An Interval Analysis Based Study for the Design and the Comparison of 3-DOF Parallel Kinematic Machines

International audienceThis paper addresses an interval analysis based study that is applied to the design and the comparison of 3-DOF parallel kinematic machines. Two design criteria are used, (i) a regular workspace shape and, (ii) a kinetostatic performance index that needs to be as homogeneous as possible throughout the workspace. The interval analysis based method takes these two criteria into account: on the basis of prescribed kinetostatic performances, the workspace is analysed to find out the largest regular dextrous workspace enclosed in the Cartesian workspace. An algorithm describing this method is introduced. Two 3-DOF translational parallel mechanisms designed for machining applications are compared using this method. The first machine features three fixed linear joints which are mounted orthogonally and the second one features three linear joints which are mounted in parallel. In both cases, the mobile platform moves in the Cartesian x-y-z space with fixed orientation

Workspace and Singularity analysis of a Delta like family robot

Workspace and joint space analysis are essential steps in describing the task and designing the control loop of the robot, respectively. This paper presents the descriptive analysis of a family of delta-like parallel robots by using algebraic tools to induce an estimation about the complexity in representing the singularities in the workspace and the joint space. A Gr{\"o}bner based elimination is used to compute the singularities of the manipulator and a Cylindrical Algebraic Decomposition algorithm is used to study the workspace and the joint space. From these algebraic objects, we propose some certified three dimensional plotting describing the the shape of workspace and of the joint space which will help the engineers or researchers to decide the most suited configuration of the manipulator they should use for a given task. Also, the different parameters associated with the complexity of the serial and parallel singularities are tabulated, which further enhance the selection of the different configuration of the manipulator by comparing the complexity of the singularity equations.Comment: 4th IFTOMM International Symposium on Robotics and Mechatronics, Jun 2015, Poitiers, France. 201

Parametric stiffness analysis of the Orthoglide

This paper presents a parametric stiffness analysis of the Orthoglide. A compliant modeling and a symbolic expression of the stiffness matrix are conducted. This allows a simple systematic analysis of the influence of the geometric design parameters and to quickly identify the critical link parameters. Our symbolic model is used to display the stiffest areas of the workspace for a specific machining task. Our approach can be applied to any parallel manipulator for which stiffness is a critical issue

A Comparative Study between Two Three-DOF Parallel Kinematic Machines using Kinetostatic Criteria and Interval Analysis

International audienceThis paper addresses the workspace analysis of two 3-DOF translational parallel mechanisms designed for machining applications. The two machines features three fixed linear joints. The joint axes of the first machine are orthogonal whereas these of the second are parallel. In both cases, the mobile platform moves in the Cartesian $x-y-z$ space with fixed orientation. The workspace analysis is conducted on the basis of prescribed kinetostatic performances. Interval analysis based methods are used to compute the dextrous workspace and the largest cube enclosed in this workspace

WORKSPACE ANALYSIS AND OPTIMIZATION OF THE PARALLEL ROBOTS BASED ON COMPUTER-AIDED DESIGN APPROACH

This paper provides workspace determination and analysis based on the graphical technique of both spatial and planar parallel manipulators. The computation and analysis of workspaces will be carried out using the parameterization and three-dimensional representation of the workspace. This technique is implemented in CAD (Computer Aided Design) Software CATIA workbenches. In order to determine the workspace of the proposed manipulators, the reachable region by each kinematic chain is created as a volume/area; afterwards, the full reachable workspace is obtained by the application of a Boolean intersection function on the previously generated volumes/areas. Finally, the relations between the total workspace and the design parameters are simulated, and the Product Engineering Optimizer workbench is used to optimize the design variables in order to obtain a maximized workspace volume. Simulated annealing (SA) and Conjugate Gradient (CG) are considered in this study as optimization tools