Rozprawy doktorskie na temat „CIRCULAR HARMONICS”
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Quellmalz, Michael. "Reconstructing Functions on the Sphere from Circular Means". Universitätsverlag Chemnitz, 2019. https://monarch.qucosa.de/id/qucosa%3A38406.
Pełny tekst źródłaDie vorliegende Arbeit beschäftigt sich mit dem Problem der Rekonstruktion einer Funktion f, die auf der d-dimensionalen Einheitssphäre definiert ist, anhand ihrer Mittelwerte entlang von Schnitten mit Hyperebenen. Im Fall d=2 sind diese Schnitte genau die Kreise auf der Sphäre. In vielen tomografischen Anwendungen sind aber nur eingeschränkte Daten verfügbar. Deshalb besteht das Interesse an der Rekonstruktion der Funktion f nur anhand der Mittelwerte bestimmter Familien von Hyperebenen-Schnitten der Sphäre. Verglichen mit dem Fall vollständiger Daten birgt dieses Problem mehrere Herausforderungen und Fragen. Die erste ist die Injektivität, also können alle Funktionen anhand der gegebenen Daten eindeutig rekonstruiert werden? Weitere Punkte sind die die Frage nach der Stabilität der Rekonstruktion, welche eng mit einer Beschreibung der Bildmenge verbunden ist, sowie der praktische Bedarf an Rekonstruktionsmethoden und -algorithmen. Diese Arbeit gibt einen detaillierten Überblick und Antworten auf diese Fragen für verschiedene Familien von Hyperebenen-Schnitten, angefangen von vertikalen Schnitten über Schnitte mit Hyperebenen durch einen festen Punkt sowie Kreisbögen. Solche Rekonstruktionsprobleme treten in diversen Anwendungen auf wie der Bildgebung mittels Compton-Kamera, Magnetresonanztomografie, fotoakustischen Tomografie, Radar-Bildgebung sowie der Tomografie seismischer Wellen. Weiterhin nutzen wir unsere Ergebnisse über sphärische Mittelwerte, um eine Singulärwertzerlegung für die Kegelstrahltomografie zu zeigen.
Khoshniat, Ali. "A Linearly and Circularly Polarized Active Integrated Antenna". DigitalCommons@USU, 2011. https://digitalcommons.usu.edu/etd/881.
Pełny tekst źródłaSalahifar, Raydin. "Analysis of Pipeline Systems Under Harmonic Forces". Thesis, Université d'Ottawa / University of Ottawa, 2011. http://hdl.handle.net/10393/19820.
Pełny tekst źródłaSantos, Nalzira Medalha dos. "Os processos circulares como instrumento para a investigação dos elementos que contribuem para a relação harmoniosa entre professor e aluno". Universidade de Taubaté, 2015. http://www.bdtd.unitau.br/tedesimplificado/tde_busca/arquivo.php?codArquivo=788.
Pełny tekst źródłaEste trabalho diz respeito a uma pesquisa sobre a relação professor-aluno realizada com dezessete professores de uma escola municipal de uma cidade do interior paulista. Os objetivos são: investigar, segundo o ponto de vista docente, quais elementos contribuem para uma relação harmoniosa entre professor e aluno e inquirir, segundo o mesmo ponto de vista, as dificuldades que caracterizam os desafios da atual relação professor-aluno. Para tanto, utilizou-se como metodologia a técnica do Processo Circular em que foram propostas algumas questões referentes à relação professor-aluno, as quais foram gravadas e posteriormente transcritas, a fim de serem analisadas segundo os constructos da análise de conteúdo de Bardin. A fundamentação teórica apoiou-se sobretudo em Vygotsky no que diz respeito à indissociação entre cognição e afetividade, ao papel do ambiente como fonte de desenvolvimento, abordando ainda a relação entre pensamento e linguagem, o sentido da palavra, sendo estes, juntamente com o conceito de perezhivanie, aportes fundamentais para esta pesquisa. De acordo com a análise das respostas colhidas a partir do relato das experiências emocionais dos sujeitos de pesquisa referentes às memórias acerca dos elementos que caracterizam a boa relação entre professor-aluno, foi possível observar que os sujeitos valorizam os aspectos humanos e afetivos, mas não deixam de considerar os aspectos de caráter técnico-pedagógico, os quais também representam o apreço e o respeito do professor pelo aluno, traduzindo-se em valorização pessoal, capaz de criar vínculos afetivos. Quanto às dificuldades e desafios da relação professor-aluno nos dias atuais, um grande percentual de respostas apresentou os fatores externos à escola (falta de valores na família e na sociedade) como os principais responsáveis. Essas respostas incentivam uma reflexão acerca de como resolver essa problemática. Na visão dos professores pesquisados, as alternativas encontradas retomam a importância de aspectos humanos e afetivos. Acredita-se que esse trabalho poderá contribuir para a reflexão sobre a convivência harmoniosa entre professores e alunos, uma vez que tal relação torna-se um fator fundamental no processo educativo.
