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### Research Papers: Design Theory and Methodology

J. Mech. Des. 2017;139(9):091101-091101-12. doi:10.1115/1.4037185.

Designers often search for new solutions by iteratively adapting a current design. By engaging in this search, designers not only improve solution quality but also begin to learn what operational patterns might improve the solution in future iterations. Previous work in psychology has demonstrated that humans can fluently and adeptly learn short operational sequences that aid problem-solving. This paper explores how designers learn and employ sequences within the realm of engineering design. Specifically, this work analyzes behavioral patterns in two human studies in which participants solved configuration design problems. Behavioral data from the two studies are first analyzed using Markov chains to determine how much representation complexity is necessary to quantify the sequential patterns that designers employ during solving. It is discovered that first-order Markov chains are capable of accurately representing designers' sequences. Next, the ability to learn first-order sequences is implemented in an agent-based modeling framework to assess the performance implications of sequence-learning abilities. These computational studies confirm the assumption that the ability to learn sequences is beneficial to designers.

Commentary by Dr. Valentin Fuster

### Research Papers: Design Automation

J. Mech. Des. 2017;139(9):091401-091401-12. doi:10.1115/1.4036780.

A critical task in product design is mapping information from consumer to design space. Currently, this process largely depends on designers identifying and mapping psychological and consumer level factors to engineered attributes. In this way, current methodologies lack provision to test a designer's cognitive reasoning and could introduce bias when mapping from consumer to design space. In addition, current dominant frameworks do not include user–product interaction data in design decision making, nor do they assist designers in understanding why a consumer has a particular perception about a product. This paper proposes a framework—cyber-empathic (CE) design—where user–product interaction data are acquired using embedded sensors. To gain insight into consumer perceptions relative to product features, a network of psychological constructs is utilized. Structural equation modeling (SEM) is used as the parameter estimation and hypothesis testing technique, making the framework falsifiable in nature. To demonstrate effectiveness of the framework, a case study of sensor-integrated shoes is presented, where two models are compared—one survey-only and one using the cyber-empathic framework model. Covariance-based SEM (CB-SEM) is used to estimate the parameters and the fit indices. It is shown that the cyber-empathic framework results in improved fit over a survey-only SEM. This work demonstrates how low-level user–product interaction data can be used to understand and model user perceptions in a way that can support falsifiable design inference.

Commentary by Dr. Valentin Fuster
J. Mech. Des. 2017;139(9):091402-091402-12. doi:10.1115/1.4037253.

The primary motivation in this paper is to understand decision-making in design under competition from both prescriptive and descriptive perspectives. Engineering design is often carried out under competition from other designers or firms, where each competitor invests effort with the hope of getting a contract, attracting customers, or winning a prize. One such scenario of design under competition is crowdsourcing where designers compete for monetary prizes. Within existing literature, such competitive scenarios have been studied using models from contest theory, which are based on assumptions of rationality and equilibrium. Although these models are general enough for different types of contests, they do not address the unique characteristics of design decision-making, e.g., strategies related to the design process, the sequential nature of design decisions, the evolution of strategies, and heterogeneity among designers. In this paper, we address these gaps by developing an analytical model for design under competition, and using it in conjunction with a behavioral experiment to gain insights about how individuals actually make decisions in such scenarios. The contributions of the paper are two-fold. First, a game-theoretic model is presented for sequential design decisions considering the decisions made by other players. Second, an approach for synergistic integration of analytical models with data from behavioral experiments is presented. The proposed approach provides insights such as shift in participants' strategies from exploration to exploitation as they acquire more information, and how they develop beliefs about the quality of their opponents' solutions.

Commentary by Dr. Valentin Fuster

### Research Papers: Design of Mechanisms and Robotic Systems

J. Mech. Des. 2017;139(9):092301-092301-9. doi:10.1115/1.4037245.

Passive dynamic systems have the advantage over conventional robotic systems that they do not require actuators and control. Brachiating, in particular, involves the swinging motion of an animal from one branch to the next. Such systems are usually designed manually by human designers and often are bio-inspired. However, a computational design approach has the capability to search vast design spaces and find solutions that go beyond those possible by manual design. This paper addresses the automated design of passive dynamic systems by introducing a graph grammar-based method that integrates dynamic simulation to evaluate and evolve configurations. In particular, the method is shown to find different, new solutions to the problem of the design of two-dimensional passive, dynamic, continuous contact, brachiating robots. The presented graph grammar rules preserve symmetry among robot topologies. A separation of parametric multi-objective optimization and topologic synthesis is proposed, considering four objectives: number of successful swings, deviation from cyclic motion, required space, and number of bodies. The results show that multiple solutions with varying complexity are found that trade-off cyclic motion and the space required. Compared to research on automated design synthesis of actuated and controlled robotic systems, this paper contributes a new method for passive dynamic systems that integrates dynamic simulation.

