DrD

I really don't think I can help you. I don't know much about robots. DrD

Why in the world do you want to put a flywheel on a DC motor? The purposes of a flywheel are (1) to smooth out irregularities in the rotational motion of the shaft (torsional vibration), and (2) to store energy in order to continue operation though a power interruption. You did not mention either of these, so I ask again, "why do you want to put a flywheel on a DC motor?"

"It gives balance to engine and load is uniformly distributed in crankshaft." This statement is totally incorrect. Torque is delivered to the crankshaft as a series of pulses, in no way uniform. In a multicylinder engine, torque will be positive at one location while it may be negative at another. What is a "four stage engine"? Do you mean four cylinder, or perhaps four stroke, or something else? All the pretty animations in the world are not worth much if the accompanying statements are nonsense. DrD

The PDF file below will show you how to solve this problem. DrDPlanetaryProb.pdf

As a starting point, you must know the MMOI for each individual component; without that, you cannot begin. Assuming that the individual component MMOI values are known, do a kinematic analysis of the planetary train to determine the velocity of the CM of each component. The use that information to formulate the kinetic energy of the entire system, all moving according to the kinematic relations. You will have to choose some rotation as a reference value, usually either the input or output rotation. The kinetic energy will have the form T = (1/2) theta-dot^2 (term1+term2+...+termlast) where theta is the reference rotation. The sum of terms indicated is the effective MMOI for the gear train. DrD

So, what else is new? DrD

Wow!! That was super exciting!! DrD

The material you posted (from a book?) is only partially visible, and cannot be completely read. The various symbols are not defined, such as Ftc, Rc,T, Wc, and alpha_c. There is no way anyone can help you with so little information. Rather than ask for help, I suggest you draw the picture and work it out for yourself. You will learn much more that way. DrD

The one thing that is very clear from your two URLs is that there is no uniform, well defined definition of "rifle barrel harmonics." There seems to be a mix of ideas about compression waves traveling down the length of the barrel and reflecting back combined with a dilatational wave propagating out from the charge ignition. The word "harmonics" seems to be more of a buzz term, to dignify the confusion. Altogether, this is simply an elastic wave propagation problem, albeit a complicated on due to the geometry involved.There are lost of people around the world who have studied wave propagation problems, and I'm sure that with the necessary experimental facilities, all of this could be studied experimentally. It may already be under investigation, either by the US Army (such as Picatinny Arsenal), or one of the rifle manufacturers (Remington, Winchester, etc). You will find the necessary mathematics quite sophisticated and well beyond the typical college graduate (lots of partial differential equations). Have fun with your inquiry. DrD

The term "rifle barrel harmonics" is not one that I recognize, and could be used to describe several possible phenomena. In order to help you, I have to ask you to describe just what sort of motions you are concerned with, what phenomena it is you wish to describe. Please write out (in words) what you think happens that interest you, and then we may be able to offer some help with the mathematical description. DrD

The term "Pan and Tilt Control System" does not have a universal definition, so no one can be sure what you are talking about. If you want help, give a detailed description of what you need to build, including one or more sketches of the proposed system. Only than can anyone give you a meaningful answer. DrD

Without more details, it is difficult to say very much. One thought that comes to mind is that you have probably neglected friction which can be very significant in a system such as this. If you want more help, please post a sketch of your system with dimensional details. DrD

Wow!! That was absolutely fascinating!! A blank page! Who can possibly top that? DrD

I'm glad you thought so. DrD

Your drawing in and of itself will not cause or prevent vibration. Its all in the way the rotor is built. You have stated a desire, but you have not asked a question. Is there anything preventing you from accomplishing that which you desire? DrD