Workspace and Kinematic Analysis of the VERNE machine

This paper describes the workspace and the inverse and direct kinematic analysis of the VERNE machine, a serial/parallel 5-axis machine tool designed by Fatronik for IRCCyN. This machine is composed of a three-degree-of-freedom (DOF) parallel module and a two-DOF serial tilting table. The parallel module consists of a moving platform that is connected to a fixed base by three non-identical legs. This feature involves (i) a simultaneous combination of rotation and translation for the moving platform, which is balanced by the tilting table and (ii) workspace whose shape and volume vary as a function of the tool length. This paper summarizes results obtained in the context of the European projects NEXT ("Next Generation of Productions Systems")

Workspace Analysis of the Parallel Module of the VERNE Machine

The paper addresses geometric aspects of a spatial three-degree-of-freedom parallel module, which is the parallel module of a hybrid serial-parallel 5-axis machine tool. This parallel module consists of a moving platform that is connected to a fixed base by three non-identical legs. Each leg is made up of one prismatic and two pairs of spherical joint, which are connected in a way that the combined effects of the three legs lead to an over-constrained mechanism with complex motion. This motion is defined as a simultaneous combination of rotation and translation. A method for computing the complete workspace of the VERNE parallel module for various tool lengths is presented. An algorithm describing this method is also introduced

Kinematic Analysis of a Serial - Parallel Machine Tool: the VERNE machine

The paper derives the inverse and the forward kinematic equations of a serial - parallel 5-axis machine tool: the VERNE machine. This machine is composed of a three-degree-of-freedom (DOF) parallel module and a two-DOF serial tilting table. The parallel module consists of a moving platform that is connected to a fixed base by three non-identical legs. These legs are connected in a way that the combined effects of the three legs lead to an over-constrained mechanism with complex motion. This motion is defined as a simultaneous combination of rotation and translation. In this paper we propose symbolical methods that able to calculate all kinematic solutions and identify the acceptable one by adding analytical constraint on the disposition of legs of the parallel module

Stiffness Analysis of 3-d.o.f. Overconstrained Translational Parallel Manipulators

The paper presents a new stiffness modelling method for overconstrained parallel manipulators, which is applied to 3-d.o.f. translational mechanisms. It is based on a multidimensional lumped-parameter model that replaces the link flexibility by localized 6-d.o.f. virtual springs. In contrast to other works, the method includes a FEA-based link stiffness evaluation and employs a new solution strategy of the kinetostatic equations, which allows computing the stiffness matrix for the overconstrained architectures and for the singular manipulator postures. The advantages of the developed technique are confirmed by application examples, which deal with comparative stiffness analysis of two translational parallel manipulators

TriP: A Python package for the kinematic modeling of serial-parallel hybrid robots

can be classified according to their mechanical structure. Serial mechanisms like robotic arms are mechanisms where each moving part (called a link) is connected to only the one before and the one after it. They are often used when a large workspace is required, meaning the robot needs a long reach. In parallel mechanisms, the links of the robot form loops causing them to be structurally stronger and stiffer. If both a large workspace and structural strength are required, hybrids that contain both serial and parallel mechanisms are used. While hybrid mechanisms combine the mechanical advantages of both parallel and serial mechanisms, they also combine their modeling disadvantages: Finding an explicit solution for either forward or inverse kinematics is often impossible. Using numerical approaches instead leads to complicated constrained optimization problems for both forward and inverse kinematics. While serial mechanisms are very well supported by current robotic frameworks, parallel mechanisms and hybrid mechanisms especially are often not supported at all. TriP is a python package designed to close this gap using a modular modeling framework. It allows the modeling of arbitrary hybrid mechanisms and is capable of calculating forward and inverse kinematics

Inverse and forward kinematics and workspace analysis of a novel 5-DOF (3T2R) parallel–serial (hybrid) manipulator:

The proposed study provides a solution of the inverse and forward kinematic problems and workspace analysis for a five-degree-of-freedom parallel–serial manipulator, in which the parallel kinematic chain is made in the form of a tripod and the serial kinematic chain is made in the form of two carriages displaced in perpendicular directions. The proposed manipulator allows to realize five independent movements—three translations and two rotations motion pattern (3T2R). Analytical relationships between the coordinates of the end-effector and five controlled movements provided by manipulator's drives (generalized coordinates) were determined. The approach of reachable workspace calculation was defined with respect to available design constraints of the manipulator based on the obtained algorithms of the inverse and forward kinematics. Case studies are considered based on the obtained algorithms of inverse and forward kinematics. For the inverse kinematic problem, the solution is obtained in accordance with the given laws of position and orientation change of the end-effector, corresponding to the motion along a spiral-helical trajectory. For the forward kinematic problem, various assemblies of the manipulator are obtained at the same given values of the generalized coordinates. An example of reachable workspace designing finalizes the proposed study. Dimensions and extreme values of the end-effector orientation angles are calculated

