Mobility Research Of The Multi-loop Planar Linkage And Spherical Six-bar Linkage

Nowadays, the plane and spatial mechanism had been already applied in many aspects, such as medical equipment, industrial robots and space technology. these applications always have closely connection with the kinematic motion analysis of plane and spatial mechanism. Mobility identification is a difficulty for the motion analysis of the planar and spatial linkage mechanism. there are some papers to research the problems Although a lot of methods have been put forward and appear a variety of different ways of mathematical modeling, but the proposed method usually only are used for some specific kinematic analysis of planar linkage institutions. In another words, they are not general and suitable. Therefore, based on the study about mobility of plane moulti-loop and spherical six-bar linkage of predecessors research, this paper put forward a set of complete theory to solve the mobility problem of the plane and spherical linkage. The main content of this article is as follows:(1) To refine a set of complete mobility theory for the planar multi-loop linkage mechanism. Based on the concepts of N-bar rotatability laws and joints rotation space, firstly,analysis the characteristics of planar four bar linkage; secondly, take a series of linkage, such as,two degrees of freedom five-bar, two-DOF seven bar, Stephenson six-bar linkages to confirm; finally, summarize the mechanism of complete rotation rule of some linkages and solve the branch and sub branch problem of planar linkages by using the Maple image recognition.(2) Solutions for singularity problems of planar complex mechanism. According to instantaneous centers of the linkages can represent the kinematic characteristics of the movement of institutions, base on the research of the planar four-bar linkage mechanism, pioneer the concept of equivalent four-bar to solve the problem of the dead point of single degree of freedom planar linkage mechanism,after that, combined with the idea of institutions degradation, a breakthrough to settle singularity problem of the multiple degrees of freedom complex linkage. at the same time use the dead center configuration of the Stephenson six-bar linkage, two degrees of freedom seven-bar linage, three degrees of freedom eight linkages to prove the feasibility of this method.(3) The mobility analysis of spherical six-bar linkage. Spherical six-bar linkage which is a planar six-bar linkage that covering all the bar is in the same sphere surface. Its various bar endpoint to have equal distance from its center. According to the similarity structure about plane and spherical six-bar linkage, the mobility analysis theory of plane multi-loop linkage can be use to solve mobility problems of spherical six-bar linkage.To sum up, this study establishes a set of mobility analysis theory for plane multi-loop and spherical six-bar linkage. This theory can explain, judge, predict and identify the mobility of plane and spherical linkage,which includes the problems of the continuity motion of mechanism(branch, assembly method or loop), smooth(sub branch or no singularity configuration space), complete rotation or a crank, movement range and order.