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IN THIS ISSUE

### Editorial

J. Mech. Des. 2011;133(3):030201-030201-1. doi:10.1115/1.4003704.
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Design education research is part of design research. This has been a JMD position for quite some time, with a special issue dedicated to the topic in July 2007 with Mike McCarthy as editor and Phil Doepker and Clive Dym as guest editors. In his introductory editorial for that issue, Mike McCarthy mentioned the following: “Clearly without the fundamentals nothing else matters, but then when the fundamentals are in place the rest of this must happen effectively for engineering to be successful. In the past our industry colleagues would teach these details, but the demands of the modern marketplace are making them less patient with our students’ inexperience. This is one of many challenges that I believe research in design engineering education can address to our benefit as researchers, educators, and engineers.”

Commentary by Dr. Valentin Fuster

### Guest Editorial

J. Mech. Des. 2011;133(3):030301-030301-2. doi:10.1115/1.4003567.
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Have you heard? Did you know? The Journal of Mechanical Design (JMD) has been accepting and publishing quality design education research papers for the last 2 years. As the associate editor handling this area, I am all too often surprised. First, I am surprised that the word has not spread widely and that there are not more design education submissions to JMD. Clearly, there is a tremendous surge in the interest of engineering educators nationwide to increase student learning and skills through design projects, often with genuine experiences and with the participation from industry, the community, or individual “customers” working with student design teams. Design education seems to be the new focus of how engineering educators are going to fix what is perceived to have been broken for many years: a content focused curriculum, lacking in the context of real problems that would motivate and engage students and deepen their learning and increase their confidence in how to think, reason, problem-solve, and apply mathematics, science, and engineering methods and tools.

Commentary by Dr. Valentin Fuster

### Research Papers

J. Mech. Des. 2011;133(3):031001-031001-10. doi:10.1115/1.4003499.

This paper presents elliptical rolling contact joints in compression as an alternative to circular rolling contact and conventional revolute joints where high quality force transmission—low friction and backlash—with variable output are desired. Parameters specific to the joint and its position are defined in terms of relative link angles and elliptical surface geometry. These relationships allow elliptical rolling contact joints to be incorporated in vector loop summations used in kinematic analysis. Notably, elliptical rolling contact is developed as the more general case of which circular rolling contact is a subset. Elliptical rolling contact joints are shown to offer several benefits over circular rolling contact, including reduced Hertz contact stresses, variable output velocity, maximum use of contact interface by distributing small rotations across surfaces of small curvature, reduced forces on constraining members, and no-slip pure rolling provided by either connecting links or flexures, without the need for gear teeth or friction.

Commentary by Dr. Valentin Fuster
J. Mech. Des. 2011;133(3):031002-031002-8. doi:10.1115/1.4003412.

A general formulation of the synthesis of the pitch cones of a pair of $N$-lobed elliptical bevel gears and the pitch surface of its conjugate crown-rack is proposed. In particular, two pitch cones and the pitch surface of their crown-rack are obtained for any number and combination of lobes and in any configuration during their pure-rolling motion. This formulation is implemented in MATLAB ; several significant examples are included, with circular bevel gears becoming a particular case thereof.

Commentary by Dr. Valentin Fuster
J. Mech. Des. 2011;133(3):031003-031003-10. doi:10.1115/1.4002978.

A recently developed metamodel, radial basis function-based high-dimensional model representation (RBF-HDMR), shows promise as a metamodel for high-dimensional expensive black-box functions. This work extends the modeling capability of RBF-HDMR from the current second-order form to any higher order. More importantly, the modeling process “uncovers” black-box functions so that not only is a more accurate metamodel obtained, but also key information about the function can be gained and thus the black-box function can be turned “white.” The key information that can be gained includes: (1) functional form, (2) (non)linearity with respect to each variable, and (3) variable correlations. The black-box “uncovering” process is based on identifying the existence of certain variable correlations through two derived theorems. The adaptive process of exploration and modeling reveals the black-box functions until all significant variable correlations are found. The black-box functional form is then represented by a structure matrix that can manifest all orders of correlated behavior of the variables. The resultant metamodel and its revealed inner structure lend themselves well to applications such as sensitivity analysis, decomposition, visualization, and optimization. The proposed approach is tested with theoretical and practical examples. The test results demonstrate the effectiveness and efficiency of the proposed approach.

