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A geometric method for computation of datum reference frames

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4 Author(s)
Gou, J.B. ; Dept. of Electr. & Electron. Eng., Hong Kong Univ. of Sci. & Technol., China ; Chu, Y.X. ; Xiong, Z.H. ; Li, Z.X.

A datum reference frame (DRF) is a coordinate system used to locate and orient part features. Constructing a DRF from a set of datum features is a complicated process involving: a) specifying a valid combination and the precedence of the datum features which define the DRF; b) developing datum from datum features of the part; and c) determining the position and orientation of the DRF from the datums. We develop a geometric theory for establishing DRFs. The theory is based on the observation that a datum feature such as a plane, a cylinder or a sphere has a symmetry subgroup G0 under the action by the group SE(3) of rigid motions in R3. Thus, the configuration space of a datum feature can be identified with the homogeneous space SE(3)/G0, and the problem of datum development can be posed as a minimization problem in SE(J)/G0. We give conditions under which a datum feature qualifies to be a secondary or a tertiary datum. We present a sequential procedure that transforms the primary, secondary and tertiary datum problems as a minimization or a constrained minimization problem in the homogeneous spaces of SE(3). We develop simple algorithms to solve these problems, and give simulation results illustrating efficiency and simplicity of the approach

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Robotics and Automation, IEEE Transactions on  (Volume:16 ,  Issue: 6 )