New Approach For Kinematic Synthesis Of Mechanism By Adaptive Curve Fitting

A unified approach for kinematic synthesis of mechanism, based on the theoretics of curvature for mechanisms, is established by means of the adaptive curve fitting method in this dissertation, which is supported by National Natural Science Foundation of China (No.59675003).At first, the adaptive curve fitting method for planar mechanism synthesis is presented tersely. In terms of the invariants and the invariable of planar curves, the adaptive curve fitting methods for three elements of planar mechanism synthesis were reviewed respectively, which are a circle curve, a line and a line-envelope circle. Then, the applications of these methods in kinematic synthesis of a crank, a slider link and an inverted slider link are discussed in details, as the continued investigations by this dissertation, both in precision-position synthesis and multi-position synthesis.Secondly, taking the constraint curve of spherical R-R binary as the unique element, kinematic synthesis for spherical mechanism is discussed. In the principle of minimum maximum fitting error, the mathematical model of adaptive fitting cone is set up in terms of invariants of a cone. The adaptive cone fitting method provides a ground basis for the existence of the spherical approximate cone points and the convergence of the optimum algorithm. Using this method, the synthesis of spherical mechanism is converted into a problem of spherical curve fitting.Thirdly, based on the invariants of constraint curve and constraint surface for general binary links of spatial mechanism, the approach of adaptive curve fitting is extended into kinematic synthesis for spatial mechanism. Four main types of spatial binary links are investigated in details for kinematic synthesis both in precision-position synthesis and multi-position synthesis. In terms of the invariants of spherical curve and cylindrical curve, the mathematical models of adaptive fitting sphere and cylinder are constructed by means of the saddle-point programming. Thus, the kinematic synthesis of S-S binary and C-S binary is converted into locating approximate spherical point and approximate cylindrical point in the moving rigid body, respectively. According to the differential geometry of ruled surface, the properties of a ruled surface can be globally described by a spherical image curve and a striction curve of the ruled surface. Thereby, the optimum synthesis of spatial mechanism with C-C binary link can be converted into two adaptive curves' fitting on a unit sphere and a cylinder respectively. And then, an approximate image spherical circle-point can be visualized as optimum synthesis of spherical mechanism. By means of the saddle-point programming, the unified mathematical model is set up for an approximate image spherical circle-point by the adaptive cone fitting and the approximate cylindrical striction-point by the cylindrical curve fitting respectively. Moreover, for the kinematic synthesis of S-C binary, an approximate spatial beam point is defined, and the mathematical model of adaptive line-envelope sphere fitting is set up. Additionally, by means of the combination of two different elements, the kinematic synthesis of four common types spatial mechanisms arediscussed, which are the RSSR mechanism, the RCCC mechanism, the RRSS mechanism, and the RSCR mechanism, including rigid-body guidance, function generation and path generation.At last, the properties of the output motion of double chainstitch machine are extensively analyzed. Then, two plans are suggested to replace the original mechanism, based on a RCCC mechanism. The dimensions of the RCCC mechanism are worked out by means of the adaptive curve fitting approaches to mechanism synthesis. The output motion of the RCCC mechanism is obtained and tested with errors in manufacturing process, it is greatly satisfied for the requirements of the double chainstitch machine.