NXOpen

The objective was to automate the process of generating parametrized geometry in CAD. In Siemens NX, expressions were created to control position, orientation, and scale of each geometric feature, allowing full geometry to be regenerated from a single parameter.

Expressions are defined for position, orientation, and scale of every control point used to loft, sweep, or extrude shapes, as well as to draw airfoil cross-sections.
Shape-specific parameters are layered on top, for example, the nosecone series constant, chord length, or twist angle.
Python writes .exp files that NX imports directly via Expressions → Import Expressions, enabling fully scriptable parameter sweeps.

Geometry Transformations

Each point passes through scale → rotate → translate before being written as an NX expression:

Position vector

$$p = \begin{bmatrix}x\\y\\z\end{bmatrix}$$

Scale

$$p_s = \begin{bmatrix}s_x&0&0\\0&s_y&0\\0&0&s_z\end{bmatrix}p$$

Rotate

$$p_r = R\,p_s, \qquad R = R_z(\psi)\,R_y(\theta)\,R_x(\phi)$$

Translate

$$p' = p_r + t, \qquad t=\begin{bmatrix}x_0\\y_0\\z_0\end{bmatrix}$$

Combined

$$p' = R\,S\,p + t$$

Parametric Nosecone Profiles

Four nosecone families are parametrized. Each is fully determined by base radius $R$, length $L$, and a shape constant.

Haack series

$$x(\theta)=\tfrac{L}{2}(1-\cos\theta)$$ $$y(\theta,C)=\frac{R}{\sqrt{\pi}}\sqrt{\theta-\frac{\sin 2\theta}{2}+C\sin^3\!\theta}$$

Elliptical

$$y(x)=\frac{R\sqrt{x(2L-x)}}{L}$$

Parabolic series

$$y(x)=R\,\frac{2\!\left(\tfrac{x}{L}\right)-K\!\left(\tfrac{x}{L}\right)^{\!2}}{2-K}$$

$0 \le K \le 1$

Power series

$$y(x)=R\!\left(\frac{x}{L}\right)^{\!n}, \quad 0\le x\le L$$

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