Geometric modeling modules

Product: Siemens NX

Geometric modeling, the study of virtualization of design in computer, is the fundamental skill for mechanical engineers. In an ever-competitive environment, aligning education with employer’s needs is the priority of classroom work. Students not only need to know how to create virtual model in CAD software, but also need to know how the geometry is created through several inputs. Because employers want creative employees rather than button pushing robots; at the same time, employees want strong fundamental knowledge to reinforce their competitiveness rather than superficial stuff.

Recent development in computer technology, especially CPU, GPU, RAM, have pushed the CAD modeling into more and more fancy style in the past two decades. But, the fundamental knowledges of geometric modeling never change, they are the rock which the fancy CAD GUI built on, such as the transformation of geometry and construction of curve and surface with points and vectors.

In recent days, most classes on geometric modeling focus on teaching students how to use one specific CAD software, which will eventually drive students into button pushing robots. On the other side, teaching students with both theoretical knowledges about geometric modelling and hands-on skills of CAD software, offer students with much wider scope view about the geometric modeling process which will eventually increase students’ competitiveness.

Department of Mechanical and Material Engineering in University of Cincinnati offers two classes in geometric modeling: Engineering Design Graphics which focus hands on skills on GUI drawing with NX, CAD for Manufacturing which partially focus on the theoretical knowledges about the construction of geometry in computer. Professor Sam Anand is the lecturer of CAD for Manufacturing. To improve students’ understanding process, the digital twins of the theoretical methods taught in classroom were created. These digital twins include several NX based geometric modeling applications which were created in his group, includes Object Rotation module, Object Reflection module, Object Scaling module, Hermite Curve Design module, Hermite Surface Design module, Bezier Curve Design module and Bezier Surface Design module. With the help of these digital twins, students can get a straight forward view about the influence of each parameters to the final result, such as the shape and normal vectors of surfaces. Furthermore, students can use these digital twins to validate their hand calculation of their homework assignments. Ultimately, these digital twins improve students’ competitiveness in future’s job-hunting.

The objective of this module is to create digital twin of the rotation method and demonstrate the rotation of any given body about specified arbitrary axis with all the intermediate steps leading to final transformation. The outcome of this module is that students can visually correlate 3D geometry transformations as shown in Figure 1 with underlying mathematical formulation and reinforce their understanding. 

The objective of this module is to create digital twin of the reflection method and demonstrate reflection of a geometry object about a plane specified by a point and normal, as Figure 2. The outcome of this module is to let students visually see the reflection process and the coordinates of the vertex at current location verse its original location. With the help of this digital twin, students can validate their hand calculation process and help them on both theoretical understanding and line algebra. 

The objective of this module is to create digital twin of the geometric scaling methods (both uniform and non-uniform) and demonstrate the shape and size change of the part, as Figure 3. The outcome of this module is helping students to understand scaling of various complex part and validate their assignments results through the digital twin.

The object of this module is to create the digital twin of Hermite curve method and plot Hermite curves by varying user inputs and calculate tangent vector at any parametric value on the Hermite curve., as Figure 4. The outcome of this digital twin module is to help students learning the impact of changes in parameters (start point, end point, tangent vectors) on the shape of curve. Students can visually see the shape of the curve and get tangent vector of any point on the curve. This digital twin offers them an easy way to check their knowledge understanding and hand calculation.

The objective of this module is to create the digital twin of the theoretical method of generate bicubic Hermite surface with normal vectors, tangent vectors and modify surface based on user inputs, as Figure 5. The outcome of this module is to increase the students’ understanding of the behavior of bicubic Hermite surface respect to the change of surface parameters (control points, tangent vectors, twist vectors). The module can output and display the coordinate of any point on the surface and its unit normal vector based on the U-W value, this can help students to crosscheck whether their calculation is right or wrong and get stright forward idea about how the surface looks like.

The objective of this module is to create digital twin of the theoretical method of Bezier curve construction and plot Bezier curves along with its control points, control polygon, tangent vector at a specific location and convex hull, as Figure 6. The outcome of this module is to help student to study the properties of a Bezier curve and the impact of parameters on the shape of the curve. With the visualization of all the parameters through this digital twin, students can get a very straight forward understanding of the methods.

The objective of this module is to create the digital twin of the method to construct a Bi-cubic Bezier surface with given control points and plot it, as Figure 7. The outcome of this module is to help students to understand how the control points influence the shape of the surface. As shown in figure, the module can display the coordinate and normal vector of any point on the surface, this is helpful for students to validate their assignment results because this digital twin can offer a straight forward visualization of the surface and its normal vector of any give location.

NX API is a powerful tool for visualization of any geometric shape. Because these geometric modelling are so basic that most people neglect them and eventually become button pushed robots. With help of NX API and powerful NX visualization capability, the digital twins of the methods for geometric modeling were created, and can be executed step by step. Through this process, students get more steady and robust understanding of the theoretical fundamental knowledges, in conjunction with the hands-on skill from Engineering Design Graphics class, it yields competitive advantages for students on the future product design and job-hunting.