The unconstrained optimization model for the forward positional analysis of a 3-RPR planar parallel manipulator

which is based on the constrained length of the bars

is presented. The simple particle swarm optimization （SPSO） has some demerits

such as relapsing into local extremum and slow convergence velocity in the late evolutionary. The improved PSO

adaptive mutation PSO （AMPSO）

based on the new difference index

is proposed to overcome the demerits of the SPSO. The adaptive mutation PSO （AMPSO） is given out to make the optimal problem for forward positional analysis of parallel mechanisms. Numerical results for the forward position analysis of 3-RPR planar parallel manipulator show that the AMPSO can solve to all assembly configurations

and possesses the performances of rather quick convergence speed and high precision.