Geometry of the precession helical trajectory model. Superluminal knots move along a helical trajectory around the jet axis defined by the function x₀(z₀) in the plane (X, Z), having an amplitude A(s₀) and phase ϕ(s₀) defined in the coordinate system (x′, y′, z′). Through transformation among the coordinate systems, the apparent trajectory and the kinematic parameters (bulk Lorentz factor, Doppler factor, apparent velocity, and viewing angle) of a knot can be derived from its spatial trajectory and spatial kinematics by using the formulas given in Sect. 2.