FASTKIT: A Mobile Cable-Driven Parallel Robot for Logistics

International audienceThe subject of this paper is about the design, modeling, control and performance evaluation of a low cost and versatile robotic solution for logistics. The robot under study, named FASTKIT, is obtained from a combination of mobile robots and a Cable-Driven Parallel Robot (CDPR). FASTKIT addresses an industrial need for fast picking and kitting operations in existing storage facilities while being easy to install, keeping existing infrastructures and covering large areas. The FASTKIT prototype consists of two mobile bases that carry the exit points of the CDPR. The system can navigate autonomously to the area of interest. Once the desired position is attained, the system deploys the CDPR in such a way that its workspace corresponds to the current task specification. The system calculates the required mobile base position from the desired workspace and ensures the controllability of the platform during the deployment. Once the system is successfully deployed, the set of stabilizers are used to ensure the prototype structural stability. Then the prototype gripper is moved accurately by the CDPR at high velocity over a large area by controlling the cable tension

Singularity Analysis of Lower-Mobility Parallel Manipulators Using Grassmann-Cayley Algebra

This paper introduces a methodology to analyze geometrically the singularities of manipulators, of which legs apply both actuation forces and constraint moments to their moving platform. Lower-mobility parallel manipulators and parallel manipulators, of which some legs do not have any spherical joint, are such manipulators. The geometric conditions associated with the dependency of six Pl\"ucker vectors of finite lines or lines at infinity constituting the rows of the inverse Jacobian matrix are formulated using Grassmann-Cayley Algebra. Accordingly, the singularity conditions are obtained in vector form. This study is illustrated with the singularity analysis of four manipulators

Contribution à l'étude cinématique et dynamique des machines parallèles

This thesis deals with the kinematic and dynamic modelling of limited degree-of-freedom parallel robots. These robots with less than six degrees of freedom are able to carry out several industrial tasks. The main reason of using such robots is to reduce the production costs by using less legs and motors. However, in some cases, these structures can produce a complex motion defined as a simultaneous combination of translation and rotation of the moving platform, which is the case of the Verne parallel module having three translation degrees of freedom. The modelling of this type of robots can prove to be complicated. This report includes five chapters. In the first chapter, a classification of parallel architectures is presented and a state of the art on important notions on kinematics and design of manipulators is exposed. The second and the third chapters are devoted to the kinematic modelling, serial singularity analysis and workspace calculation of the Verne machine. The fourth chapter deals with parallel singularity analysis of limited degrees of freedom robots using Grassmann-Cayley algebra. The geometrical conditions of existence of parallel singularities of three classes of parallel manipulators are found. Finally, the fifth chapter covers the dynamic modelling of limited degree-of-freedom parallel manipulators. A general method based on the Newton-Euler algorithm is developed. The proposed method takes in consideration all the dynamics of these robots including the legs dynamics as well as the mobile platform dynamics.Les travaux présentés dans cette thèse portent sur l’étude cinématique et dynamique des robots parallèles à mobilités restreintes. Ces robots à moins de 6 degrés de liberté permettent d’effectuer de multiples tâches demandées par l’industrie. La raison principale de l’utilisation de ces robots est la volonté de réduire le coût en utilisant moins de jambes et moins de moteurs. Cependant, ces structures peuvent dans certains cas produire un mouvement de la plate-forme contraint par un couplage entre la position et l’orientation comme pour le module parallèle de la machine Verne ayant trois degrés de liberté de translation. Dans ce cas, la modélisation peut s’avérer compliquée. Ce mémoire comporte cinq chapitres. Dans le premier chapitre, une classification des architectures parallèles est présentée et des notions importantes liées à la cinématique et à la conception des manipulateurs sont exposées. Les deuxième et troisième chapitres sont consacrés à la modélisation géométrique, à l’étude des singularités sérielles et au calcul de l’espace de travail de la machine Verne. Le quatrième chapitre traite les singularités parallèles des manipulateurs à mobilités restreintes en utilisant l’algèbre de Grassmann-Cayley. Les conditions géométriques d’existence des singularités pour trois classes de manipulateurs sont trouvées. Les chaînes de ces manipulateurs transmettent des forces et/ou couples à la plate-forme mobile. Finalement, le cinquième chapitre concerne la modélisation dynamique des manipulateurs à mobilités restreintes. Une méthode générale basée sur les algorithmes de type Newton-Euler est développée. La méthode proposée prend en compte la dynamique des jambes et de la plate-forme. Nous obtenons ainsi des modèles dynamiques complets de ces robots

Stiffness Analysis of Overconstrained Parallel Manipulators

The paper presents a new stiffness modeling method for overconstrained parallel manipulators with flexible links and compliant actuating joints. It is based on a multidimensional lumped-parameter model that replaces the link flexibility by localized 6-dof virtual springs that describe both translational/rotational compliance and the coupling between them. In contrast to other works, the method involves a FEA-based link stiffness evaluation and employs a new solution strategy of the kinetostatic equations for the unloaded manipulator configuration, which allows computing the stiffness matrix for the overconstrained architectures, including singular manipulator postures. The advantages of the developed technique are confirmed by application examples, which deal with comparative stiffness analysis of two translational parallel manipulators of 3-PUU and 3-PRPaR architectures. Accuracy of the proposed approach was evaluated for a case study, which focuses on stiffness analysis of Orthoglide parallel manipulator