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In this paper, an investigation is conducted in order to understand impacts of Particle Swarm Optimization (PSO) parameters on the convergence and the quality of the inverse kinematics solutions provided by the IK-PSO (inverse kinematics solver using PSO) – a heuristic inverse kinematics solver algorithm. Over a large panel of parameters investigations, a statistical proof of convergence is provided for 5 links to 60 links articulated system. A recommended set of parameters intervals are presented for this class of IK problems. Investigations are based on the standard inertia weight PSO, and concerned the impact of the inertia weight, the swarm size and the maximum iteration number. For a given set of parameters, the existence of a solution with a given position error is also proved. All tests were conducted over 100 times. The density of probability function, PDF, is used to approximate and analyze the fineness functions, which are the square of the position error. Results showed IK-PSO is an interesting IK solver when a set of good parameters are used. For these parameters, the algorithm showed a statistical proof of convergence with a high resolution, by mean of error position. The algorithm also showed time-effectiveness compared to CCD method, which is assumed to be a real-time IK heuristic solver used in gaming.