Herald, Christopher R., i Christopher R. Herald. "The Advent of an Artist-Composer Movement Exemplified by the Works of Saxophonists Colin Stetson, Evan Parker, and Contemporaries". Diss., The University of Arizona, 2017. http://hdl.handle.net/10150/625662.
Pełny tekst źródłaKumar, Bhunesh. "Design of Harmonic Filters for Renewable Energy Applications". Thesis, Högskolan på Gotland, Institutionen för kultur, energi och miljö, 2011. http://urn.kb.se/resolve?urn=urn:nbn:se:hgo:diva-1862.
Pełny tekst źródłaBakhshi, Shashwat. "Numerical Analysis to Study the Effect of Sag and Non-circular Whirl Orbits on the Damping Performance of a Squeeze Film Damper". University of Cincinnati / OhioLINK, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1522420027908978.
Pełny tekst źródłaDavid, Anca Hélène. "L'évolution du droit de l'environnement de l'Union européenne : un outil de mise en place de l'économie verte et circulaire". Thesis, Sorbonne Paris Cité, 2017. http://www.theses.fr/2017USPCB177.
Pełny tekst źródłaThe evolution of the European Union environmental law has led to the development of a new goal that aims to promote eco-innovation and green business models, in order to create a green and circular economy. This new goal had consequences on its form and content. The form of the European Union environmental law is dominated by framework directives and presents increased flexibility, while its content integrates new business models, particularly the circular business model. Furthermore, the transition to a green economy has an impact on how Member States transpose the European Union environmental law. The transposition process has become a vector of commercializing eco-innovation on the European market, and brings together new stakeholders in the decision-making process, namely: green companies, research and innovation laboratories, clusters, digital companies or business angels
Harouni, Zied. "Conception et caractérisation d’une Rectenna à double polarisation circulaire à 2.45 GHz". Thesis, Paris Est, 2011. http://www.theses.fr/2011PEST1026/document.
Pełny tekst źródłaThe work presented in this thesis is within the subject of wireless power transmission, power applied to the remote sensors, networks of sensors and actuators with low power consumption. This study focuses on the design, characterization, and measurement of a rectenna circuit (rectifying antenna) with dual circular polarization at 2.45 GHz, and optimisation of the conversion efficiency. A global analysis tool, based on the iterative method was developed and used to validate the feasibility of this concept by this method. The Schottky diode was modeled using surface impedance. The dual circular polarization rectenna with microstrip technology has been optimized and characterized experimentally operating at 2.45 GHz. It includes the property of harmonic rejections. Two accesses can receive either direction LHCP or RHCP sense. The conversion efficiency of 63% has been measured with a power density of 0.525 mW/cm². A DC voltage of 2.82V was measured across an optimum load of 1.6 kohm
Chen, Zhangchi. "Differential invariants of parabolic surfaces and of CR hypersurfaces; Directed harmonic currents near non-hyperbolic linearized singularities; Hartogs’ type extension of holomorphic line bundles; (Non-)invertible circulant matrices On differential invariants of parabolic surfaces A counterexample to Hartogs’ type extension of holomorphic line bundles Directed harmonic currents near non-hyperbolic linearized singularities Affine Homogeneous Surfaces with Hessian rank 2 and Algebras of Differential Invariants On nonsingularity of circulant matrices". Thesis, université Paris-Saclay, 2021. http://www.theses.fr/2021UPASM005.
