A Pair of Measures of Rotational Error for Axisymmetric Robot End-Effectors

International audienceThis paper deals with the problem of representing the rotational error of spatial robots with three orientational degrees of freedom (DOF). Typically, the errors on each of three Euler angles defining the orientation of an end-effector are analysed separately. However, this is wrong since an accuracy measure should depend only on the "distance" between the nominal pose and the actual one, and not on the choice of reference frame in which these are represented. Several bi-invariant metrics for rotational error exist but are single-parameter and, by definition, disregard the shape of the robot end-effector. Yet, robot end-effectors are typically axisymmetric. Therefore, we propose a two-parameter measure of rotational errors that is better suited for such robot end-effectors

Optimal dimensional synthesis of a symmetrical five-bar planar upper-extremity neuromotor device

Individuals with hemiplegia suffer from impaired arm movements that appear as a marked change in arm stiffness. A quantitative measure of arm stiffness would characterize rehabilitation therapy effectively, while little mechanism is designed to implement the function. A symmetrical five-bar linkage consisting of two revolute joints and three prismatic joints is presented. Inverse kinematics and forward kinematics are obtained first. Then inverse singularities and direct singularities of the mechanism are gained. Based on the results of kinematics analysis, the global stiffness index is defined. Finally, optimal dimensional synthesis of the mechanism in terms of maximum stiffness is conducted by genetic algorithms. The calculation results shows that when length of both the two linkage a=830 mm, interacting angle of the two guides 2d=4.48 radian, and maximum range of displacement of the two carriers dmax=940 mm, the mechanism achieves highest rigidity and its workspace is singularity-free, which covers the human left and right arm range of motion. The proposed novel mechanism featuring high rigidity and a singularity-free workspace can provides rehabilitation training, but also solves the problem of quantitative measure of arm stiffness

Jacobian, manipulability, condition number and accuracy of parallelrobots

Although the concepts of jacobian matrix, manipulability and condition number have been floating around since the early beginning of robotics their real significance is not always well understood. In this paper we re-visit these concepts for parallel robots and exhibit some surprising results (at least for the author!) that show that these concepts have to be manipulated with care for a proper understanding of the kinematics behavior of a robot

Appropriate Design of Parallel Manipulators

International audienceAlthough parallel structures have found a niche market in many applications such as machine tools, telescope positioning or food packaging, they are not as successful as expected. The main reason of this relative lack of success is that the study and hardware of parallel structures have clearly not reached the same level of completeness than the one of serial structures. Among the main issues that have to be addressed, the design problem is crucial. Indeed, the performances that can be expected from a parallel robot are heavily dependent upon the choice of the mechanical structure and even more from its dimensioning. In this chapter, we show that classical design methodologies are not appropriate for such closed-loop mechanism and examine what alternatives are possible

Appropriate synthesis of the four-bar linkage

International audienceThe uncertainties arising from the fabrication and operation of mechanisms, specifically the four-bar linkage, significantly affect the expected performance of the mechanism. To accommodate uncertainties during the dimensional synthesis of the four-bar linkage, the desired coupler curve response is described by any number of precision point elements and trajectory elements, where each element is specified with an allowable error. A design description which accounts for bounded uncertainties is termed an appropriate design. An appropriate synthesis method is developed to synthesize the entire set of appropriate design solutions corresponding to the desired response. This method is able to completely explore the continuous design space and each synthesized appropriate design guarantees that the resulting four-bar linkage has a corresponding coupler point which lies inside each precision point response element, and a corresponding set of continuous coupler points which remain inside the trajectory response elements from start to finish

Performance analysis and design of parallel kinematic machines using interval analysis

International audienceSome design methodologies for Parallel Kinematic Machines (PKM) have been proposed but with limitations regarding two main problems: how to improve multiple properties of different nature such as accuracy, force or singularity poses, and how to check these properties for all poses inside the PKM workspace. To address these problems, this work proposes to formulate the design problem as a feasibility problem and use a data representation which takes into account the uncertainty or variation of the involved parameters. This method, based on interval analysis, allows to evaluate several performance indexes of a PKM design. For validation purposes, this methodology is applied to a PKM, obtaining a continuous set of possible kinematic parameters values for its architecture which is capable of fulfilling several performance requirements over a desired workspace

Dimensional Synthesis of Parallel Robots with a Guaranteed Given Accuracy over a Specific Workspace

Abstract — We are considering a n d.o.f. parallel robot that has to move within a given workspace and whose geometry is defined by a set of parameters. The motion of active joints of the manipulator are measured with sensors with a known accuracy ±∆ρ. These errors together with bounded manufacturing errors on the parameters describing the geometry of the robot induces a positioning errors ∆X of the platform. We present an algorithm that allows one to determine geometries of the robot ensuring that these positioning errors will lie within pre-specified limits for any pose of the robot in its workspace even if the physical realization of the robot differs from the theoretical model while staying within the given manufacturing errors bounds. A by-product variant of this algorithm allows one to compute the maximal positioning errors of a given robot up to a predefined accuracy. I

Design of hybrid-kinematic mechanisms for machine tools

The machine tool industry is a well established, old and extremely important branch of today's manufacturing industry. With the ongoing globalization and the resulting increase of competition in this industry, the manufacturers have to push their technology to the limits in order to stay competitive. The architecture (kinematics) of most machine tools is based on a serial arrangement of joints and segments, like a human arm. The requirements regarding dynamics, stiffness and precision of these machines brought the scientists and industries to evaluate parallel kinematics for this type of application. Parallel kinematics possess a much higher potential to fulfill these demands, and they would therefore allow the access to a next level of machine performance. Whereas the success of parallel kinematics in domains like packaging is incontestable, it proved to be less evident in machine tools. The low rotation amplitudes and the complexity of the mechanism, the main weak points of parallel kinematics, slow down the development and integration of this kind of machines. In the last few years however, we could observe an increase in development, and more important, in the sales (1)(37)(54) of hybrid kinematic machines. Hybrid kinematics can, by appropriate combination of parallel and serial axes, present a well performing compromise, especially in the machine tool domain where 5 axes/mobilities and high rotation amplitudes are common. The present document is concerned with the mechanical, industrialized design of hybrid-kinematic machine tools and their mechanical elements, and will show that "Hybrid-kinematic mechanisms can outperform fully-parallel mechanisms considering all attributes for a successful and industrialized machine design." The work will point out the limits of fully-parallel mechanisms and justify the use of hybrid solutions. The most important elements of the mechanisms, thereof particularly the spherical and universal joints, will be treated in a detailed manner. Industrialization aspects will be analyzed, the difficulty for their integration will be shown, and solutions provided in order to increase the accessibility of hybrid and parallel mechanisms. A design methodology will be synthesized from all these elements and applied to three case studies. The methodology will point out important and often neglected steps and provide elements and tools to support the designer in the whole process of creation. Furthermore, by providing a broad catalogue of both new and existing hybrid and parallel kinematics, this work is intended to stimulate and inspire the creativity of the designer. The three final cases studies, each differing in their application domain and representing each an unpublished concept, will illustrate and validate the methodology. The work took place around multiple industrial projects and therefore always keeps in mind the practical feasibility, with respect to an industrial environment, and the economic aspects and risks