Workspace Analysis of a 4 Cable-Driven Spatial Parallel Robot

International audienceThis paper presents the static equilibrium workspace of an under-constrained cable-driven robot with four cables taking into account the forces and the moments due to the forces acting on the moving platform. The problem is formulated as a non-linear optimization problem with maintaining static equilibrium as the objective function. The simulations are done using MATLAB. The maximum force on the cables and tilting angle of the platform are used to define the feasible static equilibrium workspace and the results obtained are used to finalize the design of the collaborative cable-driven robot to be installed in existing production lines for the agile handling of parts in a manufacturing industry

Real Solutions of the Direct Geometrico-Static Analysis of Under-Constrained Cable-Driven Parallel Robots with Three Cables

This paper addresses the direct geometrico-static analysis of under-constrained cable-driven parallel robots with 3 cables. The task at hand consists in finding all equilibrium configurations of the end-effector when the cable lengths are assigned. This problem is known to admit 156 solutions in the complex field, but the upper bound on the number of real solutions is as yet an open issue. Finding this bound is the objective of the paper. For this purpose, three numerical iterative approaches are developed, namely a continuation procedure adapted from an algorithm originally proposed by Dietmaier and two evolutionary techniques based on a genetic algorithm and particle swarm optimization. In all cases, a number of sets of robot parameters for which the direct geometrico-static problem provides at the most 54 real configurations is found. The coherence of the obtained results leads to conjecture that the achieved bound is tight. However, formal proof is yet to be discovered

Direct Geometrico-Static Analysis of Under-Constrained Cable-Driven Parallel Robots with 4 Cables

This paper studies the direct geometrico-static problem of under-constrained parallel robots suspended by 4 cables. The task consists in determining the end-effector pose and the cable tensions when the cable lengths are assigned. The problem is challenging, because kinematics and statics are coupled and they must be solved simultaneously. An effective elimination procedure is presented that provides the complete solution set, thus proving that, when all cables are in tension, 216 potential solutions exists in the complex field. A least-degree univariate polynomial free of spurious factors is obtained in the ideal governing the problem and solutions are numerically computed via both an eigenvalue formulation and homotopy continuation. Equilibrium configurations with slack cables are also considered

Real solutions of the direct geometrico-static problem of under-constrained cable-driven parallel robots with 3 cables: a numerical investigation

This paper addresses the direct geometrico-static problem of under-constrained cable-driven parallel robots with 3 cables. The task at hand consists in finding all equilibrium configurations of the end-effector when the cable lengths are assigned. This problem is known to admit 156 solutions in the complex field, but the upper bound on the number of real solutions is as yet an open issue. Finding this bound is the objective of the paper. For this purpose, three numerical approaches are developed, namely a continuation procedure adapted from an algorithm originally proposed by Dietmaier and two evolutionary techniques based on a genetic algorithm and particle swarm optimization. In all cases, a number of sets of robot parameters for which the direct geometrico-static problem provides at the most 54 real configurations is found. The coherence of the obtained results leads to conjecture that the achieved bound is tight. However, formal proof is yet to be discovered

Inverse Geometrico-Static Analysis of Under-Constrained Cable-Driven Parallel Robots with Four Cables

This paper presents the inverse geometrico-static analysis of under-constrained cable-driven parallel robots with 4 cables. The problem consists in finding all equilibrium configurations of the end-effector when either its orientation or the center-of-mass’s position is assigned. In both cases, a further point of the end-effector is constrained to lie on a given plane. A major challenge is posed by the intrinsic coupling between kinematics and statics, which must be tackled simultaneously. The problems at hand are solved by analytical elimination procedures, thus leading to univariate polynomials free of spurious factors. All potential solutions may be real

Dynamic Recovery of Cable-Suspended Parallel Robots After a Cable Failure

International audienceThis paper studies how emergencies and failures can be managed in cable-driven parallel robots, in particular in the case of a redundant cable-suspended robot subjected to a cable breakdown. The objective is to present and test via numerical simulation the feasibility of an emergency strategy that allows the robot platform to be dynamically recovered to a safe position. Preliminary results, based on a simplified robot with a point-mass platform suspended by 4 cables, show that the proposed strategy may be an effective way to guide the platform from an unstable pose determined by the cable failure to a new static equilibrium pose