Workspace analysis of planar and spatial redundant cable robots

The present work is inspired by an industrial task, i.e. spray painting a large area by means of a robotic system consisting in a Cable-Driven Parallel Robot (CDPR). In many cases, the area of the robot workspace is smaller than the area to be painted. For this reason, the base of the robot has to be shifted several times during the painting process. These robots are referred to as Repetitive Workspace Robots (RWR). In other words, in order to accomplish the whole task, they need to be moved after they have completed a sub-task locally. A cable suspended CDPR is an ideal candidate for such tasks; it can be thin, light, flexible and cost-efficient. The question is: which is the best shape of the local workspace in these conditions? In fact, not always a larger area of the local workspace guarantees an efficient painting process. This is because the efficiency relies mainly on the shape rather than on the local workspace area itself. In this work we employ an index [Seriani S, Gallina P, Gasparetto A, 2014] to evaluate the efficiency of the workspace of a 2-link CDPR. Finally, we show how the index value changes in relation to some geometrical parameters of the robot, thus laying the foundations for a general design methodology .

2018

Finding 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.

Mechanism and Machine Theory, 2004

In this paper, we study the design and workspace of a 6-6 cable-suspended parallel robot. The workspace volume is characterized as the set of points where the centroid of the MP (MP) can reach with tensions in all suspension cables at a constant orientation. This paper attempts to tackle some aspects of optimal design of a 6DOF cable robot by addressing the variations of the workspace volume and the accuracy of the robot using different geometric configurations, different sizes and orientations of the MP. The global condition index is used as a performance index of a robot with respect to the force and velocity transmission over the whole workspace. The results are used for design analysis of the cable-robot for a specific motion of the MP. 0-7803-7860-1/03/$17.00

Journal of Mechanisms and Robotics

Cable-Driven Parallel Robots hold numerous advantages over conventional parallel robots in terms of high speed and large workspace. Cable Driven Parallel Robots whose workspace can be further increased by the modification of their geometric architecture are known as Reconfigurable Cable Driven Parallel Robots. A novel concept of Reconfigurable Cable Driven Parallel Robots that consists of a classical Cable-Driven Parallel Robot mounted on multiple Mobile Bases is known as Mobile CDPR. This paper proposes a methodology to trace the Wrench-Feasible-Workspace of Mobile Cable-Driven Parallel Robots by determining its Available Wrench Set. Contrary to classical Cable-Driven Parallel Robots, we show that the Available Wrench Set of a Mobile Cable-Driven Parallel Robot depends, not only on the cable tension limits, but also on the Static Equilibrium conditions of the Mobile Bases. The Available Wrench Set is constructed by two different approaches known as Convex Hull approach and Hyperpla...

2007

The wrench-feasible workspace (WFW) of a parallel cable-driven mechanism is the set of poses of its mobile platform for which the cables can balance any wrench in a specified set of wrenches, such that the tension in each cable remains within a prescribed range. The WFW is fundamental since it takes into account both the requirement of nonnegative cable tension and the requirement of a maximum admissible cable tension. This paper addresses the problem of the determination of the WFW of n-degree-of-freedom parallel mechanisms driven by more than n cables. Interval analysis based methods that allow to determine if a given n-dimensional box is fully included in the WFW are presented. Moreover, these methods are also able to approximate the WFW up to a chosen accuracy. The resulting approximation consists of a set of ndimensional boxes such that each box of the set is fully included in the WFW.

2014

2012

Cable-driven manipulators are traditionally designed for general performance objectives, such as maximisation of workspace. To take advantage of the reconfigurability of cable-driven mechanisms, the optimisation of cable-configurations for specific tasks is presented. Specifically, two types of task specific objectives are explored, the minimisation of cable forces over a desired trajectory and the maximisation of workspace about a desired pose. The formulation and incorporation to the optimisation problem for both task specific objectives are presented. Illustrated using a 3-DoF manipulator example, the results clearly demonstrated the advantages of optimising cable configurations for specific tasks. The potential ease of relocation in cable attachments makes task dependent reconfiguration feasible.

Advances in Robot Kinematics 2018

Although workspace is essential for the design and control of cable-driven parallel robots 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 a CDPR with 6 sagging cables whose lengths have a limited maximal value. We propose an algorithm to compute the border of horizontal cross-section of the workspace for a given altitude and orientation of the platform. We show that the singularity of the inverse kinematics equations have to be taken into account for a proper determination of the border.

In this paper, we study the design and workspace of a 6-6 cable-suspended parallel robot. The workspace volume is characterized as the set of points where the centroid of the moving platform can reach with tensions in all suspension cables at a constant orientation. This paper attempts to tackle some aspects of optimal design of a 6DOF cable robot by addressing the variations of the workspace volume and the accuracy of the robot using different geometric configurations, different sizes and orientations of the moving platform. The global condition index is used as a performance index of a robot with respect to the force and velocity transmission over the whole workspace. The results are used for design analysis of the cable-robot for a specific motion of the moving platform.

2008

This article proposes modeling, simulation and kinematic and workspace analysis of a spatial cable suspended robot as incompletely Restrained Positioning Mechanism (IRPM). These types of robots have six cables equal to the number of degrees of freedom. After modeling, the kinds of workspace are defined then an statically reachable combined workspace for different geometric structures of fixed and moving platform is obtained. This workspace is defined as the situations of reference point of the moving platform (center of mass) which under external forces such as weight and with ignorance of inertial effects, the moving platform should be in static equilibrium under conditions that length of all cables must not be exceeded from the maximum value and all of cables must be at tension (they must have non-negative tension forces). Then the effect of various parameters such as the size of moving platform, the size of fixed platform, geometric configuration of robots, magnitude of applied f...