Relevant bibliographies by topics / Half-plane method

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Half-plane method'

Author: Grafiati
Published: 4 June 2021
Last updated: 3 February 2022

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Journal articles on the topic "Half-plane method"

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Li, YingChun, and ZhiHong Liu. "Convolutions of harmonic right half-plane mappings." Open Mathematics 14, no. 1 (2016): 789–800. http://dx.doi.org/10.1515/math-2016-0069.

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AbstractWe first prove that the convolution of a normalized right half-plane mapping with another subclass of normalized right half-plane mappings with the dilatation $ - z(a + z)/(1 + az)$ is CHD (convex in the horizontal direction) provided $a = 1$ or $ - 1 \le a \le 0$. Secondly, we give a simply method to prove the convolution of two special subclasses of harmonic univalent mappings in the right half-plane is CHD which was proved by Kumar et al. [1, Theorem 2.2]. In addition, we derive the convolution of harmonic univalent mappings involving the generalized harmonic right half-plane mappings is CHD. Finally, we present two examples of harmonic mappings to illuminate our main results.
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Kontoni, Dionyssia-Pinelopi N., Dimitri E. Beskos, and George D. Manolis. "Uniform half-plane elastodynamic problems by an approximate boundary element method." Soil Dynamics and Earthquake Engineering 6, no. 4 (1987): 227–38. http://dx.doi.org/10.1016/0267-7261(87)90004-2.

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Yu-ying, Huang, and Yin Lei-fang. "A direct method for deriving fundamental solution of half-plane problem." Applied Mathematics and Mechanics 8, no. 12 (1987): 1181–90. http://dx.doi.org/10.1007/bf02450912.

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Fan, C. W., and Chyanbin Hwu. "Punch Problems for an Anisotropic Elastic Half-Plane." Journal of Applied Mechanics 63, no. 1 (1996): 69–76. http://dx.doi.org/10.1115/1.2787211.

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By combining Stroh’s formalism and the method of analytical continuation, several mixed-typed boundary value problems of an anisotropic elastic half-plane are studied in this paper. First, we consider a set of rigid punches of arbitrary profiles indenting into the surface of an anisotropic elastic half-plane with no slip occurring. Illustrations are presented for the normal and rotary indentation by a flat-ended punch. A sliding punch with or without friction is then considered under the complete or incomplete indentation condition.
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Chen, Y. Z. "Image method for Green's function of anisotropic half-plane with inclined boundary." International Journal of Engineering Science 34, no. 14 (1996): 1563–71. http://dx.doi.org/10.1016/s0020-7225(96)00054-7.

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Wang, Y., and R. K. N. D. Rajapakse. "An Exact Stiffness Method for Elastodynamics of a Layered Orthotropic Half-Plane." Journal of Applied Mechanics 61, no. 2 (1994): 339–48. http://dx.doi.org/10.1115/1.2901450.

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A method is presented in this paper to compute displacements and stresses of a multilayered orthotropic elastic half-plane under time-harmonic excitations. The half-plane region under consideration consists of a number of layers with different thicknesses and material properties. Exact layer stiffness matrices describing the relationship between Fourier transforms of displacements and tractions at the upper and bottom surface of each layer are established explicitly by using the analytical general solutions for displacements and stresses of a homogeneous orthotropic elastic medium. The global stiff ness matrix which is also symmetric and banded is assembled by considering the traction continuity conditions at the interface between adjacent layers of the multilayered half-plane. The numerical solution of the global stiffness equation results in the solutions for Fourier transform of displacements at layer interfaces. Thereafter displacements and stresses of the multilayered plane can be obtained by the numerical integration of Fourier integrals. Only negative exponential terms of Fourier transform parameter are found to appear in the elements of layer stiffness matrices. This ensures the numerical stability in the solution of the global stiffness equation. In addition, the size of the final equation system is nearly onehalf of that corresponding to the conventional matrix approach for layered media based on the determination of layer arbitrary coefficients. The present method provides accurate solutions for both displacements and stresses over a wide range of frequencies and layer thicknesses. Selected numerical results are presented to portray the influence of layering, material orthotropy, and frequency of excitation on the response of five layered systems. Time-domain solutions are also presented to demonstrate the features of transient surface displacements due to a surface loading pulse applied to layered orthotropic half-planes.
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Attiya, Ahmed M. "Transmission of Pulsed Plane Wave Into Dispersive Half-Space: Prony's Method Approximation." IEEE Transactions on Antennas and Propagation 59, no. 1 (2011): 324–27. http://dx.doi.org/10.1109/tap.2010.2090467.

