  Bicircular twisted Laguerre-Gaussian beams possess a definite torus knot
angular momentum (TKAM) as a new form of angular momentum. TKAM is conserved in
nonlinear atomic processes such as high harmonic generation and can be
classified by a time delay parameter $\tau$ and a coordination parameter
$\gamma$. These parameters are defined by the respective projected orbital
angular momentum and the energy of the two superimposed Laguerre-Gaussian
beams. We derive a consistent geometric method to determine $\tau$ and $\gamma$
from the driving beam as well as from the high harmonic radiation. This method
relates both invariance parameters ($\tau$ and $\gamma$) to the emitted high
harmonic radiation. Therefore, $\tau$ and $\gamma$ can be read off of two
different torus knots. These knots can be constructed from the spatio-temporal
evolution of the electric field of the respective high harmonic radiation or
the driving beam. We demonstrate the classification of the invariance
parameters for a planar atomic gas target irradiated by bicircular
Laguerre-Gaussian beams explicitly. Furthermore, we demonstrate that the
respective torus knots determined by $\tau$ and $\gamma$ can be mapped onto
each other within minor modifications. This geometric method yields a different
way to interpret the invariance parameters $\tau$ and $\gamma$ as well as their
underlying relation compared to a purely formal derivation. The investigations
presented in this work are in good agreement with previous findings and provide
insight into the dynamical symmetry of TKAM in the context of high harmonic
generation induced by bicircular twisted Laguerre-Gaussian beams.
