# What is the theory that makes this method work when dynamically balancing this system

Sorry for my bad english in advance I am not a native speaker. I have a system similar to the one above and we are supposed to statically and then dynamically balance it. To statically balance it we are told to set two of the masses to arbitrary angles, we chose 90 degrees away from each other. We were then told to create a vector diagram, where the lengths of the vectors correspond to the mass*radius values for each of the 4 masses. By creating a complete shape we managed to find the angles of the other two masses for which to statically balance. I understand why we do this and theory behind it.

To dynamically balance it we are given these instructions

I can follow the instructions but I do not understand why this should be done and how this relates to dynamic balancing. Would someone please be able to explain why?

• Perhaps you could start with the definition of "dynamic balancing" Is this helpful? web.mst.edu/~stutts/ME242/LABMANUAL/DynamicBalancingExp.pdf – Carl Witthoft Mar 15 '17 at 13:59
• You want your axis of rotation to be a principal axis in the combined mass moment of inertia matrix. – John Alexiou Mar 15 '17 at 15:44
• You need to show us what "Figure 4" looks like, otherwise we don't know what the instructions are asking you to do. We can problably guess what $m_n$ and $r_n$ are, but we don't know an arbitrary $m_n r_n L_n$ polygon" means. Knowing what "Step 6b" says might help, as well. – alephzero Mar 15 '17 at 21:42