We present an aqk(s) polarization-parameter model to describe product angular momentum polarization from the one-photon photodissociation of polyatomic molecules in the molecular frame. We make the approximation that the final photofragment recoil direction is unique and described by the molecular frame polar coordinates (α,φi), for which the axial recoil approximation is a special case (e.g., α = 0). This approximation allows the separation of geometrical and dynamical factors, in particular, the expression of the experimental sensitivities to each of the aqk(s) in terms of the molecular frame polar angles (χi,φi) of the transition dipole moment μi. This separation is applied to the linearly polarized photodissociation of polyatomic molecules (asymmetric, symmetric, and spherical top molecules are discussed) and to all dissociation mechanisms that satisfy our recoil approximation, including those with nonaxial recoil and multiple state interference, giving important insight into the geometrical properties of the photodissociation mechanism. For example, we demonstrate that the ratio of polarization parameters A0k(aniso)/A0k(iso) = β (where β is the spatial anisotropy parameter) is an indication that the dynamics can be explained by a single dissociative state. We also show that for asymmetric top photodissociation, the sensitivity to the a1k(s) parameters, which can arise either from single-surface or multiple-surface interference mechanisms, is nonzero only for components of the transition dipole moments within the v-d plane of the recoil frame.