Pełny tekst źródłaThe thesis consists of 6 papers. (1) We calculate the generators of SA₃(ℝ)-invariants for parabolic surfaces. (2) We calculate rigid relative invariants for rigid constant Levi-rank 1 and 2-non-degenerate hypersurfaces in ℂ³: V₀, I₀, Q₀ having 11, 52, 824 monomials in their numerators. (3) We organize all affinely homogeneous nondegenerate surfaces in ℂ³ in inequivalent branches. (4) For a directed harmonic current near a non-hyperbolic linearized singularity which does not give mass to any of the trivial separatrices and whose trivial extension across 0 is ddc-closed, we show that the Lelong number at 0 is: 4.1) strictly positive if the eigenvalue λ>0; 4.2) zero if λ is a negative rational number; 4.3) zero if λ<0 and if T is invariant under the action of some cofinite subgroup of the monodromy group. (5) We construct non-extendable, in the sense of Hartogs, holomorphic line bundles in any dimension n>=2. (6) We show that circulant matrices having k ones and k+1 zeros in the first row are always nonsingular when 2k+1 is either a power of a prime, or a product of two distinct primes. For any other integer 2k+1 we exhibit a singular circulant matrix
Ferré, Amelie. "Etude des dynamiques moléculaires sondées par générations d'harmoniques d'ordres élevés". Thesis, Bordeaux, 2014. http://www.theses.fr/2014BORD0165/document.
Pełny tekst źródłaHigh harmonic generation (HHG) spectroscopy has proven to be a promisingtool (like probe in pump-probe experiments) in revealing the atomic and molecular dynamicswith the potential for subangstrom spatial resolution and subfemtosecond temporalresolution. Then, rotational dynamics have been resolved on small molecular systems (N2,CO2). This thesis looks to extending HHG spectroscopy methods to probe the structureand the dynamic of complex molecular systems. We will describe the two sources highharmonic generation, the transient grating of excitation and the two-color high harmonicgeneration. We enable to resolve the femtosecond nuclear dynamics in N2O4 and SF6. HHGis also used like a XUV radiation source, playing the role of pump pulse. This approach hasbeen used for the study of photoelectron circular dichroism. An XUV harmonic field witha quasi-circular polarization ionizes chiral molecules. In this manuscript, we will developthis new femtosecond XUV and quasi circular polarization radiation
RICCI, ALESSANDRO MARIA. "Superconducting magnets for future accelerators". Doctoral thesis, Università degli studi di Genova, 2020. http://hdl.handle.net/11567/1002038.
Pełny tekst źródłaHarroue, Benjamin. "Approche bayésienne pour la sélection de modèles : application à la restauration d’image". Thesis, Bordeaux, 2020. http://www.theses.fr/2020BORD0127.
Pełny tekst źródłaInversing main goal is about reconstructing objects from data. Here, we focus on the special case of image restauration in convolution problems. The data are acquired through a altering observation system and additionnaly distorted by errors. The problem becomes ill-posed due to the loss of information. One way to tackle it is to exploit Bayesian approach in order to regularize the problem. Introducing prior information about the unknown quantities osset the loss, and it relies on stochastic models. We have to test all the candidate models, in order to select the best one. But some questions remain : how do you choose the best model? Which features or quantities should we rely on ? In this work, we propose a method to automatically compare and choose the model, based on Bayesion decision theory : objectively compare the models based on their posterior probabilities. These probabilities directly depend on the marginal likelihood or “evidence” of the models. The evidence comes from the marginalization of the jointe law according to the unknow image and the unknow hyperparameters. This a difficult integral calculation because of the complex dependancies between the quantities and the high dimension of the image. That way, we have to work with computationnal methods and approximations. There are several methods on the test stand as Harmonic Mean, Laplace method, discrete integration, Chib from Gibbs approximation or the power posteriors. Comparing is those methods is significative step to determine which ones are the most competent in image restauration. As a first lead of research, we focus on the family of Gaussian models with circulant covariance matrices to lower some difficulties
Yeung, Carman. "Investigation of Linear and Nonlinear Torsional Guided Waves in Hollow Circular Cylinders for Damage Detection". Thesis, 2021. http://hdl.handle.net/2440/130216.
Pełny tekst źródłaThesis (Ph.D.) -- University of Adelaide, School of Civil, Environmental and Mining Engineering, 2020
Liao, Haw-Ting, i 廖浩廷. "Fingerprint recognition with circular harmonic function". Thesis, 1994. http://ndltd.ncl.edu.tw/handle/27449301449281025513.
Pełny tekst źródłaHuang, Jen-Ting, i 黃任廷. "Isolated, Circularly-Polarized, High Harmonics Generation". Thesis, 2017. http://ndltd.ncl.edu.tw/handle/f7tyru.