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Ike, Charles Chinwuba. "Fourier Sine Transform Method for Solving the Cerrutti Problem of the Elastic Half Plane in Plane Strain." Mathematical Modelling in Civil Engineering 14, no. 1 (2018): 1–11. http://dx.doi.org/10.2478/mmce-2018-0001.

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Abstract The Fourier sine transform method was implemented in this study to obtain general solutions for stress and displacement fields in homogeneous, isotropic, linear elastic soil of semi-infinite extent subject to a point load applied tangentially at a point considered the origin of the half plane. The study adopted a stress based formulation of the elasticity problem. Fourier transformation of the biharmonic stress compatibility equation was done to obtain bounded stress functions for the elastic half plane problem. Stresses and boundary conditions expressed in terms of the Boussinesq-Papkovich potential functions were transformed using Fourier sine transforms. Boundary conditions were used to obtain the unknown constants of the stress functions for the Cerrutti problem considered; and the complete determination of the stress fields in the Fourier transform space. Inversion of the Fourier sine transforms for the stresses yielded the general expressions for the stresses in the physical domain space variables. The strain fields were obtained from the kinematic relations. The displacement fields were obtained by integration of the strain-displacement relations. The solutions obtained were identical with solutions in literature obtained using Cerrutti stress functions.
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Yeh, Chau-Shioung, Tsung-Jen Teng, Wen-Shinn Shyu, and I.-Chang Tsai. "A Hybrid Method for Analyzing the Dynamic Responses of Cavities or Shells Buried in an Elastic Half-Plane." Journal of Mechanics 18, no. 2 (2002): 75–87. http://dx.doi.org/10.1017/s1727719100002045.

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AbstractIn this paper, based on a variational formalism which originally proposed by Mei [1] for infinite elastic medium and extended by Yeh, et al. [2,3] for elastic half-plane, a hybrid method which combines the finite element and series expansion method is implemented to solve the diffraction of plane waves by a cavity buried in an elastic half-plane. The finite domain which encloses all inhomogeneities including the cavity can be easily formulated by finite element methods. The unknown boundary data obtained by subtracting the known free fields from the total fields which include the boundary nodal displacements and tractions at the interface between the finite domain and the surrounding elastic half-plane are not independent of each other and can be correlated through a series representation. Due to the continuity condition at the interface, the same series representation is still valid for the exterior elastic half-plane to represents the scattered wave. The unknown coefficients of this series are treated as generalized coordinates and can be easily formulated by the same variational principle. The expansion function of the series is composed of basis function. Each basis function is constructed from the basis function for an infinite plane by superimposing an additional homogeneous reflective term to satisfy both traction free conditions at ground surface and radiation conditions at infinity. The numerical results are made against those obtained by boundary element methods, and good agreements are found.
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Theotokoglou, E. E., and Glaucio H. Paulino. "Interaction between an Embedded Crack and an Interface Crack in Nonhomogeneous Coating System." Materials Science Forum 492-493 (August 2005): 397–402. http://dx.doi.org/10.4028/www.scientific.net/msf.492-493.397.

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A general methodology is constructed for the fundamental solution of a crack in the homogeneous half-plane interacting with a crack at the interface between the homogeneous elastic half-plane and the nonhomogeneous elastic coating in which the shear modulus varies exponentially with one coordinate. The problem is solved under plane strain or generalized plane stress condition using the Fourier integral transform method. The stress field in the homogeneous half plane is evaluated by the superposition of two states of stresses, one is associated with a local coordinate system in the infinite fractured plate, while the other in the infinite half plane defined in a structural coordinate system.
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Dissertations / Theses on the topic "Half-plane method"

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Loret, Benjamin. "Problèmes numériques et théoriques de la géomécanique." Paris 6, 1986. http://www.theses.fr/1986PA066239.

