In this paper, we propose two algorithms for the auto-calibration of the home position or the joint angle offsets for a parallel manipulator by utilizing the extra sensor(s) information (sensor redundancy), sampling over the workspace, and optimizing a suitably chosen cost function, without resorting to any other external equipment. Meanwhile, a measure or estimate of the precision of the machine is also obtained. It is very useful and convenient if the machine needs frequent re-calibration. Simulations and experiments are also performed to show 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.

Studies the dynamics of parallel manipulators. We first have a brief review and discussion on different dynamics formulations in the literature (Newton-Euler, direct Lagrangian, and Lagrange-D'Alembert formulation on the reduced system). Then we show the equivalence of these methods. Based on the concepts from differential manifolds, we prove that away from configuration singularity, there exists a projection from the joint space to parameterize the configuration space. The fact that the dynamics is well defined even at actuators singularity, end-effector singularity and other kinds of parameterization singularity is highlighted. For the method of reduced systems, there are two main drawbacks. Firstly the joints being cut for forming the tree system are presumed to have no external torque. Secondly the force and torque applied to other links of the manipulator is not considered. We propose two methods to remedy the situation. Firstly by cutting a link instead of a joint, all the joints torque can be incorporated into our equations of motion. This is useful not only for the case of actuating all the joints, but also if we consider compensating the joints friction. Secondly we propose a concept of transforming force to the generalized force space so that all the other forces and torque can be considered.

Parallel manipulators with redundant actuation present both problems and advantages. We analyze some major advantages of redundancy to demonstrate its usefulness. The dynamics of closed-chain mechanisms has been studied by many researchers. However, they often only consider the case of normal actuation. Few methods are suitable for closed-chain mechanisms with redundant actuation. In the article, the dynamic model of redundantly actuated closed-chain mechanisms is presented explicitly by applying Lagrange-D'Alembert formulations. As an illustrative example, the dynamic model of a 2-DOF planar parallel redundant manipulator is presented. A PID control algorithm in the joint space is experimentally implemented on this parallel manipulator to perform trajectory tracking. The experimental results show the validity of PID control.