# How to draw the cavity of the housing of a Wankel rotatory engine in AutoCAD/GStarCAD

The Wankel engine is a type of internal combustion engine using an eccentric rotary design to convert pressure into rotating motion.

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The housing of a Wankel engine can be mathematically defined as a pair of parametric equations for X and Y, for the formula parameter varying from 0.0 to 2*PI. The formulas can be rewritten into a calculator-like form, as follows.

X = c1*cos(r2d(3*u)) + c2*cos(r2d(u))
Y = c1* sin(r2d(3*u)) + c2*sin(r2d(u))
The parameters for this example are:
c1 = 10.0
c2 = 60.0
u = 0.0 to 2*PI

Since the oval-like housing of a Wankel engine is an epitrochoid, this can also be done with the Spirograph function of LitioLAB.

The Spirograph parameters of this example:

D = 40.0 Turns = 3
C = 1.0
R = -30.0
A0 = 0.0
L = 60.0
B0 = 0.0
N = 1000

And since these graphs are polylines, they can be extruded and used to generate AutoCAD solids for further processing and eventually, for CNC machining, or 3D printing.

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