IJAM, Volume 28, No. 3 (2015)

Abstract. The Steiner area formula and the polar moment of inertia were obtained for closed planar homothetic inverse motions by Tutar and Inan [6]. In this paper, during one-parameter closed planar homothetic inverse motions, the formula of kinetic energy is expressed. Then we show the relation between the formula of kinetic energy and the Steiner formula. We investigate some properties of closed planar homothetic motions. These motions appear between two coordinate systems, fixed and moving (inverse motion). We consider a formula proposed by Dathe [2]. Finally, we show how the results can be applied to experimentally measured motions. As an example, we consider a motion of winch in the sagittal direction. The most important part of this motion is described as a double hinge driven angles of the winch between fixed and moving arms which is a simple model for a planar homothetic motion. We conclude that, for practical purposes, the Steiner line allows us to visualize a selected direction of motion under consideration. We obtain the formula of kinetic energy for the motion of winch during one-parameter closed planar homothetic inverse motions.