Pełny tekst źródłaHUANG, SHENG-YANG, i 黃勝暘. "Microstrip-Fed Circular Ring Slot Antennas with Wideband Harmonic Suppression". Thesis, 2018. http://ndltd.ncl.edu.tw/handle/q7wcns.
Pełny tekst źródła逢甲大學
電機工程學系
106
Recently, it is a prerequisite requirement for hand-held communication products to possess the advantages such as light in weight, compact size and low manufacturing cost. To satisfy these requirements, a single structure design that comprised of an antenna integrated with the front-end circuit of the communication system is presently attracting many attentions. However, high order harmonic modes excited by the antenna can cause electromagnetic interference (EMI) problems on the active circuit, which lead to degrading the performances of the system. Hence, the common solution to solve this problem is to use low-pass or band-pass filter. However, this method will increase the circuit size, manufacture cost, and insertion loss. To resolve these disadvantages, antenna design with harmonic suppression is now an attractive topic of research interest. This thesis is divided into two parts, the first part presents a wide band harmonic suppression circular ring slot antenna that operate in the 2.45 GHz wireless local area network (WLAN) band. Here, a novel stepped impedance resonator (SIR) structure as a low-pass filter and the open stubs (OS) as a band-stop filter are integrated into the circular ring slot antenna, so that it can suppress unwanted high order harmonic modes (return losses < 3 dB) within the frequencies range from 3 to 20 GHz. Also, it is well known the conventional ring slot antenna is a half wavelength resonator whereas the SIR structure is not only regarded a LPF but also can reduce the size of antenna about 15 % by its electrical characteristic. In the second part of this thesis, a triple-band circular ring slot antenna with wideband harmonic suppression is proposed. It is noteworthy that this triple-band circular ring slot antenna with wideband harmonic suppression design has no effect on the fundamental resonate mode with etching extra slots, so that can operate in the 2.4 GHz, 5.2 GHz and 5.8 GHz WLAN application.
Yo, Tzong-Chee, i 尤宗旗. "The Wireless PoweringCharging System with Harmonic Rejection and Circular Polarization Rectenna". Thesis, 2008. http://ndltd.ncl.edu.tw/handle/45529877410711633048.
Pełny tekst źródła國立成功大學
電機工程學系碩博士班
96
In this dissertation, a RF power charging methodology is developed to provide ultimate power supply of wireless sensors in long term operation with rechargeable battery. Based on the FCC (Federal Communication Commission) regulation of the limited permissible exposure radiation density for public, the battery recharging procedure is accomplished by directly connecting to the rectenna without an additional voltage regulator. To achieve this, the input voltage promoting techniques are adopted by combining voltage transformation and voltage booster to overcome the high potential barrier of 4.2V Li-ion battery; also, the input impedance of rectifier while loading the battery is analyzed according to the output DC current for efficiency optimization. After that, to simplify the design procedure of the rectenna, the development of the circular polarization and harmonic rejection circular microstrip antenna is presented here. Such kind of the antenna is especially suitable for the rectifying antenna (rectenna) and active integrated antenna (AIA) to eliminate harmonic suppression filter. Hence, a novel rectenna using the compact circularly polarized (CP) patch antenna with RF-to-DC power conversion part at 2.45 GHz is introduced, in which the unbalanced slots structure is adopted for size reduction and 2nd harmonic rejection. To contribute a rectenna for RF power conversion, the back side of the CP antenna is the doubler rectifier circuit with 3rd order harmonic rejection radial stub for efficiency optimization and harmonic power re-radiation elimination. The adopted CP antenna built on low cost FR-4 substrate has measured 3.1dBic CP gain, bandwidth of 137 MHz (10 dB return loss) and 30 MHz CP bandwidth (3 dB axial ratio). By up to 3rd order harmonic rejection, the RF-to-DC conversion efficiency would reach 53% and 75% with 1 KΩ resistor load under ANSI/IEEE uncontrolled and controlled RF human exposure limit, respectively. In addition, the implantable rectenna (rectifying antenna) used for wireless charging lithium-ion (Li-ion) battery in biomedical implants is proposed in MICS band (402-405MHz) with power reception interface of developed implantable antenna. By the proposed methodology for input impedance based on output DC current, the potential barrier of Li-ion battery is successfully overcome for recharging. Ignoring regulators of the rectified DC voltage, the DC power can supply large enough DC voltage (>4.2V) for charging lithium-ion battery with optimized RF-to-DC conversion efficiency (76.2%) and the average efficiency of 75% from 3.7 to 4.2V. Hence, the bio-implant can prolong its operation life by wireless charging as communicating with external reader by the proposed implantable rectenna.
