# Why is this assumption about the center of mass of a link true?

In point C.8 of this page of the book Robotics and Control it is stated that "the mass of a link used in a robot can be assumed as a point mass acting at the distal end of the link".

However, I cannot see why this assumption is true. For example, I would expect for a 2-link planar manipulator as the one shown below that, in the case of considering the mass of the links as point masses, their location should be the center of mass of the link, $\frac{a_1}{2}$ for link 1 and $\frac{a_2}{2}$ for link 2 and not the distal end of the link.

Furthermore, in Example 6.7 of the book Introduction to Robotics: Mechanics and Control the same assumption is made about the links present in the Figure.

Here is an extract of the example I'm referring to (I have wiped out some non relevant parts):

How is the stated assumption valid?