Abstract
Abstract. According to the burmester theory, an infinite number of spherical or planar 4R linkages for a specific four-orientation task can be synthesized, but most of the linkage solutions calculated by this method are invalid because of motion defect, poor performance and others. In order to improve the synthesis efficiency, a program package based on Matlab is developed to find a satisfied linkage solution automatically and quickly. Firstly, the calculation on circle points and the center points based on the burmester theory in spherical problems is introduced. Secondly, the calculation methods of linkage defect discrimination, linkage type classification, linkage performance evaluation and solutions visualization based on the theory of spherical trigonometry are presented respectively. Thirdly, the synthesis calculation of program package is extended to the planar 4R linkage based on the theory of planar analytic geometry. Finally, the examples of the spherical synthesis problem and the planar synthesis problem based on solutions map are introduced to test the program package, the result proves this program package is effective and flexible.
Highlights
In this paper, the study work is to design a 4R linkage which can guide its coupler to pass four specified orientations smoothly and orderly
For each linkage solution formed by the center point i and the circle point j (j ≤ N, i = j ), the linkage type, the motion defect type and the transmission performance are calculated in turn, and the calculation results are written into the data structure of the linkage solution
N × N cubes are constructed based on the O − XY plane, and each linkage solution defined by the center point i and the center point j is described by a cube L(i, j, h), as shown in Fig. 7, where i is the x offset of cube L, j is the y offset of the cube L, h is the z offset of the cube L, i and j are determined by selected center points, and h is determined by linkage performance
Summary
The study work is to design a 4R linkage which can guide its coupler to pass four specified orientations smoothly and orderly. Compared with the previous studies, the main work of this study is as follows: the existing color-coded type map method is improved to express the discrete attribute of linkage type, and the continuous attribute such as transmission performance; a defect discrimination method based on geometric method is proposed, and a pyramid structure of the circuit, branch and order defect discrimination are defined. This method is logical, and accurate without misjudgment
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