In this
paper, the kinetic energy formula was expressed during one-parameter closed
planar homothetic inverse motions in complex plane. Then the relation between
the kinetic energy formula and the Steiner formula was given. As an example the
sagittal motion of a telescopic crane was considered. This motion was described
by a double hinge consisting of the fixed control panel of telescopic crane and
the moving arm of telescopic crane. The results were applied to experimentally
measured motion.
References
[1]
Steiner, J. (1840) Von dem Krummungs-Schwerpuncte Ebener Curven. Journal fur die Reine und Angewandte Mathematik, 21, 33-63. http://dx.doi.org/10.1515/crll.1840.21.33
[2]
Tutar, A. and Kuruoglu, N. (1996) The Steiner Formula and the Holditch Theorem for the Homothetic Motions on the Planar Kinematics. Mechanism and Machine Theory, 34, 1-6. http://dx.doi.org/10.1016/S0094-114X(98)00028-7
[3]
Muller, H.R. (1978) Verallgemeinerung einer Formel von Steiner. Abhandlungen der Braunschweigischen Wissenschaftlichen Gesellschaft, 29, 107-113.
[4]
Muller, H.R. (1978) Uber Tragheitsmomente bei Steinerscher Massenbelegung. Abhandlungen der Braunschweigischen Wissenschaftlichen Gesellschaft, 29, 115-119.
[5]
Dathe, H. and Gezzi, R. (2014) Addenda and Erratum to: Characteristic Directions of Closed Planar Motions. Zeitschrift fur Angewandte Mathematik und Mechanik, 94, 551-554. http://dx.doi.org/10.1002/zamm.201300230
[6]
Tutar, A. and Inan, E. (2015) The Formula of Kinetic Energy for the Closed Planar Homothetic Inverse Motions. International Journal of Applied Mathematics, 28.
[7]
Sener, O. and Tutar, A. (2014) The Steiner Formula and the Polar Moment of Inertia for the Closed Planar Homothetic Inverse Motions in Complex Plane. Submitted.
[8]
Dathe, H. and Gezzi, R. (2012) Characteristic Directions of Closed Planar Motions. Zeitschrift fur Angewandte Mathematik und Mechanik, 92, 2-13. http://dx.doi.org/10.1002/zamm.201100178