Commentary by Dr. Valentin Fuster
J. Mech. Des. 2011;133(3):031004-031004-10. doi:10.1115/1.4003537.

Variability is the inherent randomness in systems, whereas incertitude is due to lack of knowledge. In this paper, a generalized hidden Markov model (GHMM) is proposed to quantify aleatory and epistemic uncertainties simultaneously in multiscale system analysis. The GHMM is based on a new imprecise probability theory that has the form of generalized interval. The new interval probability resembles the precise probability and has a similar calculus structure. The proposed GHMM allows us to quantify cross-scale dependency and information loss between scales. Based on a generalized interval Bayes’ rule, three cross-scale information assimilation approaches that incorporate uncertainty propagation are also developed.

Commentary by Dr. Valentin Fuster
J. Mech. Des. 2011;133(3):031005-031005-9. doi:10.1115/1.4003539.

A function generator mechanism links its motion output and motion input with a desired functional relationship. The probability of realizing such functional relationship is the kinematic reliability. The time-dependent kinematic reliability is desired because it provides the reliability over the time interval where the functional relationship is defined. But the methodologies of time-dependent reliability are currently lacking for function generator mechanisms. We propose a mean value first-passage method for time-dependent reliability analysis. With the assumption of normality for random dimension variables with small variances, the motion error becomes a nonstationary Gaussian process. We at first derive analytical equations for upcrossing and downcrossing rates and then develop a numerical procedure that integrates the two rates to obtain the kinematic reliability. A four-bar function generator is used as an example. The proposed method is accurate and efficient for normally distributed dimension variables with small variances.

Commentary by Dr. Valentin Fuster
J. Mech. Des. 2011;133(3):031006-031006-9. doi:10.1115/1.4003410.

The computational effort for reliability based design optimization (RBDO) is no longer prohibitive even for detailed studies of mechanical integrity. The sequential approximation RBDO formulation and the use of surrogate models have greatly reduced the amount of computations necessary. In RBDO, the surrogate models need to be most accurate in the proximity of the most probable point. Thus, for multiply constrained problems, such as fatigue design problems, where each finite element (FE)-model node constitutes a constraint, the computational effort may still be considerable if separate experiments are used to fit each constraint surrogate model. This paper presents an RBDO algorithm that uses a single constraint approximation point (CAP) as a starting point for the experiments utilized to establish all surrogate models, thus reducing the computational effort to that of a single constraint problem. Examples of different complexities from solid mechanics applications are used to present the accuracy and versatility of the proposed method. In the studied examples, the ratio of the computational effort (in terms of FE-solver calls) between a conventional method and the single CAP algorithm was approximately equal to the number of constraints and the introduced error was small. Furthermore, the CAP-based RBDO is shown to be capable of handling over 10,000 constraints and even an intermittent remeshing. Also, the benefit of considering other objectives than volume (mass) is shown through a cost optimization of a truck component. In the optimization, fatigue-specific procedures, such as shot peening and machining to reduce surface roughness, are included in the cost as well as in the constraints.

Commentary by Dr. Valentin Fuster
J. Mech. Des. 2011;133(3):031007-031007-7. doi:10.1115/1.4003568.

Epicyclic gear train is a fundamental form of mechanical transmission with broad applications. Efficiency study of these trains is critical to design, optimization, and operation. It is known that the efficiencies of these systems are highly related to the internal power flows. We apply the concept of virtual power to find analytical expression of the efficiency of a two degrees of freedom train, with associated applicable ranges. The results are verified by an example.

Commentary by Dr. Valentin Fuster
J. Mech. Des. 2011;133(3):031008-031008-15. doi:10.1115/1.4003498.

