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In this paper, the kinetic energy formula was expressed during one-parameter closed planar homothetic 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 winch was considered. This motion was described by a double hinge consisting of the fixed control panel of winch and the moving arm of winch. The results were applied to experimentally measured motion. AMS Subject Classification: 53A17, 70B10

THE KINETIC ENERGY FORMULA FOR THE CLOSED PLANAR HOMOTHETIC MOTIONS IN COMPLEX PLANE