Kinematics of Redundantly Actuated Closed Chains

The instantaneous kinematics of a hybrid manipulation system, which combines the traditional serial chain geometry with parallelism in actuation, and the problem of coordination is discussed. The indeterminacy and singularities in the inverse kinematics and statics equations and measures of kinematic performance are analyzed. Finally, coordination algorithms that maintain an optimal force distribution between the actuators while avoiding or exploiting singularities are presented

Parallel Manipulators

In recent years, parallel kinematics mechanisms have attracted a lot of attention from the academic and industrial communities due to potential applications not only as robot manipulators but also as machine tools. Generally, the criteria used to compare the performance of traditional serial robots and parallel robots are the workspace, the ratio between the payload and the robot mass, accuracy, and dynamic behaviour. In addition to the reduced coupling effect between joints, parallel robots bring the benefits of much higher payload-robot mass ratios, superior accuracy and greater stiffness; qualities which lead to better dynamic performance. The main drawback with parallel robots is the relatively small workspace. A great deal of research on parallel robots has been carried out worldwide, and a large number of parallel mechanism systems have been built for various applications, such as remote handling, machine tools, medical robots, simulators, micro-robots, and humanoid robots. This book opens a window to exceptional research and development work on parallel mechanisms contributed by authors from around the world. Through this window the reader can get a good view of current parallel robot research and applications

On the false positives and false negatives of the Jacobian Matrix in kinematically redundant parallel mechanisms

The Jacobian matrix is a highly popular tool for the control and performance analysis of closed-loop robots. Its usefulness in parallel mechanisms is certainly apparent, and its application to solve motion planning problems, or other higher level questions, has been seldom queried, or limited to non-redundant systems. In this paper, we discuss the shortcomings of the use of the Jacobian matrix under redundancy, in particular when applied to kinematically redundant parallel architectures with non-serially connected actuators. These architectures have become fairly popular recently as they allow the end-effector to achieve full rotations, which is an impossible task with traditional topologies. The problems with the Jacobian matrix in these novel systems arise from the need to eliminate redundant variables when forming it, resulting in both situations where the Jacobian incorrectly identifies singularities (false positive), and where it fails to identify singularities (false negative). These issues have thus far remained unaddressed in the literature. We highlight these limitations herein by demonstrating several cases using numerical examples of both planar and spatial architectures

Elasto-geometrical modeling and calibration of redundantly actuated PKMs

International audienceRedundantlyactuated parallel kinematic machines (PKMs) offer a number of advantages compared to classical non-redundant PKMs. Particularly, they show a better stiffness thanks to singularity avoidance and they have an improved repeatability due to a better behavior against backlashes. The main problem with the calibration of these machines is that the redundancy leads to some mechanical strains in their structure. This makes it difficult to identify the geometrical errors of their structure without taking into account the effects of the elastic deformations. The main originality of this work is to propose an efficient elasto-geometrical and calibration method that allows the identification of both the geometrical and stiffness parameters of redundantlyactuated parallel mechanisms with slender links. The first part of the paper explains the proposed method through its application on a simple redundant planar mechanism. The second part deals with its experimental application to the redundant Scissors Kinematics machine