Robot kinematics | EPFL Graph Search

In robotics, robot kinematics applies geometry to the study of the movement of multi-degree of freedom kinematic chains that form the structure of robotic systems. The emphasis on geometry means that the links of the robot are modeled as rigid bodies and its joints are assumed to provide pure rotation or translation. Robot kinematics studies the relationship between the dimensions and connectivity of kinematic chains and the position, velocity and acceleration of each of the links in the robotic system, in order to plan and control movement and to compute actuator forces and torques. The relationship between mass and inertia properties, motion, and the associated forces and torques is studied as part of robot dynamics. Kinematic equations A fundamental tool in robot kinematics is the kinematics equations of the kinematic chains that form the robot. These non-linear equations are used to map the joint parameters to the configuration of the robot system. Kinematics equ

Méthode d'étalonnage d'une machine-outil à cinématique parallèle à cinq axes à grands angles d'inclinaison

Hélène Frayssinet Mazerolle

A machine-tool is able to manufacture precisely only when it is calibrated. Calibration consists in correcting the model of the machine so that it represents the real kinematics. On no account calibrating a structure consists in changing some parts of the machine. The industrial machining prototype of the Hita-STT (Stiffness Tracking Technology) machine-tool has a four-axis parallel kinematics associated to a turning table as left hand. The spindle is fixed to the parallel kinematics; the workpiece is fixed to the turning table. This new machine-tool was developed by the Laboratoire de Systèmes Robotiques from EPFL and Willemin-Macodel S.A. For its industrialization, it needs an absolute accuracy of 10 microns after calibration considering a repeatability of 5 microns. These specifications should be obtained in the entire workspace between the spindle and the turning device. This doctoral thesis deals with the calibration of the Hita-STT machine-tool. Several methods can be developed. They differ in: the geometrical model that is used. For each kinematics, three geometrical models exist: the implicit model, the forward geometrical model and the inverse geometrical model; the way the corrections are applied. Pose errors are compensated correcting the commands sent to the controller; or the parameters of the structure are identified and updated on the controller. This last solution allows to use a model for the control of the machine that is closer to the real kinematics. These different methods are presented and compared. An optimal calibration method is proposed. Whatever calibration methodology is chosen, it is divided into four steps: modeling the kinematics. An unique distribution of the parameters of the Hita-STT parallel kinematics is proposed; measurement of the pose errors. The choice and the design of the measuring device are presented. A set-up and characterization procedure is explained. It is compatible with the industrial environment. The pose errors measurements are automatic thanks to special ISO functions added to the controller. Data processing is automatic; calculation of the corrections of the model. Several methods are compared in terms of accuracy that can be obtained. An "ideal" method is proposed for the parallel kinematics calibration. It combines the two families of calibration methods, it means an identification method followed by a direct calibration method; implementation. The "ideal" method is tested on the industrial machining prototype Hita-STT. The structure of the programs used to automate the calibration process are given. Tests used to verify the calibration quality are presented. They can also be used to make sure that the parallel kinematics is accurate enough to satisfy the required quality of the manufactured parts.

EPFL2007

Optimisation de la conception du robot parallèle Delta cube de très haute précision

Tiavina Niaritsiry

In the high-precision industry, most operations require the use of robots able to accomplish highly accurate and repeatable motions. In order to meet the desired level of absolute accuracy, one has to limit or even suppress the effects of different sources of inaccuracy by means of an appropriate calibration. However, calibration techniques cannot be applied to compensate inaccuracies occuring along passive (non-actuated) degrees of freedom (e.g orientation errors on the end-effector of a 3 degrees-of-freedom (DOF) in translation robot). The main goal of this thesis is to evaluate and benchmark the effects of these different sources of inaccuracy. Moreover, a set of design rules are proposed in order to optimize flexure parallel robots regarding their absolute accuracy. The robots studied in this work are of "Delta Cube" type, having their kinematic chains composed of translational stages and space parallelograms (acting as universal joints). These robots have the following features: their 3 DOF are the (x, y, z) translations on the Euclidean space, the stroke of each DOF goes from ±1 mm to ± 4 mm, their repeatabilities are at the nanometre range (thanks to the absence of dry friction and mechanical play), their resolutions are within a few nanometers (only limited by the captors used), their small sizes go from 1,5 dm3 to 13 dm3. The analysis of the effects of the different sources of inaccuracy has been focused on the following points: the basic elements composing the robot structure (translational stage, space parallelogram). Studying the influence on the absolute accuracy caused by a variation of a given geometric dimension provides knowledge on how to optimize the overall robot dimensions regarding absolute accuracy; the assembly of the different basic elements on the kinematic chain (in particular their relative orientation) is also critical for the absolute accuracy of the robot since it may cause parasitic effects such as orientation errors in the end-effector; the type and location of the different captors, motors and the frame can also influence accuracy. The analysis of the influence of each source of inaccuracy (manufacturing tolerances, temperature variations, assembly defaults, effect of external loads) and their coupling has been mainly performed numerically by means of Finite-Element Models. Theoretical results have been verified by experimental data. Considering the simulation results for each basic structure as well as the comparison of different assembly variants, general design rules have been proposed in order to optimize a given flexure parallel robot regarding absolute accuracy and considering also the application the robot is made for. This work is a contribution to the design of high-precision flexure parallel robots regarding absolute accuracy. It is also an important tool for the engineer in order to make the calibration work easier.

EPFL2006

Orion MinAngle: A flexure-based, double-tilting parallel kinematics for ultra-high precision applications requiring high angles of rotation

Reymond Clavel, Patric Pham

If you need to design ultra-high precision devices for mechanisms with multiple axes there are not a lot of ways leading around flexure-based joints. Using this type of articulations totally eliminates backlash and friction and is, by this, providing an accurate mechanical foundation for your device. The most important disadvantage of this technology is the low range of motion. The basic joint types, blades and circular hinges, have angular limits which strongly depend on the targeted stiffness, the quantity of motion cycles and the elastic limit of the material. This article will introduce novel parallel kinematics which are totally based on 1 dof flexures and whose angular range of motion is determined by twice the range of the single joint. It is a 3 dof parallel kinematic based on 3 identical kinematic chains which produce movements in θx, θy and z. The model has been designed to constitute the left hand of a machine tool that requires orienting the workpiece in a very precise manner and with high rotation amplitudes. Additionally to this it presents very interesting characteristics of Remote-Center-of-Motion (RCM) mechanisms. This is a vital feature for applications where the linear movements are highly limited and should not be consumed by parasitic movements of other axes. All these features, combined with the advantages of parallel kinematics, make the Orion MinAngle a very interesting concept. The model has been designed with joints achieving ±7.6° leading to an output angle of ±15° on both rotation axes. The study has shown really promising results concerning the mechanical properties, the high rotation angles and the RCM capabilities. The paper presents the kinematics and its optimization method which is used to guarantee a nearly perfect division of the output angle on all pivots of the mechanism. The next chapters talk about the dimensioning of the flexible joints and generally about the design of the robot. The last part of the paper verifies the optimization trough kinematic modeling of the robot and computes the mechanical properties like stiffness, internal strains and mechanical Eigenfrequencies. At the end we propose a realistic application as a 5-axes parallel-kinematic machine tool and we come to a conclusion about the potential of the Orion MinAngle mechanism.

2005