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### Editorial

J. Mech. Des. 2017;140(1):010201-010201-2. doi:10.1115/1.4038545.
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Commentary by Dr. Valentin Fuster

### Research Papers: Design Theory and Methodology

J. Mech. Des. 2017;140(1):011101-011101-11. doi:10.1115/1.4038070.

When selecting ideas or trying to find inspiration, designers often must sift through hundreds or thousands of ideas. This paper provides an algorithm to rank design ideas such that the ranked list simultaneously maximizes the quality and diversity of recommended designs. To do so, we first define and compare two diversity measures using determinantal point processes (DPP) and additive submodular functions. We show that DPPs are more suitable for items expressed as text and that a greedy algorithm diversifies rankings with both theoretical guarantees and empirical performance on what is otherwise an NP-Hard problem. To produce such rankings, this paper contributes a novel way to extend quality and diversity metrics from sets to permutations of ranked lists. These rank metrics open up the use of multi-objective optimization to describe trade-offs between diversity and quality in ranked lists. We use such trade-off fronts to help designers select rankings using indifference curves. However, we also show that rankings on trade-off front share a number of top-ranked items; this means reviewing items (for a given depth like the top ten) from across the entire diversity-to-quality front incurs only a marginal increase in the number of designs considered. While the proposed techniques are general purpose enough to be used across domains, we demonstrate concrete performance on selecting items in an online design community (OpenIDEO), where our approach reduces the time required to review diverse, high-quality ideas from around 25 h to 90 min. This makes evaluation of crowd-generated ideas tractable for a single designer. Our code is publicly accessible for further research.

Commentary by Dr. Valentin Fuster
J. Mech. Des. 2017;140(1):011102-011102-13. doi:10.1115/1.4038252.

The gap between consumers saying that they want and selecting sustainable products can be addressed through product design. Our previous research proposed a method for creating visible product features that trigger pro-environmental behavior in consumers, termed sustainability triggers (STs). The study below designed two experiments to mimic real-world decision scenarios and demonstrated that exposure to these STs caused pro-environmental behavior in two test versus control experiments. The experiments used both realistic prototypes and images of toasters. In experiment 1, a qualitative preference-elicitation method demonstrated that exposure to STs increased thoughts of sustainability—related decision criteria. In experiment 2, subjects' prioritization of “hidden” sustainability-related attributes, shipping method and energy usage, was higher if exposed to the STs. This was indicated by choice, information search, importance rating, and eye tracking. Thus, the novel design method to create product STs is demonstrated effective in the test case and has the potential to broadly benefit the success of sustainable products in the market.

Commentary by Dr. Valentin Fuster

### Research Papers: Design Automation

J. Mech. Des. 2017;140(1):011401-011401-14. doi:10.1115/1.4038073.

This paper concerns the experimental validation of two surrogate models through a benchmark study involving two different variable shape mould prototype systems. The surrogate models in question are different methods based on kriging and proper orthogonal decomposition (POD), which were developed in previous work. Measurement data used in the benchmark study are obtained using digital image correlation (DIC). For determining the variable shape mould configurations used for the training, and test sets used in the study, sampling is carried out using a novel constrained nested orthogonal-maximin Latin hypercube approach. This sampling method allows for generating a space filling and high-quality sample plan that respects mechanical constraints of the variable shape mould systems. Through the benchmark study, it is found that mechanical freeplay in the modeled system is severely detrimental to the performance of the studied surrogate models. By comparing surrogate model performance for the two variable shape mould systems, and through a numerical study involving simple finite element models, the underlying cause of this effect is explained. It is concluded that for a variable shape mould prototype system with a small degree of mechanical freeplay, the benchmarked surrogate models perform very well.

Commentary by Dr. Valentin Fuster
J. Mech. Des. 2017;140(1):011402-011402-11. doi:10.1115/1.4038332.

A Jacobian-based topology optimization method is recently proposed for compliant parallel mechanisms (CPMs), in which the CPMs' Jacobian matrix and characteristic stiffness are optimized simultaneously to achieve kinematic and stiffness requirement, respectively. Lately, it is found that the characteristic stiffness fails to ensure a valid topology result in some particular cases. To solve this problem, an improved stiffness evaluation based on the definition of stiffness is adopted in this paper. This new stiffness evaluation is verified and compared with the characteristic stiffness by using several design examples. In addition, several typical benchmark problems (e.g., displacement inverter, amplifier, and redirector) are solved by using the Jacobian-based topology optimization method to show its general applicability.

Commentary by Dr. Valentin Fuster
J. Mech. Des. 2017;140(1):011403-011403-9. doi:10.1115/1.4038298.

In calibrating model parameters, it is important to include the model discrepancy term in order to capture missing physics in simulation, which can result from numerical, measurement, and modeling errors. Ignoring the discrepancy may lead to biased calibration parameters and predictions, even with an increasing number of observations. In this paper, a simple yet efficient calibration method is proposed based on sensitivity information when the simulation model has a model error and/or numerical error but only a small number of observations are available. The sensitivity-based calibration method captures the trend of observation data by matching the slope of simulation predictions and observations at different designs and then utilizing a constant value to compensate for the model discrepancy. The sensitivity-based calibration is compared with the conventional least squares calibration method and Bayesian calibration method in terms of parameter estimation and model prediction accuracies. A cantilever beam example, as well as a honeycomb tube crush example, is used to illustrate the calibration process of these three methods. It turned out that the sensitivity-based method has a similar performance with the Bayesian calibration method and performs much better than the conventional method in parameter estimation and prediction accuracy.

Topics: Calibration , Errors
Commentary by Dr. Valentin Fuster
J. Mech. Des. 2017;140(1):011404-011404-10. doi:10.1115/1.4038304.

