Robots designed for space applications, deep sea applications, handling of hazardous material and surgery should ideally be able to handle as many potential faults as possible. This paper provides novel indices for fault tolerance analysis of redundantly actuated parallel robots. Such robots have the potential for higher accuracy, improved stiffness, and higher acceleration compared to similar-sized serial robots. The faults considered are free-swinging joint failures (FSJFs), defined as a software or hardware fault, preventing the administration of actuator torque on a joint. However, for a large range of robots, the proposed indices are applicable also to faults corresponding to the disappearance of a kinematic chain, for example, a breakage. Most existing fault tolerance indices provide a ratio between a robot's performance after the fault and the performance before the fault. In contrast, the indices proposed in this paper provide absolute measures of a robot's performance under the worst-case faults. The proposed indices are based on two recently introduced metrics for motion/force transmission analysis of parallel robots. Their main advantage is their applicability to parallel robots with arbitrary degrees-of–freedom (DOF), along with their intuitive geometric interpretation. The feasibility of the proposed indices is demonstrated through application on a redundantly actuated planar parallel mechanism.