Mechanical Engineering / Makina Mühendisliği
Permanent URI for this collectionhttps://hdl.handle.net/11147/4129
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Article Citation - WoS: 17Citation - Scopus: 18Least Square Approximate Motion Generation Synthesis of Spherical Linkages by Using Chebyshev and Equal Spacing(Elsevier Ltd., 2013) Alizade, Rasim; Can, Fatih Cemal; Kilit, ÖzgürIn this paper, approximate motion synthesis of spherical linkages is presented. Rigid body guidance of a spherical four-bar mechanism is performed by a spherical RR open chain. In the first step, position of a point on rigid body and orientation of a rigid body on a unit sphere are described. Synthesizing function of spherical dyad is derived by means of using unit vectors that describe location of two revolute joints and tip point. Being based on the theory of function approximation and besides the linearization of nonlinear synthesis equations by using superposition method, the design procedure for real solutions of fourth order polynomial equation is developed. In the second step, approximate motion generation synthesis of spherical dyad is presented by using least-square approximation. Chebyshev spacing and equal spacing are used in the determination of poses. In the final step, two numerical examples are given to show how error graph is varied in terms of selected poses. The spherical motion generation synthesis of spherical four-bar mechanism is obtained by the combination of the two real solutions of the synthesis of two spherical dyads. © 2012 Elsevier Ltd.Article Citation - WoS: 45Citation - Scopus: 57Analytical Synthesis of Function Generating Spherical Four-Bar Mechanism for the Five Precision Points(Elsevier Ltd., 2005) Alizade, Rasim I.; Alizade, Rasim; Kilit, ÖzgürThis paper presents an analytical method for synthesis of function generating spherical 4R mechanisms for the five precision points. For the design requirements an additional parameter, reference value of output angle, ψ0, was added to angular link length parameters, α i(i = 1, ..., 4). In the dimensional synthesis procedure, a novel approach of polynomial approximation method was proposed to determine these five design parameters. Using this method, a set of five non-linear equations was easily transformed into a set of fifteen linear equations. Hence, the problem was reduced to the solution of a cubic polynomial equation. Moreover, a graphical method in a CAD environment is proposed to verify the solutions. © 2005 Elsevier Ltd. All rights reserved.