The spherical-coordinates encoder module (SCEM) is a relatively simple and inexpensive electromechanical apparatus for quickly and easily measuring three-dimensional offsets between objects at distances of the order of a few feet ( ≈1 m). The SCEM was developed specifically for measuring offsets between spacecraft payload trunnions and trunnion supports during ground-based payload-transfer operations; it could also be readily used, for example, to measure offsets to guide the maneuvering of large objects during the assembly of heavy machinery or structures. The SCEM eliminates the need for time-consuming, tedious, error-prone measurements by use of such tools as scales, tapes, and protractors, followed by equally tedious and error-prone manual calculations, manual recording of data, and verbal communication of data.

The SCEM is an electromechanical apparatus for measuring three-dimensional offsets. To measure the offset of a nearby object, one simply stretches a spring-tensioned wire from the unit to the object.

The SCEM is so named because the raw measurement data that it produces are essentially spherical coordinates. The SCEM includes a mechanical unit, part of which rotates about a nominally vertical and a nominally horizontal coordinate axis (see top part of figure). The coordinate axes are defined by mating of the nominally stationary base of the mechanical unit with a mounting bracket on the first of the two objects, the offsets between which one seeks to measure. The mechanical unit contains a spring-loaded reel, on which is wound a 0.25-in. (6.35-mm) timing belt. Two optical encoders measure the rotations about the vertical and horizontal coordinate axes (azimuth and elevation angles, respectively). A third optical encoder measures the rotation of the reel for determining the length of timing belt pulled off the reel and thus the radius from the origin of coordinates to the tip of the outstretched belt.

To perform a measurement, a technician simply pulls the wire from the wheel and places the tip of the wire on the point of interest on the second of the two objects, the offset between which one seeks to measure (see bottom part of figure). The spring tension keeps the belt straight and pulls the rotating part of the mechanical unit into an orientation along the offset vector of interest. Thus, the azimuth and elevation optical encoders provide data on the offset direction, while the reel optical encoder provides data on the offset radius.

The outputs of the optical encoders are fed to a portable computer, which is programmed with data-collection and user-interface software. The software includes components that implement the trigonometric formulas of transformation from spherical to Cartesian coordinates. The offset in Cartesian coordinates is displayed on the computer screen.

The mechanical unit fits within a 7.5-in. (19-cm) cube. At a radial offset of 18 in. (45.7 cm), the SCEM can measure azimuth angles from 0° to 340°, accurate to within an 0.30°; and it can measure elevation angles from 10° to 100°, accurate to within an average of 0.300°. The SCEM measures radius to within an average of 0.005 in. (0.13 mm). The basic SCEM can be expanded to include as many as 18 to 20 mechanical units communicating with a single computer. The information displayed on the computer screen can be updated at a rate of four times per second.

This work was done by Eduardo Lopez Del Castillo and Felix A. Soto Toro of Kennedy Space Center. For further information, access the Technical Support Package (TSP) free on-line at  under the Mechanics category.

Inquiries concerning rights for the commercial use of this invention should be addressed to

the Technology Programs and Commercialization Office
Kennedy Space Center
(407) 867-6373.

Refer to KSC-11973.

NASA Tech Briefs Magazine

This article first appeared in the February, 2000 issue of NASA Tech Briefs Magazine.

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