SOME NEW SURFACES WITHIN THE GENERAL 3-SYSTEM OF SCREWS

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