  Total rotation is a quantity that has been used for years in RSA. However,
its definition has no mathematical sense, since the Euler angles do not form a
vector space, since angles cannot define a multiplication group. With this work
I tried to give a mathematical definition of the total rotation connecting the
Euler description of the rotations with the helical axis. The approximation for
small angles was used to connect Euler's angles and helical angle. With this
approximation Euler angles acquire the properties of a vector space and it is
possible to justify the meaning of this parameter. Validation test showed that
total rotation has an approximation error between 5\% and 7\% for angles in the
range $\left[-\frac{\pi}{6}, \frac{\pi}{6} \right]$. Since usually RSA uses
smaller angle ranges, the approximation is perfectly suitable for use in RSA.
