A large number of subdivision theories were widely used in geometric design and
computer graphics for shape design, animation, multi-resolution modelling and many
other engineering applications. With many similar properties to B- spline, it allows
the design with efficient, hierarchical, local, and adaptive algorithms for modelling,
rendering and manipulating free-form objects of arbitrary topology.
By using the Loop subdivision (Loop C 2005), the data points given in triangular
mesh with arbitrary topology, could be approximated with many advantages as sim-
plicity, high speed, high scalability and generality (Yu N. 2008). The algorithm can be
realised with a given triangular/ quadrilateral mesh as a control net of a Loop/
Catmull-Clark subdivision surface.
Applying Loop subdivision into SBG machining model is an original try and some
visual experiment results will be shown in following sections.
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3.1 Separate SSM Models for Gears and Pinions
On the basis of (Suh S.H.2001), gear and pinion tooth surface models were developed
and shown in Table1 and 2 respectively. The influence factors u, w and δb1, are
shown in Fig.1. By changing u from 0 to Umax, and w from the value of large section
to small section, the spherical involute curve for straight bevel tooth were obtained,
and then after a rotation of an angle named o, the design model for SBGs was
constructed. Umax is a for-loop controlling factor for generating design surfaces, its
definition is shown in equation-1. Since functions for only one pinion surface were
represented in (Suh S.H. 2001), the more detailed introduction in this paper will give
more convenience for understanding SBGs CAD/CAM model.
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