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Traitement numérique des milieux infinis de la géomécanique: méthodes d'équations intégrales régulières et singulières pour les structures géotechniques en conditions dynamiques; méthode de couplage itérative éléments finis/équations intégrales (applications au demi-espace et demi-plan); vibration d'un pieu fiché dans le demi espace stratifié. Comportement frottant des milieux granulaires: algorithmes locaux d'intégration numérique pour matériaux élastoplastiques type Drucker-Prager; partie élastique déformation des sols; influence de la contrainte moyenne. Problèmes liés à l'anisotropie en grandes transformations (rotations plastiques). Etude de deux types de bifurcation sur les sables; conséquences macroscopiques de la structure granulaire des sables; non-linéarité incrémentale et localisation des déformations.
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Gardner, Robert Matthew. "A Wide-Area Perspective on Power System Operation and Dynamics." Diss., Virginia Tech, 2008. http://hdl.handle.net/10919/26779.

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Classically, wide-area synchronized power system monitoring has been an expensive task requiring significant investment in utility communications infrastructures for the service of relatively few costly sensors. The purpose of this research is to demonstrate the viability of power system monitoring from very low voltage levels (120 V). Challenging the accepted norms in power system monitoring, the document will present the use of inexpensive GPS time synchronized sensors in mass numbers at the distribution level. In the past, such low level monitoring has been overlooked due to a perceived imbalance between the required investment and the usefulness of the resulting deluge of information. However, distribution level monitoring offers several advantages over bulk transmission system monitoring. First, practically everyone with access to electricity also has a measurement port into the electric power system. Second, internet access and GPS availability have become pedestrian commodities providing a communications and synchronization infrastructure for the transmission of low-voltage measurements. Third, these ubiquitous measurement points exist in an interconnected fashion irrespective of utility boundaries. This work offers insight into which parameters are meaningful to monitor at the distribution level and provides applications that add unprecedented value to the data extracted from this level. System models comprising the entire Eastern Interconnection are exploited in conjunction with a bounty of distribution level measurement data for the development of wide-area disturbance detection, classification, analysis, and location routines. The main contributions of this work are fivefold: the introduction of a novel power system disturbance detection algorithm; the development of a power system oscillation damping analysis methodology; the development of several parametric and non-parametric power system disturbance location methods, new methods of power system phenomena visualization, and the proposal and mapping of an online power system event reporting scheme.<br>Ph. D.
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Books on the topic "Half-plane method"

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Epstein, Charles L., and Rafe Mazzeo. Degenerate Diffusion Operators Arising in Population Biology (AM-185). Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691157122.001.0001.

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This book provides the mathematical foundations for the analysis of a class of degenerate elliptic operators defined on manifolds with corners, which arise in a variety of applications such as population genetics, mathematical finance, and economics. The results discussed in this book prove the uniqueness of the solution to the martingale problem and therefore the existence of the associated Markov process. The book uses an “integral kernel method” to develop mathematical foundations for the study of such degenerate elliptic operators and the stochastic processes they define. The precise nature of the degeneracies of the principal symbol for these operators leads to solutions of the parabolic and elliptic problems that display novel regularity properties. Dually, the adjoint operator allows for rather dramatic singularities, such as measures supported on high codimensional strata of the boundary. The book establishes the uniqueness, existence, and sharp regularity properties for solutions to the homogeneous and inhomogeneous heat equations, as well as a complete analysis of the resolvent operator acting on Hölder spaces. It shows that the semigroups defined by these operators have holomorphic extensions to the right half plane. The book also demonstrates precise asymptotic results for the long-time behavior of solutions to both the forward and backward Kolmogorov equations.
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Book chapters on the topic "Half-plane method"

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Mitrović, Dragiša. "A Representation of Half Plane Meromorphic Functions." In The Cauchy Method of Residues Volume 2. Springer Netherlands, 1993. http://dx.doi.org/10.1007/978-94-011-2000-5_12.

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Shih, Po-Jen, Sheng-Ping Peng, Chau-Shioung Yeh, Tsung-Jen Teng, and Wen-Shinn Shyu. "Application of Steepest Descent Path Method to Lamb’s Solutions for Scattering in Thermo-elastic Half-Plane." In IUTAM Symposium on Dynamics Modeling and Interaction Control in Virtual and Real Environments. Springer Netherlands, 2011. http://dx.doi.org/10.1007/978-94-007-1643-8_34.

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Junghanns, Peter, and Robert Kaiser. "On a Collocation-quadrature Method for the Singular Integral Equation of the Notched Half-plane Problem." In Large Truncated Toeplitz Matrices, Toeplitz Operators, and Related Topics. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-49182-0_18.

