Joint Rotation Space, Workspace, and Singularity-Free Workspace of Parallel Five-Bar Manipulators

Abstract

Abstract Closed-loop manipulators, while offering some advantages over the open-loop manipulators, also introduce new topics of study such as their joint rotation space (JRS) and workspace. In the previous studies, the concept of JRS was very effective in the study of the allowable inputs of five-bar linkages[11], and the concepts of sheet and side[7] were later introduced for the purpose of clearly describing all of the joint rotation spaces associated to a parallel manipulator with two degrees of freedom. However, of the two types of singularity of parallel manipulators, only the uncertainty singularity was considered in the aforementioned studies. The stationarity singularity was not indicated in the JRS of the manipulators, which would not be sufficient in the design and trajectory planning of parallel manipulators where the one-to-one correspondence between the JRS and the wrist point workspace would be required. This paper reports an extensive study on the JRS and singularity-free workspace of the parallel five-bar manipulators. The objective of the study is to establish a one-to-one corresponding relationship between the JRS and singularity-free workspace. A concise and sufficient way is proposed to thoroughly recognize the JRS and workspace of the parallel five-bar manipulators. The result can be applied in the design and trajectory planning of parallel five-bar manipulators, and the concepts can be extended to other parallel manipulators.