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The forces transmitted through any cross-section of a machine member such as a robot arm can be reduced to a single force and torque acting on any chosen point of the cross-section. The force and torque can be measured by a sensor that replaces the cross-section. A special feature of the sensor discussed here is that it is two dimensional, i.e. that it can be manufactured as a thin, planar sandwich. This makes for simplicity, compactness, low cost and ruggedness. In this paper we derive the constraints on design that must be met in order for the output to be unbiased with respect to force and torque directions. We show that feasible planar designs exist.