Curves with equations (EQT) are widely used to create surfaces of machine parts in machine manufacture. They make beautiful surfaces that appeal to consumers. These surfaces may be free surfaces or may be assembled surfaces. If the surfaces are assembled, they must be made accurately. For example, convolute of a circle is the profile of spur gears, as well as cycloid. There are some ways to draw curves. We can draw curves by using algebra or geometry. We also draw curves by using mechanical structures. If we use algebra to draw curves, we must determine the coordinates (COD) of the points of the curve and connect them according to its rules. The more points you should find, the more accurate the curve will be. Curve drawn by these methods is sporadic and consuming of time. Moreover, some curves still exist dead points. It is not easy to determine the COD of its. Whereas, if we use a geometric model to create structures to draw a curve, we will draw every point of the curve precisely and smoothly in a very short period of time. The author will analyze a simple geometric model that helps us create a structure that can draw many curves quickly and accurately.