Abstract
The general three-system is the two-parameter system of linearly dependent screws that defines most generally first order instantaneous rigid-body motion with three degrees of freedom. Through a general point there pass three screw axes, and in a general plane there lie two screw axes. The theory is here developed further than hitherto by finding three apparently distinct surfaces: (i) The SPS, the sextic point surface that bounds those points through which pass three screw axes that are all real; (ii) the QES, the quartic envelope surface that, by considering its tangent planes, bounds those planes in which lie two screw axes that are both real; and (iii) the quartic point surface S τ at the points of which two real screws intersect one another at right angles. A closer inspection, however, reveals the QES to be none other than the SPS expressed as its tangential equation. The surfaces are described in some detail and convincingly illustrated with the help of computer-graphics techniques.
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