Bazı Küresel Mekanizma Hareketlerinin ve Mafsal Tasarımlarının Yeni SLERP İnterpolasyonları ile İncelenmesi

Abstract

Küresel mekanizmaların hareketleri robotik çalışmalarda önemli bir yer almaktadır. Çalışmamızda küresel mekanizmalardaki mafsalların tasarımı ve yörünge hareket denklemleri ilk defa tanımladığımız dizisel SLERP, dizisel fast SLERP, De-Moivre ile dizisel SLERP ve modüler SLERP interpolasyon yöntemleri ile verilmiştir. Bununla birlikte, küresel mekanizmalardaki mafsalların konumları için geometrik SLERP interpolasyon eğrisinin Serret-Frenet çatısı ve eğrilikleri hesaplanarak sayısal bir örnek verilmiştir. Ayrıca makalenin sonunda, iki ve üç serbestlik dereceli küresel mekanizmaların hareket denklemlerini üreten interpolasyon denklemleri ile ilgili birkaç sayısal örneklendirme de yapılmıştır.

Keywords

• Kuaterniyon
• Dizisel SLERP
• Hızlı dizisel SLERP
• Modüler SLERP

The Analysis of Some Spherical Mechanism Movements and Joint Designs by The New SLERP Interpolations

Abstract

The movements of the spherical mechanisms take an important place in the robotic studies. In this paper, the design and the trajectory motion equations of the joints in the spherical mechanisms were presented by the methods of the sequential SLERP, sequential fast SLERP, sequential SLERP with De-Moivre, and modular SLERP interpolation that we firstly defined. Additionally, the Serret Frenet frame and curvatures of the geometrical SLERP interpolation curve for the locations of the joints in the spherical mechanisms were computed, and then, several numerical examples on the interpolation equations that produce the motion equations of the spherical mechanisms with 2 and 3-degree of freedom were given at the end of the paper.

Keywords

• Quaternion
• Sequential SLERP
• Sequential Fast SLERP
• Modular SLERP
• Interpolation

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