Spatial motion-I: Points of inflection and the differential geometry of screws

摘要: Abstract This paper examines infinitesimal spatial motion, introducing the concept of a “differential screw” to characterize difference between two successive instantaneous screw axes (ISAs) on an axode. The locus inflection points, twisted cubic curve common three ruled quadric surfaces, is here derived in coordinate system attached fixed axode, using relationships ISA velocity and differential screw, as well ISA, acceleration. notable geometry then discussed, more familiar instances spherical planar motion are described special cases. novel approach adopted this paper, even though it does not yield any new results, essential laying groundwork for Part II [Mech. Mach. Theory27, 17–35 (1992)] that deals with accelerations equivalent Bresse circle.