SHEM, HOU-TING, i 沈厚廷. "Finite Element Analysis for Double-Circular-Arc Stress Harmonic Drive With Helical Gear". Thesis, 2019. http://ndltd.ncl.edu.tw/handle/9u486d.
Pełny tekst źródła國立臺北科技大學
製造科技研究所
107
Harmonic Drive is important in modern invention. The common tooth type is spur gear in Harmonic Drive industry at present. By many studies, the helical gear is smoother, longer life, heavier load, and less noise than the spur gear. And it is used widely in high-precision requirements. It can extend the transmission life, increase load capacity and reduce the number of replacement, that the harmonic gear combined with helical gear. This paper uses the SOLIDWORK to construct the model and used ANSYS to analyze the Von Mises stress and strain, and set the Young's modulus of the material to be E=210GPa. Then, the double-arc tooth Harmonic Drive is combined with the helical angle to analyze Von Mises stress and strain at different helical angles, observe the stress distribution at the contact surface and find the best helical angle of the double-arc tooth Harmonic Drive tooth model. In a set of Harmonic Drive, the toothed parts are the circular spline and the flex spline. The circular spline will be hardened and harder than the flex spline after the heat treatment. Therefore, this paper mainly focuses on the discussion of the flex spline.
LIN, CHIH-HENG, i 林志衡. "Coplanar Waveguide-fed Circularly Polarized Antennas with Wideband Harmonic Suppression". Thesis, 2018. http://ndltd.ncl.edu.tw/handle/u2gp8u.
Pełny tekst źródła逢甲大學
電機工程學系
106
This paper focuses on new type antennas of harmonic suppression with circular polarization. The π-shape resonator can be used to suppress the high-order frequency. They can be applied to wireless local area networks WLAN 5.8 GHz (5.725 GHz to 5.825 GHz) and DSRC 5.9 GHz (5.85 GHz to 5.925 GHz). A coplanar waveguide-fed circularly polarized antenna with harmonic suppression is initially proposed (proposed antenna 1). The antenna size is 30 mm× 30 mm× 0.762 mm. By adding two quadrant arc-shaped perturbed elements into the circular patch antenna, a circularly polarized (CP) band is excited from 5.85 GHz to 5.925 GHz. The π-shape resonator is loaded at the end of coplanar waveguide feed and coupled with the circularly polarized patch antenna. The measured 10-dB bandwidth and CP bandwidth were 660 MHz (5.67 GHz~6.33 GHz) and 75MHz (5.85 GHz~5.925 GHz), respectively. The measured maximum antenna gain and antenna efficiency were 5.5 dBic and 84.1%, respectively. The design of proposed antenna 2 is based on the architecture of proposed antenna 1. In order to increase the CP bandwidth without changing the structure of the resonator, a crescent slot is embedded into the ground plane. This design can increase the CP bandwidth to 5.72 GHz~5.88 GHz, which can cover the WLAN 5.8 GHz band (5.72 GHz~5.85 GHz). The measured 10-dB bandwidth was 850 MHz (5.7 GHz~6.55 GHz). The measured maximum antenna gain and antenna efficiency were 3.9 dBic and 81%, respectively.
林辰彥. "Vibration induced by harmonic loadings applied at circular rigid plate on layered half-space medium". Thesis, 2010. http://ndltd.ncl.edu.tw/handle/76236813452565858717.
Pełny tekst źródłaTsai, Chi-Ying, i 蔡奇穎. "Analysis of Conjugate Range for Double- Circular-Arc and Common Tangent Profile of Harmonic Drive". Thesis, 2017. http://ndltd.ncl.edu.tw/handle/858z3m.
Pełny tekst źródła國立臺北科技大學
製造科技研究所
105
Conjugate range of harmonic drive have a great influence on gear transmission performance, it depends on the tooth profile, number of teeth, structure of flexspline, and so on. Therefore, conjugate parameters have an influence on conjugate range will be discussed in this thesis. In this thesis, staring form rack tool for manufacture of flexspline, according to the standard of double-circular-arc and common tangent profile, solving the equation of tooth profile of flexspline conjugate to rack tool by tooth profile normal raw. Constructing a complete meshing model for harmonic drive. According to the B matrix method or the envelope principle, the circular spline tooth equation with the flexspline conjugate is solved. In order to avoid the error and interference caused by the harmonic drive meshing, this paper uses the exact solution for mathematical calculation. This paper uses MATLAB to write mathematical models. According to the user input engagement conditions, we can get the flexspline tooth profile and the circular spline tooth profile and conjugate range. To discuss the influence rule of tooth parameters and meshing parameters on the conjugate range. The best conjugation condition is adjusted to obtain the maximum conjugation performance.
