Abstract: Positional measurements for a robot arm are made using a light ray projector (10) mounted on the robot arm and arranged to emit light rays (50) along a multiplicity of distinct paths that are fixed relative to the projector (10), and a removable support frame (20) carrying a multiplicity of image sensors (22) at fixed positions relative to the support frame (20), the support frame surrounding the base of the robot arm. A signal processor (25) connected to the light sensors (22) determines the positions at which light rays (50) are incident on the image sensors (22), and hence determines positional information of a system of axes associated with the projector (10) relative to the frame (20). This enables relative positional measurements to be made substantially in real time, and in an accurate and cost-effective manner.