The objective of this tutorial is to learn how to use the Maths FB. We will apply it to a design application.
The most difficult challenge with the Maths FB is to enter each equation with the correct syntax.
You must derive your own equations of course.
We will use the Maths FB to enter the parametric, kinematic equations of an Epitrochoid Curve.
Epitrochoid Curve definition: '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 see we must 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 at the centre of the point and then add a Cam to the machine frame. |
If the velocity equations are not correct, the plot of 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.
It is possible to do this tutorial very quickly with a Gear-Pair (See Here). However, in this tutorial, we imagine we do not have the Add Gear-Pair tool. |
As another simple example, I have added Lissajous Figures/Curves.