This paper is devoted to the study of a nonlinear energy sink (NES) intended to attenuate vibration induced in a harmonically forced linear oscillator (LO) and working under the principle of targeted energy transfer (TET). The purpose motivated by practical considerations is to establish a design criterion that first ensures that the NES absorber is activated and second provides the optimally tuned nonlinear stiffness for efficient TET under a given primary system specification. Then a novel NES design yielding cubic stiffness without a linear part is exploited. To this end, two conical springs are specially sized to provide the nonlinearity. To eliminate the linear stiffness, the concept of a negative stiffness mechanism is implemented by two cylindrical compression springs. A small-sized NES system is then developed. To validate the concept, a sensitivity analysis is performed with respect to the adjustment differences of the springs and an experiment on the whole system embedded on an electrodynamic shaker is studied. The results show that this type of NES can not only output the expected nonlinear characteristics, but can also be tuned to work robustly over a range of excitation, thus making it practical for the application of passive vibration control.

Commentary by Dr. Valentin Fuster

### Research Papers: Design for Manufacture and the Life Cycle

J. Mech. Des. 2017;140(1):011701-011701-12. doi:10.1115/1.4038297.

This paper presents a design methodology and experimental assessment of variable-geometry dies that enable the extrusion of plastic parts with a nonconstant cross section. These shape-changing dies can produce complex plastic components at higher manufacturing speeds and with lower tooling costs than injection molding. Planar, rigid-body, shape-changing mechanism synthesis techniques are used to create the links that comprise the variable-geometry die exit orifice. Mechanical design guidelines for production-worthy dies are proposed. Several dies were designed and constructed to provide significant changes in the cross-sectional shape and area of extruded parts. Experiments were conducted in a production environment. An analysis of the repeatability of the cross-sectional profiles along the length of the part is presented.

Commentary by Dr. Valentin Fuster

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

J. Mech. Des. 2017;140(1):012301-012301-9. doi:10.1115/1.4037629.

This paper introduces a homokinetic coupling, a constant velocity universal joint (CV joint), which is fully compliant and potentially monolithic. The proposed compliant design can accommodate high misalignment angles between the input and the output rotational axes. Additional kinematic constraints are applied to well-known Double Hooke's universal joint, to guarantee a one-to-one constant velocity rotation transmission for all different misalignment angles. The influence of the extra constraints on degrees-of-freedom (DOF) of the mechanism is studied using screw theory. Furthermore, it was shown that the mechanism is yet a 1DOF linkage for rotation transmission and a 2DOF rotational joint as all universal joints. The kinematics of the mechanism is studied, and constant velocity conditions are identified. The pseudo-rigid-body model (PRBM) of the new angled arrangement of the Double Hooke's universal joint is created, and the input–output torque relationship is then studied. The different possible compliant embodiments based on the PRBM model were discussed and illustrated. Moreover, one of the proposed compliant counterparts is dimensioned as a power transmission coupling for a high misalignment angle, up to $45 deg$. Further, a prototype was manufactured for the experimental evaluation, and it is shown that the results are consistent with the PRBM and the finite element model.

Commentary by Dr. Valentin Fuster
J. Mech. Des. 2017;140(1):012302-012302-12. doi:10.1115/1.4038072.

Planetary gear trains (PGTs) are used in automatic transmission to achieve any desired speed ratios. At present, the study on the relationship between speed ratio and topology is not significant. Therefore, this paper focuses on studying the speed ratio based on topology. For this purpose, the graph theory is used to represent PGTs, and a concept of the speed topological graph is introduced. Based on the proposed graph representation, the relationship between the speed ratio and topology is studied. Three types of topological graphs are analyzed, which includes path, tree, and unicyclic graph, and necessary results are presented. The results reveal the relationship between speed ratio and topology, which helps in understanding the PGTs further. The result can help engineers to arrange the clutches and brakes to achieve desired speed ratio during the conceptual design phase, which can greatly improve the design efficiency of PGTs. The presented kinematics analysis method can be extended to analyze multi-input and multi-output planetary transmission.

Commentary by Dr. Valentin Fuster
J. Mech. Des. 2017;140(1):012303-012303-10. doi:10.1115/1.4038303.

Planetary gear trains (PGTs) are widely used in machinery to transmit angular velocity ratios or torque ratios. The graph theory has been proved to be an effective tool to synthesize and analyze PGTs. This paper aims to propose a new graph model, which has some merits relative to the existing ones, to represent the structure of PGTs. First, the rotation graph and canonical rotation graph of PGTs are defined. Then, by considering the edge levels in the rotation graph, the displacement graph and canonical displacement graph are defined. Each displacement graph corresponds to a PGT having the specified functional characteristics. The synthesis of five-link one degree-of-freedom (1DOF) PGTs is used as an example to interpret and demonstrate the applicability of the present graph representation in the synthesis process. The present graph representation can completely avoid the generation of pseudo-isomorphic graphs and can be used in the computer-aided synthesis and analysis of PGTs.

Commentary by Dr. Valentin Fuster

### Technical Brief

J. Mech. Des. 2017;140(1):014501-014501-4. doi:10.1115/1.4038296.

The paper deals with the problem of choosing the material and the cross section of a beam subjected to bending under structural safety, elastic stability, and available room constraints. An extension of the theory proposed by Ashby is presented. The Pareto-optimal set for the multi-objective problem of stiffness maximization and mass minimization under elastic stability, structural safety, and available room constraints for a beam under bending is derived analytically. The Pareto-optimal set is compared with the solution of the Ashby's selection method.

Topics: Design , Shapes , Stiffness
Commentary by Dr. Valentin Fuster

### Errata

J. Mech. Des. 2017;140(1):017001-017001-1. doi:10.1115/1.4038265.