As we will see, the most difficult challenges with the Math FB is to enter each equation with the correct syntax.
In this tutorial, we will show the equations you need to enter. You normally derive your own equations, of course.
We will use the Math FB to enter parametric and kinematic equations of an Epitrochoid Curve.
Epitrochoid Curve: the curve that is generated by a point that is within the frame of a circle, where that circle rolls without slipping around the outside of a circle that is fixed to the machine frame.
We will enter the:
1.Position Equations - to plot a Point that moves along the Epitrochoid Curve.
If the position equations are not correct, the curve will not be correct.
2.Velocity Equations - to add a cam-follower to the Point t(hat moves along the Epitrochoid Curve) and then add a Cam to the machine frame.
If the velocity equations are not correct, the contact between the Cam-Follower and the Cam is not correct.
3.Acceleration Equations to plot the Radius-of-Curvature for the Cam.
If the acceleration equations are not correct, the plot of the cam's Radius-of-Curvature is not correct.
I have added Lissajous Figures/Curves as another example of using the Math FB to generate parametric curves,
Note: You can also use a Gear-Pair (see here) and 2D-Cam to give the same results as this tutorial. However, in this tutorial, we imagine we do not have these elements.
Other important application examples include:
Add two(2) or more Motions : e.g. Mod-Sine + Velocity Ramp. This may be useful to develop a transfer to a moving conveyor.
Mechanism-Synthesis - e.g. Three Position Synthesis ; or use the Euler-Savary equation to find and use the Inflection Circle.