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Published in:
2013 | OriginalPaper | Chapter
Screws and Robotics for Metrology
Authors : Joseph K. Davidson, Samir Savaliya, Jami J. Shah
Published in: Advances in Mechanisms, Robotics and Design Education and Research
Publisher: Springer International Publishing
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The pseudoinverse of a rectangular matrix of modified screws is used to compute the least-squares fit of a set of points that have been measured along a line-profile. Tolerances on line profiles are used to control cross-sectional shapes of parts, such as turbine blades. The specified profile is treated as a moving platform of a hypothetical, redundant, and planar in-parallel-actuated robot, and all the measured points are presumed to be fixed in it. The locations of the linear actuators are represented with screw coordinates, and these are arranged in a matrix equation that relates the three small displacements of the platform to the corresponding deviations (treated as small displacements) of the measured points.