Abstract
In this paper, the Steiner area formula and the polar moments of inertia were expressed during one-parameter closed planar motions in complex plane. The Steiner points or Steiner normal concepts were described according to whe-ther rotation number was different from zero or equal to zero. The moving pole point was given with its components and its relation to the Steiner point or Steiner normal which was specified. The Steiner formula and the polar moments of inertia were expressed for the inverse motion. The fixed pole point was calculated for the inverse motion. The sagittal motion of a tele-scopic crane was considered as an example. This motion was described by a double hinge consisting of the fixed control panel of the telescopic crane and its moving arm. The results obtained in the first section of this study were applied to this motion.
Highlights
Steiner explained some properties of the area of the path of a point for a geometrical object rolling on a line and making a complete turn [1]
The Steiner area formula and the polar moments of inertia were expressed during one-parameter closed planar motions in complex plane
The Steiner formula and the polar moments of inertia were expressed for the inverse motion
Summary
Steiner explained some properties of the area of the path of a point for a geometrical object rolling on a line and making a complete turn [1]. Tutar expressed the Steiner formula and the Holditch theorem during one-parameter closed planar homothetic motions [2]. We calculated the expression of the Steiner formula firstly relative to a moving coordinate system and a fixed coordinate system during one-parameter closed planar motions in complex plane. We obtained the moving pole point for a closed planar motion. We expressed the relation between the area enclosed by a path and the polar moment of inertia. The fixed pole point was calculated for the inverse motion. The Steiner area formula, the moving pole point and the polar moment of inertia were obtained for the direct and inverse motion. The Steiner area formula, the fixed pole point and the polar moment of inertia were calculated for the example
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