FINITE DISPLACEMENTS OF POINTS, PLANES, AND LINES VIA SCREW THEORY

Geometrical elements, namely point,directed plane, and directed line, are here taken in isolation from any rigid body to which they may belo ng. The available finite screws are fully determined for a general fin ite displacement of each element. Each screw carries a quasi-pitch, or ''quatch'', that reduces to the commonly-accepted pitch when a displa cement becomes infinitesimal. Each element-displacement has its ''quat ched'' screw system, that for the line displacement being quadratic. T he quatched screw systems then intersect in twos for displacements of point-line, plane-line, and point-plane combinations, to reveal quatch ed linear two-systems. Finally the triple combination point-plane-line yields a single finite quatched screw. Applications in robotics are t ouched upon.