Joint rotation space of five-bar linkages

Unlike single degree of freedom linkages, the rotatability at a joint of a five-bar linkage is affected by the rotatability at another joint. Unless the linkage has full rotatability, the allowable inputs of a five-bar linkage are related. This article, by taking the interrelationship between the rotatability of two input angles into consideration, presents the most extensive study on the rotatability of five-bar linkages. The joint rotation space of a five-bar linkage is the region between the singular curves which represent the relationship between the input angular positions of the linkage at singular positions. By distinguishing five-bar linkages into C-C (crank-crank), C-R (crank-rocker), and R-R (rocker-rocker) types, there are totally nine C-C types, four C-R types and four R-R types of joint rotation space in classes I and II five-bar linkages. The results in this paper are essential for understanding the basic mobility and limitation of five-bar linkages. One may also find them useful in manipulators or multi-loop linkages which have a five-bar chain as the major or minor structure. The results are also applicable to spherical five-bar linkages.