Abstract
In this paper, a novel approach for solving angular constraints based on spherical geometry is presented. This method can determine the orientation of a set of parts given the mating constraints between them with the decoupled property of the angular and distance constraints. The combination of angular constraints can be categorized into two cases: operable and un-operable. The former can be solved efficiently by introducing simple spherical surface reasoning. The latter is solved by employing spherical surface four-linkage mechanism. In this way, the rotation transformation matrix of the dependent rigid body is worked out. This new method has the advantages over numerical approach and symbolic approach of clear geometric solubility, geometric operability, and avoiding simultaneously solving all the constraint equations in the model. Moreover, it is an easy and efficient way to determine whether there exist redundant constraints. The presented algorithm has been successfully implemented in our assembly prototype system, InteVue.
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This research was supported in part by the National ‘863’ High-Tech Project of China under grant 2003AA001031.
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Shi, ZL., Chen, LP. An angular constraints solving approach for assembly modeling based on spherical geometry. Int J Adv Manuf Technol 32, 366–377 (2007). https://doi.org/10.1007/s00170-006-0415-8
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DOI: https://doi.org/10.1007/s00170-006-0415-8