Abstract: In a position encoder an interpolator derives from quadrature input signals a series of sine waves equispaced in phase. These are applied to respective comparators which output a binary zero or a binary one according to whether the respective sine wave is above or below the zero crossing point. Interpolation is achieved by identifying an adjacent pair of said sine waves of which one has a value above and the other a value below zero and a counter stores a number indicative of this pair of signals.

Abstract: Apparatus for measuring velocity utilizes quadrature input signals provided by a transducer and divides the derivative of one of the signals by the magnitude of the other to obtain a measure of velocity. The apparatus may be digital or analog. It is particularly suitable for the measurement of velocity where the quadrature signals are provided by an optical grating and transducer arrangement.

Abstract: Metrological apparatus, particularly for measuring form, has a turntable 4 and a transducer 14 and associated stylus 12 mounted so that the tip 12a of the stylus is displaceable radially and vertically relative to the turntable 4. The problem of obtaining both high resolution and large range of operation is solved by using a transducer/stylus 12,14 having a resolution of 12 nanometers and a range of only 0.4 mm and mounting the transducer 14 on an arm 10 which is driven radially and/or vertically by a computer 30 in response to the output from the transducer 14 to cause the stylus 12 to follow the workpiece surface. High resolution data defining the rotary position of the turntable 4 and the radial and vertical position of the transducer 14 is provided by a photodetector/optical grating arrangement 23, 21, 31; 27, 19, 43 and associated interpolators 42, 44, 46.