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Lüneburg, Ernst. "Half-Plane Diffraction Problems Using Alternative Integral Representations." In Operator Theoretical Methods and Applications to Mathematical Physics. Birkhäuser Basel, 2004. http://dx.doi.org/10.1007/978-3-0348-7926-2_33.

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HUANG, YU YING, and WUHAN HUBEI. "A Direct Method for Deriving Fundamental Solution of Half-plane Problem." In Boundary Elements. Elsevier, 1986. http://dx.doi.org/10.1016/b978-0-08-034357-0.50088-2.

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Yao, Z. H., and J. L. Xiang. "Boundary element method for SH waves in elastic half plane with stochastic and heterogeneous properties." In Developments in Geotechnical Engineering. Elsevier, 1998. http://dx.doi.org/10.1016/s0165-1250(98)80012-6.

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Rangelov, T. V., and G. D. Manolis. "Time-harmonic Green’s function for the half-plane with quadratic-type inhomogeneity." In Recent Developments in Boundary Element Methods. WIT Press, 2010. http://dx.doi.org/10.2495/978-1-84564-492-5/11.

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Fontara, I., F. Wuttke, T. Rangelov, and P. Dineva. "A non-conventional BEM for seismic wave propagation in continuously inhomogeneous half-plane." In Numerical Methods in Geotechnical Engineering. CRC Press, 2014. http://dx.doi.org/10.1201/b17017-67.

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Kattawar, George W. "Polarization of Light in the Ocean." In Ocean Optics. Oxford University Press, 1994. http://dx.doi.org/10.1093/oso/9780195068436.003.0015.

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The effects of polarization on our perception of the environment about us have been recognized for at least 1000 years. The earliest reports were in response to the polarization in blue skylight as observed through various polarizing crystals. Since blue skylight is a source of polarized light, and atmospheric observations are a quite natural part of our daily routine, it is not surprising that an extraordinary amount of research on the polarization of skylight has been undertaken. Study of the polarization properties of the ocean and the hydrosols contained therein has, unfortunately been very limited, perhaps because man has not been a natural resident of the sea. This chapter will introduce a description of the polarized light field beneath the sea by first providing a brief history of polarization. This will familiarize the reader with its rather ubiquitous presence in our environment, even though our visual perception of it is very weak. Finally, a method is presented (Mueller matrices) to fully characterize the polarization properties of the submarine light field and the polarized effects that various hydrosols have on the light field. For a collection of the many diverse applications of polarization, the reader is referred to the excellent book by Gehrels (1974) About 1000 years ago, the Vikings discovered the dichroic properties of crystals such as cordierite. This property of exhibiting various colors when viewed from different directions is due to the selective absorption of waves oscillating along a particular plane of the crystal. When Vikings viewed the blue skylight through such crystals held in a certain orientation, they located portions of the sky relative to the solar position that seemed to disappear. With this discovery of the polarization of the blue sky, they learned to navigate even in the absence of the sun (e.g., when it was below the horizon). It was another six and one-half centuries before other polarization properties were reported (see Table 11-1 taken from Gehrels, 1974, and Können, 1985).
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Opella, S. J., and L. E. Chirlian. "A Solid-State NMR Approach to Structure Determination of Membrane-Associated Peptides and Proteins." In Biological NMR Spectroscopy. Oxford University Press, 1997. http://dx.doi.org/10.1093/oso/9780195094688.003.0017.

