Classification and Kinematic Modelling of Fully-Parallel Manipulators — A Review

The direct position analysis (DPA) of fully-parallel manipulators, basically comprises the analysis of fully-parallel kinematic chains (FPKCs) that feature two rigid bodies connected to each other via six binary links (legs) through spherical pairs. Some legs may share their endings, thus different leg arrangements are possible. The paper provides the state of the art of the DPA of all possible arrangements. In particular, the paper: i) reviews a procedure for identification and exhaustive enumeration of FPKCs, that led to the identification of twenty-one different FPKCs, and ii) after some basic ideas helpful for the DPA are outlined, reviews a technique that proved to be successful for the DPA solution of several FPKCs. Specifically, the technique focuses on the generation of the closure equations of the manipulator that is a basic stage for accomplishing the DPA solution in analytical form. Closure equations for one manipulator are also reported in order to outline the key role of the aforementioned technique.