Wrench Recovery of Parallel Manipulators for Full Retrieval of Subtasks Vahid Nazari * and Leila Notash * * Department of Mechanical and Materials Engineering, Queens University, Kingston, ON, Canada [nazariv, notash]@me.queensu.ca Abstract In this paper, the wrench recovery of parallel manipu- lators after actuator failure is investigated. To achieve the desired wrench capability, the mobile platform task is divided into the recov- erable and non-recoverable subtasks. The presented work is based on the projection of the lost wrench due to total or partial actu- ator failure onto the range space of the reduced Jacobian matrix. The force/torque of the healthy joints is adjusted such that the sec- ondary goal comprising the 2-norm of the error of non-recoverable wrench and the 2-norm of the vector of the overall forces/torques of the healthy joints is minimized without affecting the recovered components of the wrench. 1 Introduction Parallel manipulators consist of a mobile platform that is connected to a base platform through several legs/branches, each leg comprising links and active and passive joints. The advantages of parallel manipulators over the serial manipulators are large load capacity, low inertia, high acceleration, high accuracy, and high stiffness. However, small useful workspace is their drawbacks. Manipulators employed in hazardous or remote environments, where failure can lead to catastrophic consequences, are recommended to be fault tolerant. One approach in designing fault tolerant manipulators is utilizing redundancy. Redundancy in manipulators offers many advan- tages over non-redundant manipulators including optimizing fault tolerance measures Roberts and Maciejewski (1996), recovering lost force/moment (wrench) and motion Notash (2011a,b),obstacle avoidance Jamisola, Ma- ciejewski and Roberts (2003, 2004) and singularity avoidance Yoshikawa (1984). The effect of actuator/joint failures, including zero and non-zero force/torque, on the wrench capabilities of parallel manipulators was inves- tigated in Notash (2011a). Criteria were established to examine full and V. Padois, P. Bidaud, O. Khatib (Eds.), Romansy 19 – Robot Design, Dynamics and Control, CISM International Centre for Mechanical Sciences, DOI 10.1007/978-3-7091-1379-0_26, © CISM, Udine 2013