Experimental studies into aircraft stability and performance can be enhanced by using a rig in which the aircraft model support approximates free flight within a wind tunnel.Such multi-degree-of-freedom wind tunnel rigs often impose kinematic restrictions on the aircraft model's translational motion. This study investigates these kinematic effects, with particular attention to a spherical constraint where the aircraft is held at the end of a fixed length pivoting arm. Here the motions of the aircraft and kinematic constraints are derived as differential-algebraic equations and assessed numerically. The impact is found mainly on translational motion with negligible effect on the aircraft's rotation. A concept to reduce these kinematic effects on the aircraft's motion by applying an external force onto the aircraft is proposed. This compensation, which partially accounts for the constraints on the aircraft motion, is shown to reduce the effects of the arm, allowing for improved physical simulation.