Commentary by Dr. Valentin Fuster

### Research Papers: Design of Direct Contact Systems

J. Mech. Des. 2017;139(9):093301-093301-9. doi:10.1115/1.4037345.

The teeth of ordinary spur and helical gears are generated by a (virtual) rack provided with planar generating surfaces. The resulting tooth surface shapes are a circle-involute cylinder in the case of spur gears, and a circle-involute helicoid for helical gears. Advantages associated with involute geometry are well known. Beveloid gears are often regarded as a generalization of involute cylindrical gears involving one additional degree-of-freedom, in that the midplane of their (virtual) generating rack is inclined with respect to the axis of the gear being generated. A peculiarity of their generation process is that the motion of the generating planar surface, seen from the fixed space, is a rectilinear translation (while the gear blank is rotated about a fixed axis); the component of such translation that is orthogonal to the generating plane is the one that ultimately dictates the shape of the generated, envelope surface. Starting from this basic fact, we set out to revisit this type of generation-by-envelope process and to profitably use it to explore peculiar design layouts, in particular for the case of motion transmission between skew axes (and intersecting axes as a special case). Analytical derivations demonstrate the possibility of involute helicoid profiles (beveloids) transmitting motion between skew axes through line contact and, perhaps more importantly, they lead to the derivation of designs featuring insensitivity of the transmission ratio to all misalignments within relatively large limits. The theoretical developments are confirmed by various numerical examples.

Commentary by Dr. Valentin Fuster
J. Mech. Des. 2017;139(9):093302-093302-12. doi:10.1115/1.4036997.

Noise, vibration, and harshness performances are always concerns in design of an automotive belt drive system. The design problem of the automotive belt drive system requires the minimum transverse vibration of each belt span and minimum rotational vibrations of each pulley and the tensioner arm at the same time, with constraints on tension fluctuations in each belt span. The autotensioner is a key component to maintain belt tensions, avoid belt slip, and absorb vibrations in the automotive belt drive system. In this work, a dynamic adaptive particle swarm optimization and genetic algorithm (DAPSO-GA) is proposed to find an optimum design of an autotensioner to solve this design problem and achieve design targets. A dynamic adaptive inertia factor is introduced in the basic particle swarm optimization (PSO) algorithm to balance the convergence rate and global optimum search ability by adaptively adjusting the search velocity during the search process. genetic algorithm (GA)-related operators including a selection operator with time-varying selection probability, crossover operator, and n-point random mutation operator are incorporated in the PSO algorithm to further exploit optimal solutions generated by the PSO algorithm. These operators are used to diversify the swarm and prevent premature convergence. The objective function is established using a weighted-sum method, and the penalty function method is used to deal with constraints. Optimization on an example automotive belt drive system shows that the system vibration is greatly improved after optimization compared with that of its original design.

Commentary by Dr. Valentin Fuster

### Technical Brief

J. Mech. Des. 2017;139(9):094501-094501-5. doi:10.1115/1.4037110.

V-polyhedra is a Kokotsakis-type flat foldable rigid origami with increasing application in the engineering field. Currently, researches on origami mainly focused on foldability and mobility. In order to apply V-polyhedra in practical engineering, the analysis of kinematic characteristics is in need. This paper presents a displacement analysis methodology for the generic point belonging to any surfaces of foldable V-polyhedra. The rigid foldability of four-faced V-polyhedra and that of nine-faced V-polyhedra were discussed first. Then, the corresponding mathematical models are established with the rotating vector model constructed by dual quaternions. Finally, the correctness of the proposed method is verified through application of a symmetric pair of nine-faced V-polyhedra.

Commentary by Dr. Valentin Fuster
J. Mech. Des. 2017;139(9):094502-094502-6. doi:10.1115/1.4037184.

In this paper, we generalize Miura origami and propose a method for analyzing a generalized Miura origami structure. Morphological properties of the generalized Miura origami element during the deploy motion are analyzed using the proposed method, which mainly utilizes the principle of spherical trigonometry and is verified in the folding limit state. The longitudinal length, horizontal length, and height of the generalized Miura origami element are defined and obtained using the proposed method. Results show the relationship between the range of deployment and the element parameters as well as the changes of the folding plane angles in the deployment process. During the deploy motion, both the longitudinal and horizontal length increased while the height decreased. However, the change speed of horizontal length decreased, whereas those of longitudinal length and height initially increased and then decreased. The increment of the folding element angle difference $Δα$ reduced folding range and put off the severe change time of longitudinal length and height. The length parameters $Ka$, $Kb$, and $Kab$ had slight effects on the results, but their changes did not alter the change trends. These results are useful to the design of fold structure and analysis of errors in standard Miura-ori structures.

Commentary by Dr. Valentin Fuster
J. Mech. Des. 2017;139(9):094503-094503-5. doi:10.1115/1.4037109.

The early conceptual design phase often focuses on functional requirements, with limited consideration of the manufacturing processes needed to turn design engineers' conceptual models into physical products. Increasingly, design and manufacturing engineers no longer work in physical proximity, which has slowed the feedback cycle and increased product lead-time. Design for manufacturability (DFM) techniques have been adopted to overcome this problem and are critical for faster convergence to a manufacturable design. DFM tools give feedback in textual and graphical modalities. However, since information modality may affect interpretability, empirical evidence is needed to understand how manufacturability feedback modalities affect design engineers' work. A user study evaluated how novice design engineers' design performance, workload, confidence, and feedback usability were affected by textual, two-dimensional (2D), and three-dimensional (3D) feedback modalities. Results showed that graphical feedback significantly improved performance and reduced mental workload compared to textual and no feedback. Differences between 3D and 2D feedback were mixed. Three-dimensional was generally better on average, but not significantly so. However, the usability of 3D was significantly higher than 2D. Conversely, providing feedback in textual modality was often no better than not providing feedback. The study will benefit manufacturing industries by demonstrating that early 3D manufacturability feedback improves novice design engineers' performance with less mental workload and streamlines the design process resulting in cost-saving and reduction of product lead-time.

Commentary by Dr. Valentin Fuster