Mechanism for forming approximate logistic spiral

Abstract

The invention discloses a forming mechanism for an approximate logarithmic spiral, which is provided with a sliding block. The sliding block is respectively connected with a circular motion driving mechanism and a rectilinear motion driving mechanism, and the sliding block carries out circular motion and rectilinear motion simultaneously under cooperative driving of the circular motion driving mechanism and the rectilinear motion driving mechanism; and the sliding block is connected with an adjusting mechanism for adjusting radius of the circular motion. Approximation of logarithmic spiral is achieved by composition of families of straight lines and a family of quadratic curve, the rectilinear motion driving mechanism and the circular motion driving mechanism are adopted, the rectilinear motion driving mechanism achieves componental movement of linear tracks of the sliding block, the circular motion driving mechanism achieves componental movement of circular motion of the sliding block, the componental movements are synthesized, and the tracks of the sliding block at the actuating end are approximate to the logarithmic spiral. The forming mechanism only needs the common rectilinear motion driving mechanism and the common circular motion driving mechanism to achieve approximate logarithmic spiral, has a simpler structure and reduces cost greatly in comparison with a numerical control machine tool in the prior art,.

Description

technical field [0001] The invention relates to a forming mechanism for an approximate logarithmic spiral. Background technique [0002] Although the logarithmic spiral is an ancient curve, due to its good mathematical, geometric, mechanical and aesthetic properties, it has been widely used in modern disciplines such as computational geometry, industrial modeling, and computer-aided fluid surface optimization design. . Regarding the approximation of the logarithmic spiral, many experts have proposed many different approximation methods. Using complex numbers z=a+bi, where a, b≠0, using points z, z on the complex plane 2 ,z 3 ... will approach the logarithmic spiral, as long as the value interval of z is small enough, the approximated logarithmic spiral is accurate enough. In addition, based on the properties of the logarithmic spiral, the golden rectangle can also be used to approximate the logarithmic spiral. [0003] No matter it is the complex number approximation me...

AI Technical Summary

Problems solved by technology

However, the approximation to the logarithmic spiral motion is realized through the CNC machine tool. The approximation of the logarithmic spiral requires the synthesis of several motions, which cannot be realized on the ordinary CNC machine tool. It requires the multi-axis linkage of the machine tool to process, and the processing equipment structure is complex and costly. higher

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