Advances in innovation processes are critically important as economic and business landscapes evolve. There are many concept generation techniques that can assist a designer in the initial phases of design. Unfortunately, few studies have examined these techniques that can provide evidence to suggest which techniques should be preferred or how to implement them in an optimal way. This study systematically investigates the underlying factors of four common and well-documented techniques: brainsketching, gallery, 6-3-5, and C-sketch. These techniques are resolved into their key parameters, and a rigorous factorial experiment is performed to understand how the key parameters affect the outcomes of the techniques. The factors chosen for this study with undergraduate mechanical engineers include how concepts are displayed to participants (all are viewed at once or subsets are exchanged between participants, i.e., “rotational viewing”) and the mode used to communicate ideas (written words only, sketches only, or a combination of written words and sketches). Four metrics are used to evaluate the data: quantity, quality, novelty, and variety. The data suggest that rotational viewing of sets of concepts described using sketches combined with words produces more ideas than having all concepts displayed in a “gallery view” form, but a gallery view results in more high quality concepts. These results suggest that a hybrid of methods should be used to maximize the quality and number of ideas. The study also shows that individuals gain a significant number of ideas from their teammates. Ideas, when shared, can foster new idea tracks, more complete layouts, and a diverse synthesis. Finally, as teams develop more concepts, the quality of the concepts improves. This result is a consequence of the team-sharing environment and, in conjunction with the quantity of ideas, validates the effectiveness of group idea generation. This finding suggests a way to go beyond the observation that some forms of brainstorming can actually hurt productivity.

Topics: Design , Project tasks , Teams
Commentary by Dr. Valentin Fuster
J. Mech. Des. 2011;133(3):031009-031009-9. doi:10.1115/1.4003538.

This paper develops new design criteria for lamina emergent mechanism (LEM) flexures with particular application to sheet-metal-formed metal flexures. The LEM flexure design criteria are based on the relative performance between the LEM flexure and a section of lamina that is of the same overall length, width, and thickness as the LEM flexure. Novel metal revolute and torsional LEM flexures are presented and evaluated against the LEM flexure design criteria. Both flexures meet the proposed criteria, and their performance is evaluated in the design of a basic crank-slider mechanism. When compared with unformed flexures of the same dimensions, the revolute and torsional metal LEM flexures are found to improve the crank-slider performance.

Commentary by Dr. Valentin Fuster
J. Mech. Des. 2011;133(3):031010-031010-11. doi:10.1115/1.4003578.

Some theoretical developments are presented, which lead to approximate analytical results on quasi-static transmission errors valid for low and high contact ratio spur and helical gears. Based on a multidegree-of-freedom gear model, a unique scalar equation for transmission error is established. The role of profile relief is analyzed by using Fourier series and it is shown that transmission error fluctuations depend on a very limited number of parameters representative of gear geometry and profile relief definition. An original direct solution to the optimum relief minimizing transmission error fluctuations is presented, which is believed to be helpful for designers. The analytical results compare well with the numerical results provided by a variety of models and it is demonstrated that some general laws of evolution for transmission error fluctuations versus profile modifications can be established for spur and helical gears.

Commentary by Dr. Valentin Fuster
J. Mech. Des. 2011;133(3):031011-031011-9. doi:10.1115/1.4003684.

This paper proposes an optimum design method, based on our level set-based topology optimization method, for maximizing thermal diffusivity in problems dealing with generic heat transfer boundaries that include design-dependent boundary conditions. First, a topology optimization method using a level set model incorporating a fictitious interface energy for regularizing the topology optimization is briefly discussed. Next, an optimization method for maximizing thermal diffusivity is formulated based on the concept of total potential energy. An optimization algorithm that uses the finite element method when solving the equilibrium equation and updating the level set function is then constructed. Finally, several numerical examples are provided to confirm the utility and validity of the proposed topology optimization method.

Commentary by Dr. Valentin Fuster