Rigid Body Guidance of Planar 4R Linkages Based on Gray-coded Type Map

In order to improve the calculation efficiency of 4-position guidance of 4R linkages based on burmester theory, and to solve the problem of blindness in center point choice, a computer aided method of gray-coded type map was proposed in this paper. Firstly, center curve and circle curve in burmester theory were calculated respectively by the methods of projective geometry and vector subtraction; then, all the combinations of center points were mapped into a two-dimensional set that was gray-coded according to the transmission performance of linkages; finally, 8 subsets of gray-coded map were redrew according to linkage type, on this basis, solutions satisfied the 4-position task were easily found by this map. The method proposed by this paper could improve the calculation efficiency of rigid body guidance.1 INTRODECTION The synthesis of linkages is the inverse process of kinematics and dynamics analysis. Taking the 4 position rigid body guidance as an example, the center curve and circle curve based on burmester theory can be obtained by kinematic analysis of the 4R linkage defined by pole (or image pole) points [1-2]. Since the number of the center points is infinite (∞), the number of the 4R linkage solutions for 4 specified positions is ∞2. Thus, with the increase of the segmentation accuracy of the center curve the number of the 4R linkage solutions increases sharply, and most of the solutions are infeasible because of the poor transmission performance or the 1Guangming Wang, Hongyang Zhao, Limin Liu, Tianqi Zhang, Xiaoming Wang, College of Mechanical and Electronic Engineering, Shandong Agricultural University, Shandong, China, 271018. Hongwei Xu, Shandong Weifang Luzhong Tractor Co., Ltd, Shandong, China, 261000.