In this work, geometric and kinematic modeling of the gear-based crank mechanism engine (GBCM) was performed. To this aim, a mechanical approach based on projective computational methods and mechanism theory laws is applied, to which a parametric study has allowed a conclusion on the geometrical and kinematic behaviors of the moving links. The study concluded that the kinematic quantities at connecting rod head are one-half of those at the piston top head. The extrinsic behavior like the stroke of the connecting rod head is twice the crank radius and the piston kinematic are identical to the conventional engine with the same crankshaft ratio regardless of the compression ratio and any gear wheel radius. Hence, all the extrinsic kinematic properties of a classic crankshaft mechanism of the fixed compression ratio engine remain valid for a gear-based crank mechanism engine and can be used for dynamic calculation purposes.