THE GENERALIZED HOLDITCH THEOREM FOR THE HOMOTHETIC MOTIONS ON THE PLANAR KINEMATICS


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Abstract

W. Blaschke and H. R. Müller [4, p. 142] have given the following theorem as a generalization of the classic Holditch Theorem: Let E/E′ be a 1-parameter closed planar Euclidean motion with the rotation number ν and the period T. Under the motion E/E′, let two points A = (0, 0), B = (a + b, 0) ∈ E trace the curves kA, kBE′ and let FA, FB be their orbit areas, respectively. If FX is the orbit area of the orbit curve k of the point X = (a, 0) which is collinear with points A and B thenIn this paper, under the 1-parameter closed planar homothetic motion with the homothetic scale h = h(t), the generalization given above by W. Blaschke and H. R. Müller is expressed andis obtained, where ∃t0 ∈ [0, T].

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