Abstract: The geometrical model is presented to describe the spatial and symmetrical 4-PRUR parallel mechanism which is intended to provide four degrees of freedom with one translation and three rotations (1T3R). The screw theory is employed to analyze the principles that this mechanism can perform the above motions and discuss the rationality of chosen input pairs. The link-length of the mechanism is regarded as the restrictive condition to obtain nonlinear equations (NLEs) for its displacement analysis. To improve the global searching ability and convergence speed of differential evolution (DE) algorithm, an adaptive DE with double subpopulations (ADEDS) algorithm is proposed, in which chaotic migration, weighted best individuals, and escaping strategies of the whole population are gradually self-adapted by learning from their previous experiences. Consequently, the NLEs are transformed to unconstrained optimizations (UOs) which can be solved by the ADEDS algorithm. The results of numerical verification show that, through the ADEDS algorithm, forward solutions can be precisely found that are very coincident with the inverse ones.

Key words: Adaptive strategy, Differential evolution algorithm, Displacement analysis, Double subpopulations, Parallel mechanism, Screw theory