The study and optimization of kinematically redundant parallel manipulators

并联机械手是由一个末端执行器组成的机构，该末端执行器通过至少两条链连接到其底座。一个众所周知的用途是飞行模拟器。与串联机械手相比，这些机械手具有一定的优势，特别是在刚性和有效载荷与机械手质量的比率方面。然而，工作空间较小，并且存在称为奇异的配置，其中机械手无法抵抗外力或力矩。将额外的连杆和运动类型添加到链中时，将获得运动学冗余。这扩大了工作空间，减少或消除了奇点，并改变了性能。本研究项目是我们以前工作的延伸，将重点放在运动学冗余度并联机器人上。该研究计划的第一个目标是研究冗余度对并联机器人性能的影响。将研究不同的性能标准，同时改变冗余度的数量。第二个目标是研究不同冗余度的运动冗余度并联机器人的动力学行为。特别是，冗余度对跟随带有尖角的轨迹或在奇点附近通过的机械手的性能的影响将被考察。第三个目标是进行运动学冗余度并联机器人的综合。综合问题需要确定结构参数，例如连接点的位置、构件的长度或末端执行器的尺寸以满足特定的标准。这个问题很复杂，因为存在无限多可能的几何参数。此外，当存在运动学冗余时，即使在建筑参数已知的情况下，指定姿势的可能关节值也是无限多的。为了执行综合，使用优化算法，该优化算法评估用于不同结构参数组合的性能标准，并且改变后者以改进该标准。例如，如果需要指定的工作空间，则优化会修改架构参数以获得尽可能接近所需的解决方案。如果希望同时优化另一个性能标准，则需要进行另一次优化，以获得联合变量的最佳组合。因此，需要进行两级优化，第一级用于获取体系结构参数，第二级用于优化性能。并联机械手在某些工业应用中被使用，特别是用作飞行模拟器和机床。有必要进行研究，以确定运动学冗余是否有益。本文的研究结果对并联机器人的设计具有一定的参考价值。

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.