Add a Cam to the Epitrochoid Curve
We will show the difference between a Cam when we do not, and then we do add the Velocity Equations to the Maths FB.
A Cam is a good example, because we need the velocity of the Cam-Follower relative to the Cam before MechDesigner can find the correct Cam track coordinates.
We must symbolically differentiate the X and Y coordinate equations, given in Step 18.1, to find the velocity equations.
Remember, MechDesigner does these calculations automatically with a Gear-Pair. We are doing this with a Maths FB only as an example of how to use the Maths FB.
Add a Cam-Track; BUT the Velocity Equation is not in the Maths FB
The two Sliders move with the parametric equations to generate the the Epitrochoid Curve But, can we add a Cam and get the coordinates Cam-Coordinates? |
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Add a Cam-Follower to the Piggyback Slider 1.Edit the Piggyback Slider Part 2.Add a Circle to it - typically at the 'Origin' of the Part 3.Exit the Part-Editor 4.Add a Profile to the Circle
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Add a 2D-Cam 1.Click Add 2D-Cam 2.Select the Base-Part as the 'Part' 3.Click the new Cam-Follower
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Cycle or Move the Master Machine to a different Machine Angle You can see the Cam does not follow the Cam-Follower. The Cam is not correct. |
Add the Velocity Equation to the Maths FB
You need to differentiate the Parametric Curves for the Epitrochoid Curve with respect to t. To make your life easier, here are the two parametric equations for the velocity components: •Xvel = -(a+b)*sin(t) - h*((a+b)/b)*cos((a+b)/b)*t) •Yvel = (a+b)*cos(t) - h*((a+b)/b)*sin((a+b)/b)*t) These are written in the Maths FB as: •-(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)) |
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These are the 6 equations in the Maths 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 of X & Y respectively. |
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Review the 2D-Cam You can see the Cam is correct. |
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