Uniqueness domains and non singular assembly mode changing trajectories

Parallel robots admit generally several solutions to the direct kinematics problem. The aspects are associated with the maximal singularity free domains without any singular configurations. Inside these regions, some trajectories are possible between two solutions of the direct kinematic problem without meeting any type of singularity: non-singular assembly mode trajectories. An established condition for such trajectories is to have cusp points inside the joint space that must be encircled. This paper presents an approach based on the notion of uniqueness domains to explain this behaviour

Cusp points in the parameter space of RPR-2PRR parallel manipulators

International audienceThis paper investigates the existence conditions of cusp points in the design parameter space of the R\underline{P}R-2P\underline{R}R parallel manipulators. Cusp points make possible non-singular assembly-mode changing motion, which can possibly increase the size of the aspect, i.e. the maximum singularity free workspace. The method used is based on the notion of discriminant varieties and Cylindrical Algebraic Decomposition, and resorts to Gröbner bases for the solutions of systems of equations

Non-Singular Assembly Mode Changing Trajectories of a 6-DOF Parallel Robot

International audienceThis paper deals with the non-singular assembly mode changing of a six degrees of freedom parallel manipulator. The manipulator is composed of three identical limbs and one moving platform. Each limb is composed of three prismatic joints of directions orthogonal to each other and one spherical joint. The first two prismatic joints of each limb are actuated. The planes normal to the directions of the first two prismatic joints of each limb are orthogonal to each other. It appears that the parallel singularities of the manipulator depend only on the orientation of its moving platform. Moreover, the manipulator turns to have two aspects, namely, two maximal singularity free domains without any singular configuration, in its orientation workspace. As the manipulator can get up to eight solutions to its direct kinematic model, several assembly modes can be connected by non-singular trajectories. It is noteworthy that the images of those trajectories in the joint space of the manipulator encircle one or several cusp point(s). This property can be depicted in a three dimensional space because the singularities depend only on the orientation of the moving-platform and the mapping between the orientation parameters of the manipulator and three joint variables can be obtained with a simple change of variables. Finally, to the best of the authors' knowledge, this is the first spatial parallel manipulator for which non-singular assembly mode changing trajectories have been found and shown

Kinematics and workspace analysis of a 3ppps parallel robot with u-shaped base

This paper presents the kinematic analysis of the 3-PPPS parallel robot with an equilateral mobile platform and a U-shape base. The proposed design and appropriate selection of parameters allow to formulate simpler direct and inverse kinematics for the manipulator under study. The parallel singularities associated with the manipulator depend only on the orientation of the end-effector, and thus depend only on the orientation of the end effector. The quaternion parameters are used to represent the aspects, i.e. the singularity free regions of the workspace. A cylindrical algebraic decomposition is used to characterize the workspace and joint space with a low number of cells. The dis-criminant variety is obtained to describe the boundaries of each cell. With these simplifications, the 3-PPPS parallel robot with proposed design can be claimed as the simplest 6 DOF robot, which further makes it useful for the industrial applications

Workspace and joint space analysis of the 3-RPS parallel robot

International audienceThe Accurate calculation of the workspace and joint space for 3 RPS parallel robotic manipulator is a highly addressed research work across the world. Researchers have proposed a variety of methods to calculate these parameters. In the present context a cylindrical algebraic decomposition based method is proposed to model the workspace and joint space. It is a well know feature that this robot admits two operation modes. We are able to find out the set in the joint space with a constant number of solutions for the direct kinematic problem and the locus of the cusp points for the both operation mode. The characteristic surfaces are also computed to define the uniqueness domains in the workspace. A simple 3-RPS parallel with similar base and mobile platform is used to illustrate this method

Constraint Singularity-Free Design of the IRSBot-2

International audienceThis paper deals with the constraint analysis of a novel two-degree-of-freedom (DOF) spatial translational parallel robot for high-speed applications named the IRSBot-2 (acronym for IRCCyN Spatial Robot with 2 DOF). Unlike most two-DOF robots dedicated to planar translational motions this robot has two spatial kinematic chains that provide a very good intrinsic stiffness. First, the robot architecture is presented and its constraint singularity conditions are given. Then, its constraint singularities are analyzed in its parameter space based on a cylindrical algebraic decomposition. Finally, a deep analysis is carried out in order to determine the sets of design parameters of the IRSBot-2 that prevent it from reaching any constraint singularity. To the best of our knowledge, such an analysis is performed for the first time

Workspace and joint space analysis of the 3-RPS parallel robot

International audienceThe Accurate calculation of the workspace and joint space for 3 RPS parallel robotic manipulator is a highly addressed research work across the world. Researchers have proposed a variety of methods to calculate these parameters. In the present context a cylindrical algebraic decomposition based method is proposed to model the workspace and joint space. It is a well know feature that this robot admits two operation modes. We are able to find out the set in the joint space with a constant number of solutions for the direct kinematic problem and the locus of the cusp points for the both operation mode. The characteristic surfaces are also computed to define the uniqueness domains in the workspace. A simple 3-RPS parallel with similar base and mobile platform is used to illustrate this method

Workspace, Joint space and Singularities of a family of Delta-Like Robot

International audienceThis paper presents the workspace, the joint space and the singularities of a family of delta-like parallel robots by using algebraic tools. The different functions of SIROPA library are introduced, which is used to induce an estimation about the complexity in representing the singularities in the workspace and the joint space. A Groebner 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 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

A comparative study of 4-cable planar manipulators based on cylindrical algebraic decomposition

International audienceThe aim of this paper is to present a systematic method for verifying the force-closure condition for general 3-DOF fully-constrained cable manipulators with four cables as based on the CAD (Cylindrical Algebraic Decomposition). A fundamental requirement for a cable manipulator to be fully controllable is that all its cables must be in tension at any working configurations. In other words, all the cable forces must be positive (assuming a positive cable force representing a tension and a negative cable force being a compression). Such a force feasibility problem is indeed referred to a force-closure problem (also called vector-closure problem assuming that the vectors of interest are the row vectors of the Jacobian matrix of the manipulator). The boundaries of the workspace can be obtained by the study of the Jacobian matrix of the manipulator. Therefore, this is equivalent to study the singularity conditions of four 3-RPR parallel robots. By using algebraic tools, it is possible to determine the singularity surfaces and their intersections yielding the workspace. Thus, it will be shown that the use of the CAD allows to get an implicit representation of the workspace as a set of cells. A comparative workspace analysis of three designs of mobile platforms, a line, a square and a triangle will be presented and discussed in this paper for a planar 4-cable fully-constrained robot

Solution regions in the parameter space of a 3-RRR decoupled robot for a prescribed workspace

International audienceThis paper proposes a new design method to determine the feasible set of parameters of translational or position/orientation decoupled parallel robots for a prescribed singularity-free workspace of regular shape. The suggested method uses Groebner bases to define the singularities and the cylindrical algebraic decomposition to characterize the set of parameters. It makes it possible to generate all the robot designs. A 3-RRR decoupled robot is used to validate the proposed design method