LCS - 08b - Rotational mechanical systems with gears - Example

This lecture explains the mathematical modeling of mechanical systems with rotational displacements and involving gears therein. Two examples are presented, one with ideal gears and other with more realistic situation where the gears have their own inertia.

[@Vivezoz]

5:51 in and i feel ready for my assignment. My uni lecturer failed to explain the steps in over an hour

[@Malik_Naeem]

Thanks a lot Sir. I got everything every concepts by this Vedio. 🙌🏼👑

[@unstoppableguy7896]

You illuminated me!! Thank you so much

[@AI-Creations-088]

Asslam-o-alaikum sir
Sir at 3:47 why are you ignoring to Q2

[@MAFarooqi]

WA
What do you mean by Q2? Are you asking about theta2?

[@MAFarooqi]

WA
What do you mean by Q2? Are you asking about theta2?

[@AI-Creations-088]

Yes sir

[@AI-Creations-088]

While at 3:11 you are putting theta 2 and theta 3 this one is also not understand

[@MAFarooqi]

​@@AI-Creations-088 Theta_2 is linearly dependent upon Theta_1, that is, Theta_2 can be simply obtained by multiplying Theta1 with a scalar (teeth ratio). Therefore, a separate equation for theta2 is not required.
Furthermore, if transfer function between theta2 and the torque T is required, it can be easily obtained from the transfer function between theta1 and T.

[@ZionJair.]

Can you tell me which book the problem comes from? I want solve another problems. Can you help me?

[@MAFarooqi]

Control systems engineering by Norman Nise.

[@ZionJair.]

Thankyou so much​@@MAFarooqi

[@muhammadsaboor1142]

In the 2nd example, instead making equations can we reflect all the impedences directly to theta1 just like u did in exmp 1 ?

[@MAFarooqi]

Yes, you may do that.

[@asifimtiaz6353]

sir i find the ans of example-1 is
Theta2(s)/T(s) =
1/10
---------------------------------
850s^2 + 2000s + 600
i think it is the right ans. can you give a suggestion?

[@natanoliveira554]

It was very helpful, thanks!

[@ahmadirtisam9593]

Sir can you mention the video where you explain the state space model?

[@MAFarooqi]

Lectures on state space modeling and analysis were not recorded last time. I plan to do it in this semester.

[@ahmadirtisam9593]

@@MAFarooqi can you do it quickly please we have mids coming we need you :)

[@abdullahmahmoud9063]

thank you so much . excellent explanation

[@karanmathur56]

very helpful and detailed lecture , thankyou sir.

[@MAFarooqi]

Thanks and welcome

[@AndreiaCuaton]

sir i think question no. 1 K (spring) value should be 3 not 6? 300(5/50)^2 is = 3 not 6
1/10
--------------------
8.5s+20s+3

[@MAFarooqi]

There is a second spring as well, if you add its effect, then you will get the transfer function given in the slides.

[@cogitateandabet]

Which book are you using?

[@MAFarooqi]

Control Systems Engineering by Norman Nise.

[@wahabmustafa7360]

Control Systems Engineering, 6th Edition by Norman S. Nise

[@cogitateandabet]

Got it

[@wahabmustafa7360]

@@MAFarooqi today, you made my day, I will get INSHA Allah 90% + marks with the help of Allah and u. You are a grade saver.

[@midnightmadness1714]

SO thankful isr, thank you so much

[@muhammadfirdausmohdnoor646]

it is wrong to move/refer J2,3 to J1 since the middle shaft has two independent angular displacement. J1 and J4 should refer to middle shaft. this question should have two equations and solve by using cramer's rule

[@MAFarooqi]

There are multiple ways to obtain mathematical model for this system. You may proceed as described in the lecture, or you may refer all the impedances to the central shaft (as you have discussed), or you may refer all the impedances to the right most shaft. In all the three cases, you will obtain the same mathematical model.
Even if J1 and J3 have different angular displacements, still these can be referred to the left most shaft (If you are an electrical engineering student, you may establish an analogy of this mechanical system with an electrical circuit with a transformer. If the secondary side of the transformer has two parallel branches with impedances, you may still refer all impedances to the primary side of the transformer, although each impedance may have different current (current in electrical circuits is analogous to position in mechanical systems) flowing through it).
Since there are three linearly independent displacements in this mechanical system, you will get three equations.

[@muhammadfirdausmohdnoor646]

@@MAFarooqi so basically there are three independent angular displacement? i see.. thank you for the explanation 👍🏻

[@edgycuber9285]

Thank you sir!

[@Malik_Naeem]

Sir Can you please give the drive link of all slides of this course 🙌🏼❤️

[@MAFarooqi]

I shall shortly share it with you.

[@danishali4951]

Thank u so much sir

[@mustafahelvaci9690]

so good thanx

[@bruh6267]

isnt it supposed to be N2/N1?

[@giovasquez3549]

I love you

[@cgames5671]

example 1 final answer is wrong. It should be Theta2(s)/T(s) = 10/1300s^2+4000s+550

[@MAFarooqi]

Please re-check.

[@mysteriousasn4164]

Well

[@cupoftea411]

👍🏼