Abstract: A new approach for plane mechanisms synthesis by an adaptive saddle-fitting is presented. The principal of cure fitting is firstly taken as the minimum maxim fitting error. Then, the simple curves, such as an circle, a line as well as a line-envelop circle, are adopted to fit the path of the moving point or line adaptively, which can be uniquely determined according to the path by the adaptive fitting method. However, three types of approximately characteristic points are strictly defined, which include an approximately circle-point, an approximately slide-point and an approximately beam-point. Meanwhile, three definitions and theorems are respectively given, which provided a solid theoretic base for the existence of the approximately characteristic points and the convergence of the optimum algorithm. The unified mathematical model is set up to search out an approximately characteristic points on the moving body or the fixed frame by combining the adaptive fitting method and saddle-point programming. Therefore, a four-bar mechanism can be synthesized to generate approximately multiply given positions. And also, the mechanism synthesis for retracing a given path and an input output function can be treated as that for position guidance by searching the three types of approximately characteristic points according to the relative motion principal. At last, some examples are given to show the feasibility and validity of the approach.

Key words: Adaptive, Mechanisms synthesis, Saddle-fitting, dissimilar titanium joints, ineria friction welding, microstructure, mechanical property