The study and optimization of kinematically redundant parallel manipulators

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A parallel manipulator is a mechanism that consists of an end effector that is linked to its base by at least two chains. A well-known use is a flight simulator. These manipulators have certain advantages compared to serial manipulators, especially when it comes to rigidity and the ratio of the payload to the mass of the manipulator. However, the workspace is smaller and there exists configurations that are called singular in which the manipulator cannot resist to external forces or moments. Kinematic redundancy is obtained when extra links and joints are added to a chain. This enlarges the workspace, reduces or eliminates singularities and modifies the performance. This research program is an extension of our previous work and will focus on kinematically redundant parallel manipulators. The first objective of this research program is to study the effects of the number of degrees of redundancy on the performance of parallel manipulators. Different performance criteria will be studied while varying the number of degrees of redundancy. The second objective is to study the dynamic behavior of kinematically redundant parallel manipulators with different degrees of redundancy. In particular, the effect of redundancy on the performance of a manipulator that is following a trajectory with sharp corners or that passes near a singularity will be examined. The third objective is to perform the synthesis of kinematically redundant parallel manipulators. The synthesis problem requires the determination of the architectural parameters, for example the position of the attachment points, the length of the members or the dimensions of the end effector to satisfy certain specified criteria. This problem is complex since an infinite number of possible geometric parameters exist. Furthermore, when there is kinematic redundancy, there are an infinite number of possible joint values for a specified pose even when the architectural parameters are known. To perform the synthesis, an optimisation algorithm that evaluates a performance criterion for different combinations of architectural parameters and that changes the latter to improve the criterion is used. For example, if a prescribed workspace is desired, the optimisation modifies the architectural parameters to obtain a solution as close as possible to that desired. If it is desired to optimise another performance criterion at the same time, another optimisation is necessary to obtain the best combination of joint variables. A two-level optimisation will thus be necessary, a first to obtain the architectural parameters and a second within the first to optimise the performance. Parallel manipulators are used in certain industrial applications, in particular as flight simulators and as machine tools. Studies are necessary to determine if kinematic redundancy is beneficial. The results of this research will be beneficial to designers of parallel manipulators.