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Structural biology relies on detailed descriptions of the three-dimensional structures of peptides, proteins, and other biopolymers to explain the form and function of biological systems ranging in complexity from individual molecules to entire organisms. NMR spectroscopy and X-ray crystallography, in combination with several types of calculations, provide the required structural information. In recent years, the structures of several hundred proteins have been determined by one or both of these experimental methods. However, since the protein molecules must either reorient rapidly in samples for multidimensional solution NMR spectroscopy or form high quality single crystals in samples for X-ray crystallography, nearly all of the structures determined up to now have been of the soluble, globular proteins that are found in the cytoplasm and periplasmof cells and fortuitously have these favorable properties. Since only a minority of biological properties are expressed by globular proteins, and proteins, in general, have evolved in order to express specific functions rather than act as samples for experimental studies, there are other classes of proteins whose structures are currently unknown but are of keen interest in structural biology. More than half of all proteins appear to be associated with membranes, and many cellular functions are expressed by proteins in other types of supramolecular complexes with nucleic acids, carbohydrates, or other proteins. The interest in the structures of membrane proteins, structural proteins, and proteins in complexes provides many opportunities for the further development and application of NMR spectroscopy. Our understanding of polypeptides associated with lipids in membranes, in particular, is primitive, especially compared to that for globular proteins. This is largely a consequence of the experimental difficulties encountered in their study by conventional NMR and X-ray approaches. Fortunately, the principal features of two major classes of membrane proteins have been identified from studies of several tractable examples. Bacteriorhodopsin (Henderson et al., 1990), the subunits of the photosynthetic reaction center (Deisenhofer et al., 1985), and filamentous bacteriophage coat proteins (Shon et al., 1991; McDonnell et al., 1993) have all been shown to have long transmembrane hydrophobic helices, shorter amphipathic bridging helices in the plane of the bilayers, both structured and mobile loops connecting the helices, and mobile N- and C-terminal regions.
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Conference papers on the topic "Half-plane method"

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Akira, Sasamoto, and P. A. Krutitskii. "Integral representation of voltage in half-plane conductor with embedded crack by D.C. potential difference method." In 11TH INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS 2013: ICNAAM 2013. AIP, 2013. http://dx.doi.org/10.1063/1.4825513.

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Akira, Sasamoto, and P. A. Krutitskii. "Integral representation of voltage in half-plane conductor with crack from surface by D.C. potential difference method." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2012: International Conference of Numerical Analysis and Applied Mathematics. AIP, 2012. http://dx.doi.org/10.1063/1.4756234.

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Grzebyk, W. E. "Method for measuring of emission using half double loaded circular frame antenna located perpendicularly over a conductive plane." In 2016 International Symposium on Electromagnetic Compatibility - EMC EUROPE. IEEE, 2016. http://dx.doi.org/10.1109/emceurope.2016.7739304.

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Lin, Yuan, and Timothy C. Ovaert. "Thermal Distortion of an Anisotropic Elastic Half-Plane and Its Application in Contact Problems Including Frictional Heating." In ASME/STLE 2004 International Joint Tribology Conference. ASMEDC, 2004. http://dx.doi.org/10.1115/trib2004-64040.

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The thermal surface distortion of an anisotropic elastic half-plane is studied using the extended version of Stroh’s formalism. In general, the curvature of the surface depends both on the local heat flux into the half-plane and the local temperature variation along the surface. However, if the material is orthotropic, the curvature of the surface depends only on the local heat flux into the half-plane. As a direct application, the two-dimensional thermoelastic contact problem of an indenter sliding against an orthotropic half-plane is considered. Two cases, where the indenter has either a flat or a parabolic profile, are studied in detail. Comparisons with other available results in the literature show that the present method is correct and accurate.
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Bo Zhao, Xin Bo Wang, Jia Lin Cai, Wei Bing Lu, and Tie Jun Cui. "Analysis of periodic array structures in half space with infinite electric plane using sub-entire-domain basis function method." In 2008 International Workshop on Metamaterials (Meta2008). IEEE, 2008. http://dx.doi.org/10.1109/meta.2008.4723598.

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Su, Shigong, and Xianzhong Su. "Generalized Characteristic Method for Orthotropic Media." In ASME 1995 Design Engineering Technical Conferences collocated with the ASME 1995 15th International Computers in Engineering Conference and the ASME 1995 9th Annual Engineering Database Symposium. American Society of Mechanical Engineers, 1995. http://dx.doi.org/10.1115/detc1995-0549.

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Abstract A new method is developed to solve two dimensional transient problems of elastodynamics in orthotropic media. The real solutions of the characteristic equation for the Navier equations in orthotropic media can be analytically continued to the complex domain in which they are called generalized characteristics. The generalized characteristics are employed to prove that a set of algebraic equations of the velocity components is equivalent to the Navier equations. To illustrate how to use the present method in elastodynamics for orthotropic media, the problems of time domain Green’s functions in an unbounded medium, and Lamb’s problem for a buried concentrated line force are solved by applying the derived algebraic equations. The reflection coefficients and Snell’s law on the surface of a half-space are obtained for incident non-plane transient waves. The direct waves, reflected waves, and head wave in a half-space are analyzed directly in terms of generalized characteristics. Finally, some numerical results for the particle displacement at receivers (on and below the surface) are shown for four typical crystals and composite materials.
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Yu, John J., and Nicolas Péton. "Obtaining Influence Coefficients in Different Formats With Reduced Number of Trial Runs on Two-Plane Balancing." In ASME Turbo Expo 2020: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2020. http://dx.doi.org/10.1115/gt2020-14191.