Liang, Tsair-Chun, i 梁財春. "Optical pattern recognition using a composite 2-D symmetrical edge detection filter and circular harmonic filter". Thesis, 1995. http://ndltd.ncl.edu.tw/handle/41949326936088438729.
Pełny tekst źródłaSHIH, MING-CHOU, i 施名洲. "Scattering Problem of a Vertical Transverse Isotropic Circular Cylindrical Cavity Subjected to Time-Harmonic Elastic Wave". Thesis, 2017. http://ndltd.ncl.edu.tw/handle/8r96d5.
Pełny tekst źródłaTien, Ling, i 田翎. "The Design of Near-Field Coupled Circular Sector Microstrip Antenna Pair with Harmonic-Rejection for Wireless Power Transmission". Thesis, 2017. http://ndltd.ncl.edu.tw/handle/cjqar8.
Pełny tekst źródła國立臺北科技大學
電子工程系研究所
105
In this dissertation, a design of transmitting-receiving antenna pair in the near-field coupled for Wireless Power Transmission (WPT) is proposed. It can be applied in two different situations is near-field transmission and far-field transmission, respectively. In the near-field, by analyzing the field distribution and the reflector of the transmit-receive antenna pair within the reactive near-field region, the transmission coefficient of the proposed antenna pair can be optimized. On the other hand, the receiving antenna combined with the rectifier circuit can be seen as a rectenna at 2.4GHz when receiving antenna standalone. The proposed antenna pair utilized two different structure of circular sector microstrip Antenna. Through the relevance between the angle of circular sector and Bessel Function can achieve harmonic suppression effect. In order to improve the transmission efficiency, use the observation surface to observe the electromagnetic field distribution, and adjust the antenna structure parameters. Finally, the transmission efficiency of the antenna pair up to 92.3% at 2.45GHz. The proposed structure combine antenna with rectifier circuit, the receiving RF energy which in front of the antenna, through the rectifier circuit can convert to DC output. The maximum overall efficiency of the proposed antenna pair is more than 80% where the transmitted power reached 19 dBm. This architecture is ideal for wireless power transmission.
Cheng, Yun-Hao, i 程雲豪. "Study on the Tooth Profile Design and Finite Element Analysis (FEA) of Harmonic Drives with Involute Profile and Double-Circular-Arc Profile". Thesis, 2017. http://ndltd.ncl.edu.tw/handle/34774t.
Pełny tekst źródła國立中央大學
機械工程學系
105
The purpose of this study is to analyze the meshing characteristics of harmonic drives (HD) with involute profile and double-circular-arc profile. Firstly, the 2-D mathematical model of flexsplines (FS) with involute tooth profile and double-circular-arc profile were developed by using respective rack cutter based on the theory of gearing. Then the engaging circular spline (CS) with conjugate tooth profile of FS was derived based on the enveloping theory and kinematic model of HD. Additionally, a mesh generation program was developed to discretize the FS based on the 2-D mathematical model. Furthermore, 2-D FEA was conducted to explore the engagement movement of the FS, the torsional stiffness, transmission ratio, fillet stress and contact stress of the FS during meshing process and the engaged area of teeth of the HD under various conditions. In this study, an optimization method was adopted in the parametric design of 2-D tooth profile. The optimization aims to achieve the maximum torsional stiffness, and the constraints are that the stress is smaller than the fatigue limit of the FS material and no interference between the teeth of FS and CS is presented. An 2-D tooth profile optimization processing combining c++, finite element analysis and optimization algorithm was successfully performed. Moreover, a preliminary 3-D FEA was conducted to explore the torsional stiffness and the engaged area of teeth of the HD under two conditions, such as HD with lead crowning or HD without lead crowning by adding in axial parameters, including cup length, tooth width and so on. Finaly, The results from 2-D FEA and 3-D FEA were compared and discussed. The proposed methodology in this study paved the way for future investigations of 3-D FEA and 3-D optimization. keywords:harmonic drive, torsional stiffness, engaged area of teeth, involute tooth profile, double-circular-arc profile, finite element analysis, optimization