Computing cross-sections of the workspace of cable-driven parallel robots with 6 sagging cables

International audienceFinding the workspace of cable driven parallel robots (CDPR) with sagging cables (i.e. elastic and deformable cables) is a problem that has never been fully addressed in the literature as this is a complex issue: the inverse kinematics may have multiple solutions and the equations that describe the problem are non-linear and non algebraic. We address here the problem of determining an approximation of the border of horizontal cross-sections of the workspace for CDPR with 6 cables. We present an algorithm that give an outline of this border but also rises several theoretical issues. We then propose another algorithm that allow to determine a polygonal approximation of the workspace border induced by a specific constraint. All these algorithms are illustrated on a very large CDPR

Computing cross-sections of the workspace of suspended cable-driven parallel robot with sagging cables having tension limitations

International audienceAlthough workspace is essential for the design and control of cable-driven parallel robots (CDPR) very few works have been devoted to this topic when sagging cables are considered , most probably because of the complexity of the cable model. In this paper we consider suspended CDPR with sagging cables that can support only a limited tension. We propose an algorithm to compute the border of horizontal cross-sections of the workspace for a given altitude and orientation of the platform. We show that singularities of the kinematics equations have to be taken into account for a proper determination of the border and that the workspace can be separated in several components according to the branch of the inverse kinematics on which the robot is evolving. We also compare the workspace obtained for ideal and sagging cables

Singularity of cable-driven parallel robot with sagging cables: preliminary investigation

International audienceThis paper addresses for the first time the singu-larity analysis of cable-driven parallel robot (CDPR) with sagging cables using the Irvine model. We present the mathematical framework of singularity analysis of CDPR using this cable model. We then show that, besides a cable model representation singularity, both the inverse and forward kinematics (IK and FK) have a singularity type, called parallel robot singularity, which correspond to the singularity of an equivalent parallel robot with rigid legs. We then show that both the IK and FK have also full singularities, that are not parallel robot singularity and are obtained when two of the IK or FK solution branches intersect. IK singularity will usually lie on the border of the CDPR workspace. We then exhibit an algorithm that allow one to prove that a singularity exist in the neighborhood of a given pose and to estimate its location with an arbitrary accuracy. Examples are provided for parallel robot, IK and FK singularities. However we have not been able to determine examples of combined singularity where both the IK and FK are singular (besides parallel robot singularity)

Influence of uncertainties on the positioning of cable-driven parallel robots

International audiencePositioning accuracy of cable-driven parallel robots is influenced by many factors such as geometry, actuator sensor accuracy and disturbances in the applied wrench. Another uncertainty source is the elasticity of the cables. While the influence of many factors may be decreased by calibration and/or sensor fusion, elasticity parameters are difficult to estimate and their effect on the positioning errors has yet to be determined. In this paper we consider a generic cable model that include cable elasticity and the effect of cable weight and we propose a generic algorithm that allows one to safely calculate the minimum and maximum of the positioning error at a given pose when the elasticity parameters are constrained to lie within some given bounds. The algorithm is designed for being able to manage the effect of different uncertainties sources and we compare the influence of elasticity versus the effect of uncertainties in the cable lengths

On the Determination of Cable Characteristics for Large Dimension Cable-Driven Parallel Mechanisms

International audienceGenerally, the cables of a parallel cable-driven robot are considered to be massless and inextensible. These two characteristics cannot be neglected anymore for large dimension mechanisms in order to obtain good positioning accuracy. A well-known model which describes the profile of a cable under the action of its own weight allows us to take mass and elasticity into account. When designing a robot, and choosing actuator and cable characteristics, a calculation of maximal tension has to be done. However, because cable mass has a significant effect on cable tensions, a model including cable mass has to be included in the design step. This paper proposes two methods to determine the appropriate cable and hence the maximal tensions in the cables. Applied to a large dimension robot, taking cable mass into account is proved to be necessary in comparison with an equivalent method based on the massless cable modeling. In this paper, only moving platform static equilibria are considered (slow enough motions)