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Abstract Previously conversion equations of influence coefficients between multi-plane and static(in-phase)-couple(180 degrees out-of-phase) methods have been established. Sometimes one may have influence coefficients due to weight from one end only, but not both ends, plus those due to static or couple pair weight only but not both pairs. It has been found now that obtaining or knowing half of influence coefficients in the first method, plus half of those in the second method, can yield the other half of influence coefficients in both methods. In the other words, all influence coefficients in different formats can be obtained without a further trial run once one has half of influence coefficients in both methods. The above findings and conversion equations have been obtained analytically and verified by experimental results. A real application example is presented to demonstrate its efficiency in dealing with balancing tasks. The corresponding spreadsheets that can easily convert influence coefficients between different formats have been developed and used in real cases. Up to this point, all possible conversion equations of influence coefficients in different formats have been successfully discovered.
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Fernandes, Ralston, James G. Boyd, Dimitris C. Lagoudas, and Sami El-Borgi. "Plane Strain Sliding Contact Between a Rigid Cylinder and a Pseudoelastic Shape Memory Alloy Half-Space." In ASME 2018 Conference on Smart Materials, Adaptive Structures and Intelligent Systems. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/smasis2018-8243.

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This study uses the finite element method to analyze the sliding contact behavior between a rigid cylinder and a shape memory alloy (SMA) semi-infinite half-space. An experimentally validated constitutive model is used to capture the pseudoelastic effect exhibited by these alloys. Parametric studies involving the maximum recoverable transformation strain and the transformation temperatures are performed to analyze the effects that these parameters have on the stress fields during indentation and sliding contact. It is shown that, depending on the amount of recoverable transformation strain possessed by the alloy, a reduction of almost 40 % of the maximum stress in the pseudoelastic half-space is achieved when compared to the maximum stress in a purely elastic half-space. The studies also reveal that the sliding response is strongly temperature dependent, with significant residual stress present in the half-space at temperatures below the austenitic finish temperature.
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Jin, X., L. M. Keer, and E. L. Chez. "Behavior of a Horizontal Fluid Filled Crack Under Moving Hertzian Load." In World Tribology Congress III. ASMEDC, 2005. http://dx.doi.org/10.1115/wtc2005-64087.

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Numerical analysis is presented for a fluid filled subsurface crack in an elastic half plane loaded by Hertzian contact stresses. The opening volume of the horizontal Griffith crack is fully occupied by an incompressible fluid. In the presence of friction, a moving Hertzian line contact load is applied at the surface of the half plane. The stress intensity factors at the tips of the fluid filled crack are analyzed on condition that the change of the opening crack volume vanishes due to the fluid incompressibility. The method used is that of replacing the crack by a continuous distribution of edge dislocations. As a cycle of rolling can be viewed as shifting the Hertzian contact stresses across the surface of the half plane, the results of this analysis may prove useful in the prediction of rolling fatigue of an elastic rolling body containing a soft inclusion.
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Han, Jianyou, and Tong Yang. "A Novel Synthesis Method for Three-Position Motion Generation With Planar Four-Bar Mechanisms." In ASME 2012 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/detc2012-70162.

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This paper deals with the three-position motion generation problem with two specific grounded link lengths. There are two infinities of solutions for selecting the two links on the derived contours of the link lengths. These points on the contours are circle points or center points. After one half of the basic four bar had been selected on the contour, two infinities of solutions remained. These solutions can be mapped in a plane to determine where the particular types of mechanisms occur. Furthermore after one half of the basic four bar had been selected on the contour, one infinity of solutions still remained on the other contour. This indicates two infinities of solutions are still remained for the two given link lengths. These contours can be displayed in the solution space in which the motion generation is defined. With these significant useful information the better mechanism can be obtained, which satisfies more design conditions. Expressions of the contours are derived. Two numerical examples are used for illustration, but the results can be applied to any three-position motion generation problem.
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