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Keywords: polynomials
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Journal Articles
Publisher: ASME
Article Type: Research Papers
J. Mech. Des. December 2011, 133(12): 121005.
Published Online: December 9, 2011
... polynomials, approximated constraints are sometimes unable to ensure feasibility when highly nonlinear and/or nonconvex constraint functions are approximated in RBDO. We explore the development of a new MLSM based meta-model that ensures the constraint feasibility of an optimal solution in RBDO. A constraint...
Journal Articles
Publisher: ASME
Article Type: Research Papers
J. Mech. Des. December 2011, 133(12): 121003.
Published Online: December 9, 2011
...Vilmos V. Simon In this study, polynomial functions of orders up to five are applied to induce variations in the cradle radial setting and the velocity ratio in the kinematic scheme of the machine tool for the generation of the pinion tooth surfaces corresponding to reduced transmission error...
Journal Articles
Publisher: ASME
Article Type: Technical Briefs
J. Mech. Des. October 2011, 133(10): 104503.
Published Online: October 18, 2011
... in detail. Design of multicomponent systems under inertia forces is presented using polynomial interpolation models; constraints to the centroid position, moment of inertia, and volume fraction are included. Applications to piezoelectric multi-actuated microtools and integrated layout design of bridge...
Journal Articles
Publisher: ASME
Article Type: Research Papers
J. Mech. Des. September 2011, 133(9): 091003.
Published Online: September 7, 2011
... by piecing together a set of trigonometric and/or polynomial functions that satisfy the constraints. For most problems, there are many profile solutions that satisfy the constraints. In this paper, a relatively new optimization technique known as particle swarm optimization (PSO) is applied...
Journal Articles
Publisher: ASME
Article Type: Research Papers
J. Mech. Des. August 2010, 132(8): 081003.
Published Online: July 21, 2010
... to eight precision points in polynomial equations. Classical elimination methods are used to reduce the formulation to a system of seven sixth-degree polynomials. A constrained homotopy technique is employed to eliminate degenerate solutions, mapping them to solutions at infinity of the augmented system...
Journal Articles
Publisher: ASME
Article Type: Research Papers
J. Mech. Des. April 2010, 132(4): 041004.
Published Online: April 13, 2010
.... It is possible to analyze the tooth contact pattern of the spiral bevel gears with consideration of the tooth flank form errors expressing the errors as polynomial equations. Finally, the influence of alignment errors due to assembly on the tooth contact pattern is also investigated analytically...
Journal Articles
Publisher: ASME
Article Type: Research Papers
J. Mech. Des. March 2010, 132(3): 031001.
Published Online: March 1, 2010
... on the cradle-type hypoid generator conducted by optimal polynomial functions up to the fifth-order. By using the corresponding computer program, the motion graphs of the CNC hypoid generator are determined for the manufacture of spiral bevel gears, based on the optimal variation in the velocity ratio...
Journal Articles
Publisher: ASME
Article Type: Research Papers
J. Mech. Des. October 2009, 131(10): 101004.
Published Online: September 3, 2009
...B. Demeulenaere; G. Pipeleers; J. De Caigny; J. Swevers; J. De Schutter; L. Vandenberghe This paper develops a general framework to synthesize optimal polynomial splines for rigid motion systems driven by cams or servomotors. This framework is based on numerical optimization, and has three main...
Journal Articles
Publisher: ASME
Article Type: Research Papers
J. Mech. Des. April 2009, 131(4): 041007.
Published Online: March 23, 2009
...Vilmos V. Simon A method for the determination of the optimal polynomial functions for the conduction of machine-tool setting variations in pinion teeth finishing in order to reduce the transmission errors in spiral bevel gears is presented. Polynomial functions of order up to 5 are applied...
Journal Articles
Publisher: ASME
Article Type: Research Papers
J. Mech. Des. December 2007, 129(12): 1294–1302.
Published Online: December 30, 2006
... of a universal face-hobbing hypoid gear generator is applied to investigate the ease-off deviations of the design parameters—including cutter parameters, machine settings, and the polynomial coefficients of the auxiliary flank modification motion. Subsequently, linear regression is used to modify the tooth...
