Presents an inertia equivalence principle that exposes the relation between the dynamics of a parallel manipulator, and that of its arbitrary reduced tree systems. This principle, along with the D'Alembert principle, leads to a precise proof of the nontrivial fact that the virtual work principle is also valid for the two different physical systems, a parallel manipulator and its reduced tree system, under a given condition. The dynamics of parallel manipulators and its properties are then given. Two control algorithms are then provided. Firstly, we implement a geometric control algorithm that is based on the Riemannian metric structure associated with the kinetic energy of the manipulator. Motivated by this, an adaptive control algorithm is then proposed in which only dynamic parameters are required to be updated. Geometric reinterpretation of this algorithm as the passive port controlled system is given. Its asymptotic stability is therefore obvious. The new content of this algorithm compared with the traditional ones is discussed. Experimental results are reported that demonstrate the effectiveness of the algorithms.

As we all know, singularity is commonly encountered in parallel mechanisms. It is shown that the behavior of singularity of parallel mechanisms could be more complicated than that of serial ones. However, it is not very clear whether singularity will bring problems to kinematics, dynamics or other characteristics and what result will be caused when parallel mechanisms fall into the neighborhood of a singularity. We focus on the study of the undesired effects of singularity in parallel mechanisms and propose a method to solve them, namely the method of redundancy. Three kinds of redundant methods are developed and their advantages are discussed. In the experiments, we concentrate on the control of redundantly actuated parallel mechanisms. We control the parallel mechanisms tracking a given trajectory by kinematic control method and dynamic control method respectively. Experimental results verified the efficiency of the proposed algorithms.

Singularity is a fundamental problem in the analysis of parallel mechanisms. The distribution of singularity in the workspace will determine to a great extent the properties of parallel mechanisms. We study the distribution of actuator singularity, which can also be applied to analyze end-effector singularity. A very important observation has been made that these two kinds of singularities are caused by the parameterization of a configuration manifold by actuator coordinates or end-effector coordinates. Despite the various styles of singularities of parallel mechanisms, there are some rules which govern the behavior of stable singularities. These rules provide some useful ideas in the design of redundant parallel mechanisms so as to achieve better performance in high speed motion and improve their stiffness. Optimal kinematic and dynamic control algorithms are designed and implemented which make use of the redundancy of the parallel mechanism. Experimental results agree with our expectation.