Space Linkage Path Synthesis Theory And Methods

Based on differential geometry, a new approach of path synthesis for spatial mechanism is proposed and the software is introduced in the dissertation. In the spatial kinematic synthesis problem, the given trajectory is regenerated by floating pole of spatial mechanisms of three freedoms with the R binary link at first. Then if we can determine which lines are such that their loci have multiple position satisfying the constraints composed of combinations of some kinematic pairs, a closed-chain mechanism of one freedom is synthesized. The initial parameters that determine the motion of open-chain mechanisms must be inputted, and in the dissertation, they are given by the method derived from the theoretical analyses of characters of working space of mechanisms through the given trajectory. Based on the geometrical invariant of some typical constraint ruled surfaces, the spherical image curve is to be approximated to a circle on a unit sphere. On the other hand the trajectory of the center point of the constant inclination ruled surface is to be approximated to a curve on the cylinder. As a result, the unified mathematics model of the path synthesis is established by means of such idea. In fact, the mathematics model is a kind of special non-differential mini- max optimal problem with inequality constraints. By the method of maximum entropy, the problem can be transformed as a differential optimal model with a single constraint, which objective function is to minimize the maximum error. Some numerical examples have been given to show the reasonableness of the initial parameters and prove the correctness of algorithm in the dissertation.