• The Pure and Applied Mathematics
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• v.14 no.3
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• pp.191-196
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• 2007

The main components in the generalized Mandelbrot sets are under a theoretical investigation for their parametric boundary equations. Using the boundary geometries, a fast construction algorithm is introduced for the generalized Mandelbrot set. This fast algorithm definitely reduces the construction CPU time in comparison with the naive algorithm. Its graphic implementation displays the mysterious and beautiful fractal sets.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2005.06a
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• pp.1652-1655
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• 2005

All teeth on the cycloidal plate gear exist in the contact motion with rollers and the forces are interacted between roller gears with cycloidal plate gears. So, the contact forces and friction forces must be required to improve the accuracy in design procedures of cycloidal speed reducers. This paper presents a force analysis considered the friction effect approach derived by static force equilibrium condition, geometrical adaptation, instant velocity center method and relative velocity method. Finally, the paper develops CAD-program for the construction of the design automation using the proposed method.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2004.10a
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• pp.1398-1401
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• 2004

This paper proposes a new approach for the shape design of the rotating outer-ring type epicycloid plate gear by using instant velocity center. First, this method defines the instant velocity centers for rotating outer-ring type epicycloid plate gear and calculates the contact angles and the contact points by using the geometric relationships and the kinematic properties of the reducer. Second, it generates the full shape of the cycloidal plate gear. Finally, the paper develops CAD-program for construction of the design automation using the proposed method. This CAD-program is developed to have the functions of the friendly user interface and the simulation of the real operation for the cycloid reducer.

• Journal of applied mathematics & informatics
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• v.16 no.1_2
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• pp.221-229
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• 2004

It is known that the parametric boundary equation for the main component in the Mandelbrot set represents a cardioid. We derive an epicy-cloidal boundary equation of the main component in the degree-n bifurcation set by extending the parameter which describes the cardioid in the Mandelbrot set. Computational results as well as some useful properties are presented together with the programming source codes written in Mathematica. Various boundaries are displayed for $2\leqn\leq7$7 and show a good agreement with the theory presented here. The known boundary equation enables us to significantly reduce the construction time for the degree-n bifurcation set.