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Swept volumes: void and boundary identification



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PII S0010 4485 98 00054 2 Computer Aided Design Vol 30 No 13 pp 1009 1018 1998 Copyright 1999 Elsevier Science Ltd All rights reserved Printed in Great Britain 0010 4485 99 see front matter Swept volumes void and boundary identification Karim Abdel Malek1 Harn Jou Yeh2 and Saeb Othman3 detection of robotic manipulators it is equally important to define the exact envelope of each moving link especially those trajectories that are due to a multiple of parameters This paper presents a new method for the identification of boundary curves and surface patches of a swept volume of any parameter Although the problem has been treated to some extent in the past the proposed method is based on mathematical criteria derived from acceleration analysis adapted from kinematics A broadly applicable formulation and its accompanying algorithm are presented The first introduction of a rigorous formulation for calculating critical curves from a moving solid was introduced by Wang and Wang 22 Sweeps involving a larger number of parameters have become necessary in CAD systems where subsequent sweeps yield more complex shapes Swept volumes of higher order parameters based on Jacobian rank deficiency conditions have been presented by the first two authors 1 and was shown to handle multiple sweeps resulting in more than three parameters Work presented by Hu and Ling 12 13 introduces the swept volume generated by natural quadratic surfaces This work uses instantaneous screw axis motion used in kinematics to determine the sweep of a surface implicitly described but does not address the existence or the identification of voids in the workspace Also using the envelope theory Martin and Stephenson 18 evaluated the swept volume of a three dimensional object moving along an arbitrary path Although they addressed self intersection of the envelope they did not address the identification of boundaries to voids Kieffer and Litvin 15 developed an algorithm for the determination of all surfaces and



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