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In environments that are remote and hazardous, tasks such as repairing and maintaining a robot manipulator can be extremely difficult and costly. Under such conditions, the operational reliability of a robotic system is very important and motivates the problem of designing optimally fault-tolerant manipulators. One solution to increasing the fault tolerance of a robotic system is to use kinematically redundant manipulators, as their extra degree of redundancy could be used to compensate for the failure in joint actuators. However, simply adding kinematic redundancy does not guarantee fault tolerance, rather it should be strategically added to ensure optimally fault-tolerant system. In this article the authors design nominal manipulator Jacobians that are optimally fault-tolerant to multiple joint failures. The special case when the manipulator is equally fault-tolerant to any two simultaneous joint failures is considered. While it is possible to design a six degree-of-freedom (DOF) robot manipulator to be equally fault-tolerant to any two simultaneous joint failures for three-dimensional workspaces, it is shown that no manipulator operating in a 4 or 5 dimensional workspace can be equally fault-tolerant to two failures.