<< Click to Display Table of Contents >> Navigation: Getting Started Tutorials  MechDesigner > Tutorial 18: Math 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 Math FB to calculate the X,Y coordinates of the Lissajous Curve. The parametric equations for the Lissajous Curve of curves are: x = cos(a*t) y = sin(b*t) If you change a parametricconstants (a, b), you will plot a different Lissajous Curve. Parameters and Variables a = the frequency of the motion along the Xaxis b = the frequency of the motion along the Yaxis t = the independent variable: 0 to 360 (or 2*pi) Three(3) Inputs: a, b, and t Two(2) Outputs: x and y. 
InputConnectors We need three inputconnectors: three parameters (a, b) and one variable (t) 1.Doubleclick the Math FB to open a Math FB dialogbox 2.Click Add Input button to add three inputs to the Math FB 3.Click the Update button 

OutputConnectors We need two outputconnectors to give the data for the X and Yaxes 1.Doubleclick the Math FB to open the Math FB dialogbox 2.Click the Add Output button to add two outputs from the Math FB The units for the outputchannel is dependent on the Output Data Type. 3.Set the Output Data Type to Linear Coordinates 4.Click the Update button 
Equations for the Position (Displacement) for the two outputs. The Lissajous equations for the X and Y coordinates are given here again: •x = cos(a×t) ..... Equation 1 •y = sin(b×t) ..... Equation 2 We must rewrite these for the Math FB. Each parameter or variable at the input is represented by: p(0) = t p(1) = a p(2) = b 

1.Enter the equations very carefully  see the image to the left. •Equation 1 = cos((p(1)× 1000)× p(0)) •Equation 2 = sin((p(2)× 1000)× p(0)) 2.Click Update button to confirm changes. The output a Sin and a Cos functions each have a range of ±1 unit (a minimum of 1 and a maximum of 1) Inside the Math FB, all parameters are converted to SI units. Thus a Range of 1 is a range of 1 meter. Outside the Math FB, the range of ±1m will be a range of ±1000mm at the X and Yaxis Piggyback Sliders. 

Thus, we may need to scale the output to reduce its range. To Scale the Range we can use •Add Gearing FBs. For example, a Gearing Ratio of 0.1 will give a range of ±100 at the Xand Yaxis Sliders or •Edit the Equations in the Math FB. For example, we divide each equation by 10 to give a range of ±100 at the Xand Yaxis Sliders <<< We have now add /10 to the equations to give a Slider Range of 100mm 
The Top Output Connector is for the Xaxis motion The Bottom OutputConnector is for the Yaxis motion. We must add two Sliders, in the Piggyback configuration. We can then •connect the Top connector to the MotionDimension to move the horizontal Slider •connect the Bottom connector to the MotionDimension to move the vertical Slider. We add TracePoint it the n the Piggyback Slider will plot the Lissajous Figures  when the equations are correct! 

The Mechanical model in MechDesigner Because we will use parametric equations for X the Yaxes, we will use Piggyback Sliders. 

The Math FB  input connectors •t .... the angle of the function from 0 to 2*pi  from the output of a LinearMotion FB •a ... the frequency of oscillation of the Xaxis  from a Gearing FB (Add after GearingRatio) •b ... the frequency of oscillation of the Yaxis  from a Gearing FB (Add after GearingRatio) Note: Outside the Math FB the Range of t is 0  360 degrees Inside the Math FB the Range of t is 0  20*pi radians 

Math FB  output variable connectors The Math FB has two outputs: •x ... the horizontal position of the XSlider •y ... the vertical position of the YSlider 

The TracePoint of the Piggyback Slider We can add a TracePoint to show the Path, of the Yaxis Slider as that combines the motion of the Xaxis and the Yaxis The values of p(1) = a = 2 p(2) = b = 7 