Mathematical models for wave energy converters (WECs) are naturally germinated from the models in classical offshore engineering applications, where the assumption of linear kinematics and dynamics is commonplace. However, while the assumption of linear, small amplitude, motion fits traditional offshore problems (it is desirable to stabilize ships, boats and offshore platforms), it is not representative of the expected (and desired) motions of a WEC, since the main objective is to enhance the response and maximize power extraction. The inadequacy of linear models for many wave energy applications has led to an increasing number of publications and codes implementing nonlinear hydrodynamics. However, nonlinear kinematics has received little attention, since few models yet consider six degrees of freedom (DoFs) and large rotations. This paper implements a nonlinear kinematic model for one of the most well established WEC concepts: an axisymmetric heaving point absorber with single taut line mooring. The influence of the nonlinear kinematics are demonstrated and potential sources of numerical instability in yaw are discussed. Finally, the model is also used to articulate parametric resonance in roll/pitch.