A Curve Design Method with Shape Control

The high energy density actuation potential of shape memory alloy (SMA) wire is tempered by conservative design guidelines set to mitigate complex factors such as functional fatigue (shakedown). In addition to stroke loss, shakedown causes practical problems of interface position drift between the system and the SMA wire under higher stress levels if the wire does not undergo a pre-installation shakedown procedure. Constraining actuation strain eliminates interface position drift and has been reported to reduce shakedown as well as increase fatigue life. One approach to limit actuation strain is using a mechanical strain limiter, which sets a fixed Martensite strain position—useful for the development of in-device shakedown procedures, which eliminates time-consuming pre-installation shakedown procedures. This paper presents a novel conglomerate stabilization curve design method for SMA wire actuators, which accounts for shakedown with and without the use of mechanical strain limiters to enable higher stress designs to maximize actuator performance. Shakedown experimental data including the effect of strain limiters along with stroke and work density contours form the basis for this new design method. For each independent mechanical strain limiter, the maximum of the individual postshakedown Austenite curves at a range of applied stress are combined into a conglomerate stabilization design curve. These curves over a set of mechanical strain limiters including the zero set provide steady-state performance prediction for SMA actuation, effectively decoupling the shakedown material performance from design variables that affect the shakedown. The use and benefits of the conglomerate stabilization curve design method are demonstrated with a common constant force actuator design example, which was validated in hardware on a heavy duty latch device. This new design method, which accounts for shakedown, supports design of SMA actuators at higher stresses with more economical use of material/power and enables the utilization of strain limiters for cost-saving in-device shakedown procedures.

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Pitch curve design defects modification for non-circular bevel gear

Proceedings of the Institution of Mechanical Engineers Part C Journal of Mechanical Engineering Science ◽

10.1177/0954406214556666 ◽

2014 ◽

Vol 229 (12) ◽

pp. 2231-2241 ◽

Cited By ~ 2

Author(s):

LV Gang

Keyword(s):

Design Method ◽

Spherical Surface ◽

Mathematical Expression ◽

Bevel Gear ◽

Design Parameters ◽

Curve Design ◽

Modification Method ◽

Parallel Axis ◽

Design Defects ◽

Pitch Curve

A novel pitch curve design method for non-circular bevel gear is presented to simplify design of non-circular bevel gear. Pitch curve equation for non-circular bevel gear is deduced based on geometrical relationships between pitch cone surface of non-circular gear with parallel axis and spherical surface. Then, transmission ratio function is transformed into pitch curve design defects modification equation and mathematical expression between modification factor and pitch curve design parameters for non-circular bevel gear is derived. By using the expression, modification value of pitch curve can be determined rapidly and accurately. Simulation results for high-order elliptical bevel gear and Pascal curve bevel gear demonstrate that the proposed modification method can be applied to pitch curve design for other types of non-circular bevel gear. Design and verification efficiency for non-circular bevel gear are improved effectively by employing the proposed pitch curve design defects modification method.

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Geometric Curve Design Method of Fuzzy Reliability Based on Random Processing Errors

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.199-200.72 ◽

2011 ◽

Vol 199-200 ◽

pp. 72-77

Author(s):

Zhi Su Zhao ◽

Xing Hua Zhang

Keyword(s):

Design Method ◽

Failure Process ◽

Point Of View ◽

Design Stage ◽

Gradual Change ◽

Fuzzy Reliability ◽

Reliability Design ◽

Curve Design ◽

Processing Errors ◽

The Impact

In order to foresee the influence of random processing errors on geometric curve in design stage, meanwhile including success and failure process during the gradual change process in the forecast. Based on probabilistic fuzzy reliability point of view, the success or failure determination will be extended to fuzzy events. The geometric curve deign method will be also given when taking the impact of random engineering error into account. Related analysis formulae and the fuzzy criterion of success or failure of designing the curve process are established and derived. Through which, design and engineering process are integrated, the designer will be more reliably to predict the success or failure of the geometric curve design during the design stage. The processing error of lack of statistical data and the objectivity of the success or failure determination criterion will be easily solved. Economy cost and reliability design of geometrical curve design will be also considered.

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Shape control of curve design by weighted rational spline

Korean Journal of Computational & Applied Mathematics ◽

10.1007/bf03009947 ◽

1999 ◽

Vol 6 (3) ◽

pp. 537-547

Author(s):

Qi Duan ◽

Botang Li ◽

K. Djidjeli ◽

W. G. Price ◽

E. H. Twizell

Keyword(s):

Shape Control ◽

Curve Design ◽

Rational Spline

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α Extension of the Cubic Ball Curve

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.235.85 ◽

2012 ◽

Vol 235 ◽

pp. 85-89

Author(s):

Cheng Wei Wang

Keyword(s):

Shape Control ◽

Bézier Curve ◽

Bezier Curve ◽

Shape Design ◽

Shape Preserving ◽

Curve Design ◽

Extension Curve ◽

Cad Cam ◽

Control Capability ◽

Better Than

Ball curve； curve design； shape parameter Abstract. Ball curve is found similar to Bézier curve，also it has a good property of shape preserving，and in some respects，it has better properties than the Bézier curve. Therefore, In the shape design，Ball curve is paid more and more attention, it has a wide application. By introducing the concept of weights in NURBS curve into a blending technique, the paper extends the representation of the cubic Ball curve. The generalized cubic Ball curve is denoted as α extension cubic Ball curve, whose shape-control capability is shown to be much better than that of Ball curve. The representation and properties of the extension curve are studied. The curve is easy and intuitive to reshape by varying the parameters; so it is useful in some applications of CAD/CAM.

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Shape Modification forλ-Bézier Curves Based on Constrained Optimization of Position and Tangent Vector

Mathematical Problems in Engineering ◽

10.1155/2015/735629 ◽

2015 ◽

Vol 2015 ◽

pp. 1-12 ◽

Cited By ~ 1

Author(s):

Gang Hu ◽

Xiaomin Ji ◽

Xinqiang Qin ◽

Suxia Zhang

Keyword(s):

Constrained Optimization ◽

Shape Control ◽

Control Parameter ◽

Tangent Vector ◽

Control Points ◽

Shape Modification ◽

Shape Preserving ◽

Bezier Curves ◽

Bézier Curves ◽

Curve Design

Besides inheriting the properties of classical Bézier curves of degreen, the correspondingλ-Bézier curves have a good performance on adjusting their shapes by changing shape control parameter. Specially, in the case where the shape control parameter equals zero, theλ-Bézier curves degenerate to the classical Bézier curves. In this paper, the shape modification ofλ-Bézier curves by constrained optimization of position and tangent vector is investigated. The definition and properties ofλ-Bézier curves are given in detail, and the shape modification is implemented by optimizing perturbations of control points. At the same time, the explicit formulas of modifying control points and shape parameter are obtained by Lagrange multiplier method. Using this algorithm,λ-Bézier curves are modified to satisfy the specified constraints of position and tangent vector, meanwhile the shape-preserving property is still retained. In order to illustrate its ability on adjusting the shape ofλ-Bézier curves, some curve design applications are discussed, which show that the proposed method is effective and easy to implement.

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