Math FB
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. The Epitrochoid Curve is the curve of a point that rotates with a circle that 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 - we can add a Follower-Roller to the Point (that moves along the Epitrochoid Curve) and then add a 2D-Cam to the Base-Part. If the velocity equations are not correct, the contact between the Follower-Roller and the Cam-Profile is also not correct. 3.Acceleration Equations - when theto 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 automatically for you the Position, Velocity, and Acceleration values, to give 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