Flexure joints are widely used to ensure manipulator mobility in difficult environmental conditions such as for micro-manipulation and in aerospace application. The use of flexure joints may imply complex kinematic behaviors that need to be considered to increase the device accuracy. This paper proposes, compares and analyzes three incremental models of the flexure joints used in an active wrist parallel telescope. A spherical joint model, a model issued from the beam theory and a stiffness model are considered. Because of uncertainties on the model parameters, an accurate experimental calibration with photogrammetry data is used to choose the most suitable model considering the telescope requirements. The experiments show that observability issue in calibration is the main factor limiting the model complexity in our case.