# Parametric Design, Tensors: Introduction

For today’s lecture, I present two designs of simple hinges to illustrate the engineering aspects of the manufacture of such a simple device. The Timeline of one of these can be found here.
The slides for today’s lecture are in three parts. The first two are slow motion versions of the above timeline and they are shown next:

and

A Summary of the first 12 pages of the Recommended Text with solutions.

Solved Problems:

## 20 comments on “Parametric Design, Tensors: Introduction”

1. Thank you very much for these slides. Would go through them and let you know my thoughts

The cross product of basic vectors. the last explanation was not very comprehensive.

• oafak says:

Can you be specific? What page and what particular set of slides are you referring to?

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4. Emmanuel Chukwu says:

Sir my autodesk package installer is not even attempting to install.

5. Ayo-Ola Laughter says:

The slides and video were very helpful in creating the hinge

6. Ojodu opeyemi says:

Sir, in the problems and solution slide, question number 2.3.
Was it intentional that you used different matrix values from the one in the textbook or just an error?

• oafak says:

Deliberate.

• Ojodu opeyemi says:

Oh thank you sir.

• Ojodu opeyemi says:

One more thing sir,if a matrix B= B(i-alpha), does the transpose of the same matrix necessarily have to be B(alpha-i) or it can be the same B(i-alpha).

I just want to know if the same rule(same answer no matter in what order the indices
are given) we applied in earlier exercises applies for transpose as well.

• oafak says:

Don’t take my words for it! Find out for yourself by giving values to the indices and expanding. Do this with a 3 by 3 matrix. after that it will be clear to you.

7. oafak says:

Also note that Problem 2.11b is a general result: The product of two entities, one symmetric and the other anti symmetric in shared dummy indices will always vanish. The Kronecker Delta is symmetric; The alternating (Levi Civita Symbol) is antisymmetric. Their product is zero. 2.11a expresses the converse: If the product of two tensors is zero and you know that one of them is anti-symmetric, you can conclude that the other is symmetric. Hence, 2.11a is also a general result.

• Ojodu opeyemi says:

Noted sir, thank you sir!

8. Salaudeen Taiwo Hassan says:

I’m actually very confused with page 12 and 13 of the tensor slides, There are different indices, yet you referred to same answer. I need a explicit answer Pls.

Though from what I read I thin that of page 12 should be correct

• oafak says:

There is nothing explicit in “I’m actually very confused …”. Before requesting an explicit answer, you have a duty to ask an explicit question! Tell me specifically what you are confused about!

• Salaudeen Taiwo Hassan says:

The difference in the indices is what is confusing me sir

• oafak says:

Salaudeen, let’s talk about it in class

9. Sumayyah says:

Thanks very much for the solutions sir, however the solution to 2.10 is not included, you noted that you have a better example, but I think you forgot to add it

• oafak says:

Go back to the solved problems again. 2.10 is included in a much general way. All you need do is to plug in the numbers and the results will come out.
Furthermore, the question you asked me in class shows you were looking at my answers without the context of the question asked in 2.11! Look at these again with the current notes on the web.

10. Emmanuel says:

sir please in 2.6 how did the delta mn vanish?