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This paper examines robot performance about a target point where the linearized robot dynamics can be used. We introduce a task-space performance index characterized in terms of a Linear Quadratic cost criterion for a class of robots. The performance in dex encapsulates the robot kinematics and dynamics, robot pose, the task and motor torques. The index is examined under var ious conditions: low, medium and high levels of motor torque. We assume that the linearized robot dynamics are a perfect rep resentation of the real-world robot and that the sensors are ideal and unfettered by noise. Results are obtained under each of these conditions and we also derive the expression for the best possi ble task-space performance. Task-space performance is related to more physically meaningful quantities such as robot bandwidth and RMS motor torque. Given actual motor torque limits, the theoret ical RMS torque calculations allow us to ascertain realistic levels of performance for the real-world robot. Examples of task-specific performance are given for the Puma 560 wrist-partitioned robot, the Rediestro robot and the Stanford Arm for a simple task.