Journal Articles
Publisher: ASME
Article Type: Research Papers
J. Mech. Des. December 2007, 129(12): 1265–1268.
Published Online: December 13, 2006
... satisfy a certain relationship. This degeneracy yields a double root of the characteristic polynomial in t = tan ( φ ∕ 2 ) , which could be erroneously interpreted as two coalesce assembly modes. However, unlike what arises in nondegenerate cases, this double root yields two sets of solutions...
Journal Articles
Publisher: ASME
Article Type: Research Papers
J. Mech. Des. December 2007, 129(12): 1278–1284.
Published Online: December 10, 2006
...Chiu-Fan Hsieh; Yii-Wen Hwang Vacuum pump plays an important role in the vacuum system. In this paper, a new method is proposed to design the Roots rotor that was the trochoidal curve with variable trochoid ratio. The fifth-order polynomial and cubic spline functions are used to generate smoothly...
Journal Articles
Publisher: ASME
Article Type: Research Papers
J. Mech. Des. August 2007, 129(8): 831–843.
Published Online: July 2, 2006
... buckling members are modeled using polynomial functions fitted to nonlinear inextensible exact elastica theory. The displacement analysis of the mechanisms is done quasi-statically using loop closure theory, static equilibrium of flexible parts represented by polynomial load deflections. One example...
Journal Articles
Publisher: ASME
Article Type: Research Papers
J. Mech. Des. April 2007, 129(4): 397–405.
Published Online: April 18, 2006
... that exhibit a continuum of possible configurations). The method is based on the fact that this problem can be reduced to finding the roots of a polynomial system of linear, quadratic, and hyperbolic equations, which is here tackled with a new strategy exploiting its structure. The method is conceptually...
Journal Articles
Publisher: ASME
Article Type: Research Papers
J. Mech. Des. March 2007, 129(3): 320–325.
Published Online: February 23, 2006
... is reduced to solving an eighth-degree polynomial in the square of the tangent of the half-angle between one of the limbs and the base plane. Hence, there are at most 16 assembly configurations for the manipulator. In addition, it is shown that the 16 solutions are eight pairs of reflected configurations...
Journal Articles
Publisher: ASME
Article Type: Technical Briefs
J. Mech. Des. November 2006, 128(6): 1352–1356.
Published Online: December 29, 2005
..., and integrating elementary deflections along the whole spring. The inverse process to obtain the spring load from its length is assimilated to solve a fourth order polynomial. Two analytical models are obtained. One to determine the length versus load curve and the other for the load versus length curve...
Journal Articles
Publisher: ASME
Article Type: Research Papers
J. Mech. Des. July 2006, 128(4): 776–786.
Published Online: October 4, 2005
...Hai-Jun Su; J. Michael McCarthy This paper formulates the inverse static analysis of planar compliant mechanisms in polynomial form. The goal is to find the equilibrium configurations of the system in response to a known force/moment applied to the mechanism. The geometric constraint of the linkage...
Journal Articles
Publisher: ASME
Article Type: Technical Papers
J. Mech. Des. July 2005, 127(4): 621–630.
Published Online: August 29, 2004
... mechanics approach, without employing a local element coordinate system. In this study, linear polynomials are used to interpolate both the transverse and longitudinal components of the displacement. This is different from other absolute nodal-coordinate-based beam elements where cubic polynomials are used...
Journal Articles
Publisher: ASME
Article Type: Technical Papers
J. Mech. Des. March 2004, 126(2): 262–268.
Published Online: May 5, 2004
...Andrew J. Sommese; Jan Verschelde; Charles W. Wampler For many mechanical systems, including nearly all robotic manipulators, the set of possible configurations that the links may assume can be described by a system of polynomial equations. Thus, solving such systems is central to many problems...
Journal Articles
Publisher: ASME
Article Type: Technical Papers
J. Mech. Des. June 2003, 125(2): 292–301.
Published Online: June 11, 2003
.... The kinematics of the Linear Delta are solved via the polynomial method. The mobility, workspace and manipulability characteristics are examined. It is shown that the Linear Delta’s manipulability generally exhibits relatively little variation when compared to space utilization. The tendency exists...