DUAL SYSTEMS OF FINITE DISPLACEMENT SCREWS IN THE SCREW TRIANGLE

It has recently been shown that finite displacement screws of a partic ular form enter into linear patterns of combination-displaying the fam iliar structures of the screw systems-when they are used to describe i ncompletely specified displacements. Certain kinematic situations demo nstrate the same simple linearity if normal usage is extended to admit dual coefficients of combination, the system then being referred to a s a dual system. The screw triangle rule for composing the resultant d isplacement screw of two given finite displacement screws is examined in this paper. On regarding the lines of the given screws as fixed, an d the displacement movements about them as variable, it is found that all available resultant screws occupy a structure which can be various ly described as a dual 3-system (which contains infinitely many real 3 -systems) or as the sum of two axially-orthogonal dual 2-system (each of which contains all linear combinations, using complementary dual si nusoidal coefficients, of two basis screws). The basis screws and noda l lines for these systems are found to lie on the triad of mutually or thogonal mirror-symmetry axes for the lines of the given screws. (C) 1 997 Elsevier Science Ltd.