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Journals / Recep Tayyip Erdoğan Üniversitesi Fen ve Mühendislik Bilimleri Dergisi / 2026 / Cilt: 7 Sayı: 1

Design of Non-Circular Gears Using a Generalized Parametric Algorithm and Verification via Additive Manufacturing

Dairesel Olmayan Dişlilerin Genelleştirilmiş Parametrik Algoritma ile Tasarimi ve Eklemeli İmalat ile Doğrulanması

Mehmet Yazar(Çanakkale Onsekiz Mart Üniversitesi)0000-0003-3999-3233
Mithat Yanıkören(BİLECİK ŞEYH EDEBALİ ÜNİVERSİTESİ)0000-0003-1075-313X
Pages
209–222
Publication Date
2026-06-30
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

The results demonstrate that the proposed approach can be generalized to different geometries, is feasible, and is applicable to engineering applications requiring variable-speed transmission.

📌 3 Key Takeaways

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Objective & Hypothesis:Although non-circular gears offer significant advantages in mechanical systems that require variable transmission ratios, they are not widely used due to the limited availability of design methods that can be generalized to different geometries and the complexity of manufacturing processes.
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Key Findings & Data:The developed algorithm automatically generates mating tooth profiles based on user-defined parameters such as module, number of teeth, number of lobes, and eccentricity.
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Conclusion & Impact:The results demonstrate that the proposed approach can be generalized to different geometries, is feasible, and is applicable to engineering applications requiring variable-speed transmission.
🔬Design:Modeling & Simulation
📍Scope:Comprehensive Sample
⚙️Variables:Dairesel olmayan dişliler · Parametrik tasarım · Kinematik modelleme

Abstract

Although non-circular gears offer significant advantages in mechanical systems that require variable transmission ratios, they are not widely used due to the limited availability of design methods that can be generalized to different geometries and the complexity of manufacturing processes. In this study, a generalized parametric algorithm is presented that enables the design of non-circular gears with different numbers of lobes. The proposed approach is based on a parametric definition of the step curve and enables the derivation of elliptical and polygonal geometries within a single mathematical framework. The developed algorithm automatically generates mating tooth profiles based on user-defined parameters such as module, number of teeth, number of lobes, and eccentricity. In addition, the problem that the classical parametric model produces a constant speed ratio in symmetric cases has been identified, and an improved kinematic model incorporating a harmonic term has been proposed to address this issue. The resulting gear geometries have been modeled in a computer-aided design (CAD) environment and manufactured using a Fused Deposition Modeling (FDM)-based additive manufacturing process. Tests conducted on the prototypes confirmed that the gear pairs operated without interference and that the periodic speed variation predicted by the proposed model can be observed experimentally. The results demonstrate that the proposed approach can be generalized to different geometries, is feasible, and is applicable to engineering applications requiring variable-speed transmission.

Özet

Dairesel olmayan dişliler, değişken iletim oranları gerektiren mekanik sistemlerde önemli avantajlar sunsa da, farklı geometrilere genelleştirilebilen tasarım yöntemlerinin sınırlı olması ve üretim süreçlerinin karmaşıklığı nedeniyle yaygın olarak kullanılmamaktadır. Bu çalışmada, farklı lob sayılarına sahip dairesel olmayan dişlilerin tasarımını mümkün kılan genelleştirilmiş bir parametrik algoritma sunulmuştur. Önerilen yaklaşım, adım eğrisinin parametrik tanımına dayanmakta olup eliptik ve poligon benzeri geometrilerin tek bir matematiksel çerçevede elde edilmesini sağlamaktadır. Geliştirilen algoritma, kullanıcı tanımlı modül, diş sayısı, lob sayısı ve eksantrisite parametreleri doğrultusunda eşlenik diş profillerini otomatik olarak üretmektedir. Ayrıca, klasik parametrik modelin simetrik durumlarda sabit hız oranı üretmesi problemi tespit edilmiş ve bu durumu gidermek amacıyla modele eklenen harmonik terim ile geliştirilmiş bir kinematik model önerilmiştir. Elde edilen dişli geometrileri CAD ortamında modellenmiş ve FDM tabanlı eklemeli imalat yöntemi ile üretilmiştir. Üretilen prototipler üzerinde gerçekleştirilen testlerde, dişli çiftlerinin girişimsiz çalıştığı ve önerilen modelin öngördüğü periyodik hız değişiminin deneysel olarak gözlemlendiği doğrulanmıştır. Sonuçlar, önerilen yaklaşımın farklı geometrilere genellenebilir, üretilebilir ve değişken hız iletimi gerektiren mühendislik uygulamaları için uygulanabilir olduğunu göstermektedir.

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Cite This Article

Yazar, M., Yanıkören, M. (2026). Design of Non-Circular Gears Using a Generalized Parametric Algorithm and Verification via Additive Manufacturing. Recep Tayyip Erdoğan Üniversitesi Fen ve Mühendislik Bilimleri Dergisi, Cilt: 7 Sayı: 1, 209–222. https://doi.org/10.53501/rteufemud.1921319

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