This article introduces a new geometric vector modeling method of serial kinematic robot consistent with the identification process. This method is based on the definition of position and orientation of the robot joint invariants. For example, the invariant of the rotational joint is a straight-line (rotational joint axis). Thus, only independent geometrical parameters are introduced to model the joint axis position and orientation in space. Note that, the orientation is not constrained as in the Denavit-Hartenberg (DH) formalism. This article presents the methodology to define these geometrical parameters and the geometrical model. In this context, the identification method relies on "Circle Point Analysis". The points are measured with a laser tracker. Indeed, with a relevant processing of the measured points, we directly identify the invariants of joints. This method is applied to a SCARA robot geometric modeling. After an identification process, this methodology allows improving inverse kinematic error compared to the classical DH geometrical model with first and second-order defects. Moreover, the obtained residual error mean value is close to the accuracy of the measurement process.