerical approaches appear more practical in actual implementations...
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