# Analytic equations to make algorithm of 3D printer

I have a project in the 3D printing. the aim of the project is to realize the control of the 3D printing.

the type of the printer is a printer with cables.

the problem seems to have some development both in mechanical and robotics engineering.

first of all, as our tutor said, we should find the dynamical and the geometrical equations and from those equations, we can find the algorithm to control the system of the 3 D printing.

Well, my question is particularly about the dynamical equations in 2D as you can see in the picture above.

the idea is to find equations of : - L1 and L2 in terms of xa and ya : which I already found as you can see in the picture - xa and ya and teta in terms of L1 and L2: which I cannot find ! I would lilke you to help in this point.

thank you in advance And here, I add the dynamic equations and I would like you to check if it is ok • Also, I would like to ask you some questions about the dynamical equations. as I am new in this forum, should I post my question in another post?. (the reason why I didn't ask you in the comment, because I want to share a picture where there is the mathematical calculations, as I cannot share a picture in the comment) – zaatifi Mar 19 '16 at 9:28
• Zaatifi: Thank you for adding a picture to your question. If the dynamic equations you mention are not directly related to this question, I suggest you ask about those in a new question. Also, if the question is not directly relatable to 3D-printing, you might want to ask it in either the Mathematics or Robotics sites instead. You can find links to other Stack Exchange sites from the menu in the upper left corner of this page. – Tormod Haugene Mar 19 '16 at 15:03
• In addition, the title of a question is the first thing any other users will see. Would you consider making the title more specific? Perhaps add what kind of printer and what kind of equations the question is about. That will make it easier to differentiate from other questions in the future. – Tormod Haugene Mar 19 '16 at 15:07
• thank you very much for your guidance. I still have 2 questions to be familiar with this nice forum. 1. how can I modify the title of this post ? 2. my new question about dynamical equation concerns this post and concerns the 3D printing for making houses, and I want to share this question in a picture in comment, but I notice I cannot add a picture in comment, how should I do? thanks for advance – zaatifi Mar 19 '16 at 18:57
• A fairly common way to add additional information to your question in response to other users answers, is to edit your own question, and add a section at the bottom with a header perhaps saying "Update: ...", and so on. This way, you can add extra images, code snippets, and so on. To edit your question, press the edit-link below your post. Here you can also change the title, add tags, etc.. Hope that helps. :-) – Tormod Haugene Mar 19 '16 at 20:42

## 1 Answer

As shown, the mechanics are under-constrained. You can't solve for theta because you have three degrees of freedom (X, Y, theta) and only two constraints (L1, L2). Gravity will tend to bias theta in a particular orientation, but the geometrical stiffness of this arrangement will be so low that it will not be possible to do 3D printing.

To calculate the free-hanging orientation of theta, you will need to know the center of gravity of the end-effector, and solve a system of equations to find the angles and tensions for each cable that produce force vectors which sum to equilibrium with the gravity force vector through the COG. Unfortunately, the tensions will be a function of the angles, so it's not trivial to solve. As a hint, the virtual intersection of the two cables will be coincident with or directly above the COG in all equilibrium positions, and the horizontal components of the tensions in the two cables will be equal.

• M. Ryan thank you for your question. Exactly, you view is right. In fact, it's impossible to solve this equation as my tutor said. – zaatifi Mar 19 '16 at 18:52
• As you can see I added the dynamic equations in the picture 2, can you check if is it all right ? – zaatifi Mar 21 '16 at 10:56