Branch Identification of Planar Two-DOF Seven-Bar Linkages

Abstract

Mobility identification mainly refers to the problems with the motion continuity and smoothness of a potential design or plan. In any linkage synthesis or robot navigation, it is highly desirable that the ability of any of the numerous design candidates to reach the desired positions in a favorable manner can be determined in a single decisive step automatically rather than through a blind trial or even a physical experiment. Mobility of complex linkages has been one of the most troublesome problems in linkage synthesis and programming and the problem is further complicated with multiple degrees-of-freedom. For multiloop parallel manipulators this paper may represent the first mobility analysis method that can not only decisively and unambiguously rectify motion continuity between discrete positions but also provide clear geometric insight or interpretation regarding the formation of discontinuity. The treatment is based on the principle that the mobility of a multiloop linkage is affected by the mobility of each individual loop as well as the interaction between loops. Since the N-bar rotatability laws govern the mobility of an individual loop, the main mobility issue for multiloop linkages is how the mobility of these loops affects each other. One may find that the concept of joint rotation space (JRS) offers simple and intuitive explanation on how the mobility is affected by the combination of loops. The treatment is very suitable for an automated computer-aided mobility analysis. Examples are employed to demonstrate the proposed method. Continuity is a pivotal issue in linkage mobility analysis. Once the continuity can be rectified, problems with smoothness or singularity, which are discussed in the companion paper [28], can be resolved.