Morphological Classification And Evolution Of Link Curve

The point on the plane of the connecting rod mechanism can reproduce the complex algebraic curve.This characteristic has important application value in the actual engineering.The plane curve of the plane mechanism refers to the linkage of the connecting rod Point in the rack fixed coordinate system under the track curve.The nature and distribution of the connecting curve reflect the geometric properties of the plane motion of the connecting rod and the important theoretical basis of the institutional integration.The connecting rod curve of the planar four-bar mechanism can be divided into goose-shaped,pear-shaped,raindrop-shaped,banana-shaped,"8"-shaped and double "8",but the qualitative understanding of the link curve,lack of quantitative mathematics Measurement indicators or imperfect,it is difficult to move the movement characteristics of the curve and the characteristics of the curve linked.With the development of numerical map method,the institutional scholars put forward the numerical recognition method from the point of view of storage and retrieval speed according to the need of the link trajectory matching parameter extraction in the numerical map method,that is,using the specific deviation formula to calculate the whole curve and sample And then according to the corresponding comprehensive deviation value of the trajectory curve classification and identification,the method aims to use the curve between the integrated deviation of the trajectory curve recognition classification,there are certain advantages,but it is difficult Directly through the curve of the characteristic parameters to understand the morphological characteristics of the curve,or can not link the curve of the mutation and gradient law and institutional scale changes linked.Since the 20 th century,Muller et al.Have established and perfected the curvature theory of plane motion geometry,the Euler-Savary formula in Savary curvature theory,Cauchy's rigid plane motion,the Bobillier theorem,the Ball point,the Burmester point,etc.The distribution of the local geometric characteristics of the plane connecting rod curve is gradually revealed,and the change of the connecting curve curve usually depends on the mutation of its local geometric features.This is based on the morphological analysis of the connecting rod curve based on the motion characteristics of the mechanism Provided the conditions.In this paper,the position information of the singularity is combined with the mechanism scale change information,According to the geometric constraint relations of plane four-bar linkage mechanism,the constraint equations of singular point are solved.The cusp points,two-point and two-point points are analyzed by using the geometric curvature theory of modern geometrical theory.And the gradient characteristic of the self-tangent point,the mathematical description of the relative topological relation and position information between the singular points of the curves of linkage mechanism is realized,and the singular point topological ring of the curves of linkage mechanism is obtained.and the morphological features of the connecting curve are described by the topological structure between the singular points.This has certain advantages for the analysis of the scale variation of the connecting curve.