Screw Coordinates Research Articles

Dynamic Analysis of Mechanisms Using Screw Coordinates

A method is described using screw coordinates for the dynamical analysis of systems of pair-connected rigid bodies, such as plane and three-dimensional mechanisms, including gyroscopes. The use of screw coordinates leads to general, linear, and computationally efficient numerical procedures, which are illustrated by a dynamic analysis of a constrained spatial RSKR (or R4S) linkage.

Kinematic Analysis of Spatial Mechanisms by Means of Screw Coordinates. Part 1—Screw Coordinates

The concept of screw coordinates is developed in terms of motor algebra, and applied to the kinematics and statics of rigid bodies, in particular to the computer-aided motion analysis of spatial mechanisms. The laws of the composition and transformation of screw coordinates and their application to the kinematics and statics of rigid bodies are developed. These results form the basis for the development of numerical methods for the kinematic analysis of spatial mechanisms.

Kinematic Analysis of Spatial Mechanisms by Means of Screw Coordinates. Part 2—Analysis of Spatial Mechanisms

The basic concepts of screw coordinates described in Part I are applied to the numerical kinematic analysis of spatial mechanisms. The techniques are illustrated with reference to the displacement, velocity, and static-force-and-torque analysis of a general, single-degree-of-freedom spatial mechanism: a seven-link mechanism with screw pairs (H)7. By specialization the associated computer program is capable of analyzing many other single-loop spatial mechanisms. Numerical examples illustrate the results.

A computer program for the transformation of lunar observations from celestial to selenographic coordinates

A program has been devised which is suitable for mapping observations onto the nighttime surface of the Moon. It can be extracted from the present paper without being understood in detail, and familiarity with computer programming is not required. The basic data used in the program are the universal times, right ascensions, and declinations of points of interest on the Moon which are recorded from the telescope's coordinate circles and a Greenwich clock. Focal plane precision screw coordinates may be substituted if desired. In addition, for part of these points, selenographic coordinates are input. This subset, necessarily contained on the sunlit portion of the Moon, is used as a set of standards from which to derive a function describing the translation of the center of the Moon on the celestial sphere relative to the vernal equinox. The balance of input data are limiting conditions which may be read directly without interpolation from the ephemeris. Results are presented from test data which show an average geodesic residual of 0.5 degrees fairly independently of which of several versions of the computer program are used. The error is thus random gear train error in the telescope, which can be expected to decrease in future applications inasmuch as the test data were gathered when the telescope installation was new and not yet tightly adjusted.