No abstract

No abstract

No abstract

The inverse kinematics problem is formulated as a parameterized autonomous dynamical system problem, and respective analysis is carried out. It is shown that a singular point of work space can be mapped either as a critical or a noncritical point of the autonomous system, depending on the direction of approach to the singular point. Making use of the noncritical mapping, a closed-loop kinematic controller with asymptotic stability and velocity limits along degenerate singular or near-singular paths is designed. The authors introduce a specific type of motion along the reference path, the so-called natural motion. This type of motion is obtained in a straightforward manner from the autonomous dynamical system and always satisfies the motion constraint at a singular point. In the vicinity of the singular point, natural motion slows down the end-effector speed and keeps the joint velocity bounded. Thus, no special trajectory replanning will be required. In addition, the singular manifold can be crossed, if necessary. Further on, it is shown that natural motion constitutes an integrable motion component. The remaining, nonintegrable motion component is shown to be helpful in solving a problem related to the critical point mapping of the autonomous system. The authors design a singularity-consistent resolved acceleration controller, which they then apply to singular or near-singular trajectory tracking under torque limits. Finally, the authors compare the main features of the singularity-consistent method and the damped-least-squares method. It is shown that both methods introduce a so-called algorithmic error in the vicinity of a singular point. The direction of this error is, however, different in each method. This is shown to play an important role for system stability.

In our previous work, we developed a compact 6-DOF haptic interface as a master device which achieved an effective manual teleoperation. The haptic interface contains a modified Delta parallel-link positioning mechanism. Parallel mechanisms are usually characterized by a high stiffness, which, however, is reduced by elastic deformations of both parts and bearings. Therefore, to design such a parallel mechanism, we should analyze its structural stiffness, including elastic deformations of both parts and bearings. Then we propose a simple method to analyze structural stiffness in a parallel mechanism using bearings. Our method is based on standard concepts such as static elastic deformations. However, the important aspect of our method is the manner in which we combine these concepts and how we obtain the value of the elasticity coefficient of a rotation axis in a bearing. Finally, we design a modified Delta mechanism, with a well-balanced stiffness, based on our method of stiffness analysis.