Aiming at the characteristics that the function of probability density of chaotic sequence for Logistic map is the non-uniformed function in interval（0

1）

the Logistic map with adaptive carrier based on power function（LMACPF） is proposed.The chaotic orbit of the LMACPF has uniformed probability density and good ergodic property.A new Newton iterative method（NIM） based on the LMACPF is presented.The new method utilizes the good ergodic property of LMACPF to produce sensitive initial points of NIM

which is taken to solve nonlinear equations（NLEs）.The new method can find many or all solutions of NLEs quickly

and has advantages such as simplicity

high efficiency.Taking a 6DOF symmetrical 6-RUS parallel manipulator as an example

the length of six links in this manipulator is regarded as the restrict condition to obtain NLEs for solving forward positional.The new method is used to solve NLEs for forward displacement analysis of this manipulator.At last

a numerical example shows that the new method can quickly find all forward positional and they are very coincident with the inverse ones.