Combining with Newton optimization iteration methods based on chaos and mechanism synthesis theory

non-linear equations of mechanism synthesis is transformed to optimization problem.Then

repulsion two cycle point equation is constructed

repulsion two cycle point Z

J

is found by inverseimage iteration

therefore

all solutions are obtained by making use of the chaos phenomena and fractal structures of basins of attractions of points Z

J

. As an example the problem of function generation for planar four-link mechanism is considered

synthesis of planar-linkage was studied and some mechanism projects are obtained for synthesis and approximate synthesis to given positions.This enables to multi-projects selection.This method is adaptive to planar multi-linkage and special mechanism.It is a new simple realization method for mechanics design.