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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

### 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