Failure and Workspace Analysis of Parallel Robot Manipulators
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A failure recovery methodology based on decomposing the platform task space into the major and secondary subtasks is proposed which enables the manipulator to minimize the least-squares error of the major subtasks and to optimize the secondary criterion. A methodology for wrench recovery of parallel manipulators is proposed so that the platform task is divided into the recoverable and non-recoverable subtasks based on the number and type of actuator failures, manipulator configuration and task/application purposes. It is investigated that when the Jacobian matrix of the manipulator is of full row-rank and the minimum 2-norm of the joint velocity vector satisfies the velocity limits of the joints, the full recovery of the platform twist will be provided. If the full recovery of the platform twist cannot be achieved, the optimization method followed by the partitioned Jacobian matrix is used to deal with the failure recovery. It is verified that the optimization method recovers as many as possible components of the platform velocity vector when the objective function, 2-norm of the overall velocity vector of the healthy joints, is minimized. To model uncertainty in the kinematic parameters, the interval analysis is proposed. Different interval-based algorithms to enclose the solution set to the interval linear systems are applied and the solution sets are compared. A novel approach in characterizing the exact solution of the interval linear system is proposed to deal with the failure recovery of parallel manipulators with velocity limits of the joints and uncertainty in the kinematic parameters. Simulation results show how the solution sets of the joint velocity vector are characterized by introducing uncertainties in the kinematic parameters. The calculation of the exact solution takes more computation time compared to the interval-based algorithms. However, the interval-based algorithms give the wider solution box with less computation time. The effect of variations and/or uncertainties in design parameters on the workspace of wire-actuated parallel manipulators without and with gravity is investigated. Simulation results show how the workspace size and shape are changed under variations in design parameters.