Math FB
As you will see, the most difficult challenge with the Math FB is to enter each equation with the correct syntax.
In this tutorial, we give you the equations that you need to enter in the Math FB. You normally derive your own equations, of course.
This Tutorial
You enter the parametric and kinematic-equations into the Math FB to plot an Epitrochoid-Curve. Epitrochoid Curve: the curve of a point within the radius of a circle, where that circle rolls without slipping around the outside of a different circle that is fixed to the machine frame. You enter the: 1.Position Equations - to move the Point along the Epitrochoid-Curve. If the position equations are not correct, the Point will not move along an Epitrochoid-Curve. 2.Velocity Equations - to add a Follower-Roller to the Point (that moves along the Epitrochoid Curve) and then add a 2D-Cam to the machine frame. If the velocity equations are not correct, the contact between the Follower-Roller and the Cam-Profile is also not correct. 3.Acceleration Equations - to plot the Radius-of-Curvature for the Cam-Profile. If the acceleration equations are not correct, the plot of the Radius-of-Curvature is also not correct. Bonus: Lissajous Figures/Curves is another simple example of how to use the Math FB to plot parametric curves. |
Note: You can also use a Gear-Pair (see here) to plot an Epitrochoid-Curve. Because the Gear-Pair is kinematically-defined, we calculate for you the Position, Velocity, and Acceleration values for the Epitrochoid-Curve. |
Other important applications 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 ; use the Euler-Savary equation in the Math FB to find and use the Inflection Circle. |
Math FB