<< Click to Display Table of Contents >> Navigation: Getting Started Tutorials  MechDesigner > Tutorial 18: Maths FB > Step 18.4: Lissajous Figures 
We only need the position equations to plot the Lissajous Curve.
These are simple parametric curves.
This topic here is only because they look nice to me!
We will use parametric equations in the Maths FB to calculate the X,Y coordinates of the Lissajous Curve. One equation will calculate the Xaxis coordinates. Another equation will calculate the Yaxis coordinates. 
The parametric equations for the epitrochoid family of curves are: •x = cos(a*t) •y = sin(b*t) Parameters and Variables a = indicate the frequency of the Slider along the Xaxis b = identifies the frequency of the Slider along the Yaxis t = the independent variable: 0 to 360 (or 2*pi) Inputs: three parametricconstants: a, b, and the independent variable, t Outputs: two: x and y. 
The parametric equations, above, give the family of Lissajous Curves. This means if you change a 'parametricconstants' (a, b), you will plot a different Lissajous Curve. 
We will use Option 2. InputConnectors We need three inputconnectors: three parameters (a, b) and one variable (t) 1.Doubleclick the Maths FB to open a Maths FB dialogbox 2.Click the Add Input button three times to add three inputs to the Maths FB 3.Click the 'Update' button at the bottom of the Maths FB dialogbox 

OutputConnectors We need two outputconnectors to give the data separately to the X and Yaxes 1.Doubleclick the Maths FB to open the Maths FB dialogbox 2.Click the Add Output button two times to add two outputs to the Maths FB in the graphicarea The units for the outputchannel is dependent on the Output Data Type you specify. 3.Set the Units to Linear Units 4.Click the 'Update' button at the bottom of the Maths FB 
Equations for the Position (Displacement) for the two outputs. The Lissajous equations for the X and Y coordinates are given here again: The parametric equations for the epitrochoid family of curves are: •x = cos(a×t) •y = sin(b×t) We must rewrite these for the Maths FB. Each parameter or variable at the input is represented by: p(0) = a p(1) = b p(2) = t 

Parametric Equations for Lissajous Curves. 
1.Enter the equations very carefully  see the image to the left. Add the righthand side of these equations. X = cos((p(0)× 1000)× p(2)) Y = sin((p(0)× 1000)× p(2)) 2.Select the Output Data Type as Linear Coordinates 3.Click Update button to confirm changes. Note: The parametric constants (p(0) and p(1)) are multiplied by 1000. This is because the distances are in SI units in the Maths FB, which means 5 (outside) becomes 0.005 (inside). A more typical value is 5. 
We give the X and Y position coordinates to two outputconnectors. We can then use a wire to: •connect the output for the X equation to move a horizontal slider •connect the output for the Y equation to move a vertical Piggyback Slider, Then, a TracePoint in the Piggyback Slider will plot the Lissajous Figures  when the equations are correct! 

The Mechanical model in MechDesigner Because we will use parametric equations, it is very convenient to use Piggyback Sliders 

The 'Variable' Inputs to the Maths FB We will use MotionDimensions for Slider as the Parametric Constant The BaseValue of each MotionDimension FBs can be define a, b, or h . The Linear Motion FB can be used as the angle, t, as the independent variable 

The Maths FB  input variable connectors The Maths FB has four inputs to represent: •a ... the radius of the fixed circle •b ... the radius of the rolling circle •h ... the radius of the point from the center of the rolling circle •t .... angle of the center of the rolling circle from 0 to 360º 

Maths FB  output variable connectors The Maths FB has two outputs: •x ... the horizontal position of the point, P, at machine angle, t, relative to the center of the fixed circle •y ... the vertical position of the point, P, at machine angle, t, relative to the center of the fixed circle 

Video of Lissajous Curves with changing parameters. 
The TracePoint of the Piggyback Slider When the outputs from the Maths FB are connected to the X and Y Piggyback Sliders, and we add a TracePoint to to show the Path, then you can see the Lissajous Curve. The video shows a number of Lissajous Curves. I have put the parameters 'a' and 'b' in a DesignSet to make them faster and easier to edit. 