The ability to position an object at various locations corresponding to a portion of a spherical surface has long been accomplished using nested goniometers, in which, as observed from above, the apparent motion is readily described in a Cartesian ("XY") frame. In certain applications, however, a more suitable basis of motion would be described in a polar coordinate ("R-Theta") frame. The implementation and advantages of such a device is described here.

Figure 1. In the R-Theta Goniometer, any position on the spherical surface centered on "O" within the solid angle Ω is accessible to the carriage using R (radial distance from rotation axis) and q (rotation about axis) motions.

Figure 1 schematically depicts a proposed device that produces R-Thetabased goniometric motion. The curved radial stage, while functionally the same as a conventional single-axis goniometer, is mounted to a rotary stage offset to one end of the radial stage. The resulting device can position an object mounted on the radial stage carriage to any location on the surface of the sphere defined by the curvature and extent of the radial stage.

Figure 2(a) shows the R-Theta device compared to the XY form. As compared to the typical XY nested-goniometer approach, the R-Theta implementation has only 25 percent of the mass, and occupies only 25 percent of the volume. Further, the moving mass of the R-Theta form is 50 percent that of the XY form. Note that these percentages are approximate, and will depend on the exact implementation chosen for the device (for example, material choice and light-weighting techniques, if utilized).

Figure 2. The Advantages of R-Theta to XY Goniometric Approaches are as follows: (a) The R-Theta design has a total mass of approximately 25 percent of the XY design and a moving mass of approximately 50 percent. These percentages will increase somewhat with the addition of a derotation stage to the R-Theta design and will also be a function of the exact stage designs. (b) In packaging of four R-Theta goniometers with overlapping fields-of-motion (where the four regions Ω all lie on the same spherical surface), the figure illustrates the ability to create significant overlaps in the regions to a degree impossible to achieve with conventional XY goniometric devices.

The initial application for which the R-Theta form was designed was for a multiple telescope platform, which required the ability to move four independent telescopes in such a way that all four pointed through a common point in space, while maintaining a fixed distance from that point. In addition, the scientific requirements of the mission were best served if the four telescopes could also have partially overlapping fields-of-regard on the sky. If implemented in the typical XY form, the necessity of maintaining clearances between all of the moving elements would have forced a larger than desired separation between the telescopes, and could not provide the overlapping fields-of-regard without significantly restricting the total motion of one or more telescopes. By using the R-Theta form instead, a denser packing could be achieved, and by judicious trajectory planning, the significant overlap in the telescope fields-of-regard could be implemented [Figure 2(b)].

As a final note, it is apparent that the carriage on the radial stage experiences a rotation with respect to a global coordinate system as the rotary stage is actuated. If this effect should be undesirable in a given application, a synchronized derotation stage could be added on top of the radial stage carriage; such a stage could also be used to provide arbitrary orientations, if desired.

This work was done by Jeffrey M. Oseas and Robert J. Calvet of Caltech for NASA's Jet Propulsion Laboratory.

NPO-20795

Topics:
Imaging and visualization Motion Control Optics Telescopes