<< Click to Display Table of Contents >> Navigation: Getting Started Tutorials - MechDesigner > Tutorial 18: Math FB > Step 18.2: Velocity: Add a Cam to the Epitrochoid Curve |
We will show the difference between a 2D-Cam when:
•We do enter the Velocity-Equation correctly
•We do not enter the Velocity-Equation incorrectly.
A 2D-Cam is a good example, because MechDesigner must know the velocity of the Cam-Follower relative to calculate the correct Cam-Coordinates.
In this Tutorial Step, we symbolically differentiate the X and Y position equations, given in Step 18.1, to find the velocity equations.
We will enter those equations into the Math FB
MechDesigner does these calculations automatically with a Gear-Pair. We are doing this as an example of how we can use the Math FB.
Symbolically differentiate the X and Y Parametric Equations for the Epitrochoid-Curve with respect to Θ. These are the two Parametric Equations for the X and Y Velocity Components: PXvel = -(a+b)*sin(Θ) + h*((a+b)/b) * sin((a+b)/b)*Θ) PYvel = (a+b)*cos(Θ) - h*((a+b)/b) * cos((a+b)/b)*Θ) As before we must replace: a with p(0) ; b with p(1) ; h with p(2) ; Θ with p(3) In the Math FB they are: - (( p(0)+p(1))*sin(p(3))) + p(2)*(((p(0)+p(1))/p(1)))*sin(((p(0)+p(1) ) / p(1)*p(3))) ((p(0)+p(1))*cos(p(3))) - p(2)*(((p(0)+p(1))/p(1)))*cos(((p(0)+p(1))/p(1)*p(3))) |
![]() Position and Velocity Equations |
These are the 6 equations for the two output-connectors As entered the Math FB: •Equations 1 & 2: Position and Velocity of the X -axis •Equations 4 &5: Position and Velocity for the Y-axis •Equations 3 & 6: Default - acceleration for X-axis & Y-axis respectively - not yet entered. |
Cut and paste the Parametric-Equations into the Math FB dialog-box.
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The two Sliders move with the parametric equations to generate the the Epitrochoid Curve But, can we add a 2D-Cam and get the Cam-Coordinates? We will find that if the Velocity equations are not correct, the Cam will not be correct. |
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Add a Cam-Follower to the Y-Slider of the Piggyback Sliders
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Add a 2D-Cam
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Look closely at the Cam and the Cam-Follower.
You can see the contact between the 2D-Cam and the Cam-Follower. The 2D-Cam is not correct.
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Check and correct the Velocity Equations in the Math FB. Now, the 2D-Cam is correct. Now you can get the Cam-Coordinates in the usual way. |