Representing Points: Examples and Applications in Dynamics of Machines

[mech-eng]

Hi, I have to find examples,application about points which represent a rigid body.In the lecture dynamics of machines we call them substantial points. the points have a mass which is equal to
rigid body for example a mechanism. to do this we use kinetic energy equalities.

1/2(ma*_va2)=($\sum(Ek)$)i and 1/2 (ma *va^2)=∑(1/2 mi*vi^2 + 1/2*Ii*wi^2)

these two are the formulas: ma:(induced,reduced?) point A, mi: mass of the İth body(in the ∑ symbol), vi is the velocity of center of mass of the İth body, Ii is the moment of inertia of the ith body and wi is the angular velocity of the ith body.

we also study (reduced?) moment of inertia of the machine( for example a fourbar mechanism) to
a mile(or axle). here is the formula 1/2*I*w^2=∑1/2*mp*vp^2

here: I is the moment of inertia student has to find which represents I think all the kinetic energy
mp is the mass of pth body of the machine(or mechanism)

I want to make a google search about this but I don't know true words for this subject. Can you
help me. And have ever met this subject in the books about dynamics of machines I have never met with them in english books. at least reduced( or equivalent) momet of inertia part.

 

[mech-eng]

my first question is about two or three mass models - two or three points which represents the rigid body
and second question is about generalized moment of inertia or reduced moment of inertia to a point, for example ,on the mechanism.

 

[mech-eng]

this is the picture of equation