Optimum design of the 5R symmetrical parallel manipulator with a surrounded and good-condition workspace

This paper concerns the optimum design issue of the 5R symmetrical parallel manipulator with a surrounded workspace. Generally, such a manipulator has a very large workspace. With different working modes, a manipulator will have different singular loci and workspaces. In this paper, the singularity and the usable workspace without singularity inside will be determined for the manipulator with a specified mode. The usable workspace can be used to define the global conditioning index (GCI). In order to obtain the optimum design of the manipulator, a non-dimensional design space is established. Because each of the non-dimensional manipulators in the established design space can represent the performances of all of its possible similarity manipulators, the design space is a very useful tool for guaranteeing a global comparative result. Within the design space, the singularity, usable workspace and control accuracy (evaluated using the GCI) are studied and the corresponding atlases are constructed. Based on the atlases, one can synthesize link lengths of the manipulator studied with respect to specified criteria. One example will be given to show how to use the atlases. In particular, an example will be presented of reaching the optimum dimensional result with respect to a desired practical workspace based on the optimum non-dimensional result identified from the atlases. For the reason that using the atlases presented in this paper a designer can obtain the optimum result with respect to any specification, the optimum design method proposed in this paper may be accepted by others.