If you are an engineering student or have a mathematics background, you must have encountered curves at some point. From simple harmonic motion curves to sine waves, to motion curves. Solidworks has an exciting feature called Equation driven curves that we can use to generate these curves from their equations; parametric or explicit.

In this example, we will examine equation driven curves in 2D and see basics of surfacing for more exciting visual results.

Let’s start with a basic simple harmonic motion curve.

x(t) = A cos (t+Փ)

where A = amplitude, measured in units of length (mm or m) = 5mm

= angular frequency = 2s^{-1}

Փ = phase shift, measured in radians = 5 radians, and

t = time, measured in seconds. We would investigate the motion from t=0 to t=5

Step 1: Jump into Solidworks, create a new part, and start sketching on the front plane. Select “Equation driven curve” (underlined red) in the sketch tab.

Step 2: Once the Equation driven curve is selected, the design tree changes to reflect more options. In the 2D environment, Solidworks allows us to choose between parametric and explicit equations. Explicit equations are when we have the dependent variable on one side of the equation, and the independent variables on the other side of the equation. In parametric equation, each geometric coordinate (x, y, z) is written in terms of an independent variable, t.

For this example, we will be using the explicit equation type. In the equation field, type out this expression we defined earlier in this post:

5*cos(2*x+5)

Then, define the end conditions, x_{1 }and x_{2} as 0 and 5*pi respectively. A sinusoidal wave can be seen in yellow on the drawing area. That is the curve from the equation. If you decide to plot a graph manually, you would end up with the same shape.

The example pretty much ends here, but if you want to take things a little bit further, you can move to step 3.

Step 3: To make things more exciting, I decided to show you how to create a surface from the equation curve we got in step 2.

Go to the Surface tab and select “Extruded surface”. If you don’t have the surface tab enabled on your interface, right-click anywhere on any tab and check the “Surface” box under tabs.

Extrude the curve to your desired length and you’re done.