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### Research Papers: Design Theory and Methodology

J. Mech. Des. 2018;140(6):061101-061101-9. doi:10.1115/1.4039448.

During the development planning of a new product, designers and entrepreneurs rely on the prediction of product performance to make business investment and design strategy decisions. Moore's law and the logistic S-curve model help make such predictions but suffer several drawbacks. In this paper, Lotka–Volterra equations are used to describe the interaction between a product (system technology) and the components and elements (component technologies) that are combined to form the product. The equations are simplified by a relationship table and maturation evaluation in a two-step process. The performance data of the system and its components over time are modeled by simplified Lotka–Volterra equations. The methods developed here allow designers, entrepreneurs, and policy makers to predict the performances of a product and its components quantitatively using the simplified Lotka–Volterra equations. The methods also shed light on the extent of performance impact from a specific module (component technology) on a product (system technology), which is valuable for identifying the key features of a product and for making outsourcing decisions. Smartphones are used as an example to demonstrate the two-step simplification process. The Lotka–Volterra model of technology evolution is validated by a case study of passenger airplanes and turbofan aero-engines. The case study shows that the data fitting and predictive performances of Lotka–Volterra equations exceed those of extant models.

Commentary by Dr. Valentin Fuster
J. Mech. Des. 2018;140(6):061102-061102-12. doi:10.1115/1.4039340.

Prototyping is an essential part of product development in companies, and yet it is one of the least explored areas of design practice. There are limited ethnographic studies conducted within companies, specifically around the topic of prototyping. This is an empirical and industrial-based study using inductive ethnographic observations to further our understanding of the various roles prototypes play in organizations. This research observed the entire product development cycle within three companies in the fields of consumer electronics (CE), footwear (FW), and medical devices (MD). Our guiding research questions are: What is a prototype? What are the roles of prototypes across these three companies? Through our analysis, we uncovered that prototypes are tools for enhanced communication, increased learning, and informed decision-making. Specifically, we further refine these categories to display the types of communication, learning, and decision-making that occur. These insights are significant because they validate many prior prototyping theories and claims, while also adding new perspectives through further exploiting each role. Finally, we provide newly modified definitions of a prototype and prototyping based on this empirical work, which we hope expands designers' mental models for the terms.

Commentary by Dr. Valentin Fuster

### Research Papers: Design Automation

J. Mech. Des. 2018;140(6):061401-061401-11. doi:10.1115/1.4039009.

We present an effective optimization strategy that is capable of discovering high-quality cost-optimal solution for two-dimensional (2D) path network layouts (i.e., groups of obstacle-avoiding Euclidean Steiner trees) that, among other applications, can serve as templates for complete ascent assembly structures (CAA-structures). The main innovative aspect of our approach is that our aim is not restricted to simply synthesizing optimal assembly designs with regard to a given goal, but we also strive to discover the best tradeoffs between geometric and domain-dependent optimal designs. As such, the proposed approach is centered on a variably constrained multi-objective formulation of the optimal design task and on an efficient coevolutionary solver. The results we obtained on both artificial problems and realistic design scenarios based on an industrial test case empirically support the value of our contribution to the fields of optimal obstacle-avoiding path generation in particular and design automation in general.

Commentary by Dr. Valentin Fuster
J. Mech. Des. 2018;140(6):061402-061402-12. doi:10.1115/1.4039637.

Linkage mechanisms are typically designed to generate a specific functional relationship or path. Because the uncertain dimensions and joint clearances severely affect the output motion accuracy, designers urgently need a reliability-based design approach with high confidence and efficiency. However, the traditional kinematic reliability synthesis, which focuses on several discrete time points, cannot satisfy the accuracy requirement over a continuous time interval. Accordingly, to ensure high accuracy over a time period, this study presents a reliability synthesis approach that considers the time-dependency effect of motion error. The exact statistical characteristics of clearances and dimensions may be unavailable because of the limited sample information in practical engineering. Thus, by qualifying the uncertainties as unknown but bounded variables, the time-dependent reliability index is assessed based on a combination of the nonprobabilistic interval process and first-passage theories. Two engineering examples are presented to demonstrate the validity and applicability of the developed methodology.

Commentary by Dr. Valentin Fuster
J. Mech. Des. 2018;140(6):061403-061403-11. doi:10.1115/1.4039689.

Various stochastic validation metrics have been developed for validating models, among which area metric is frequently used in many practical problems. However, the existing area metric does not consider experimental epistemic uncertainty caused by lack of sufficient physical observations. Therefore, it cannot provide a confidence level associated with the amount of experimental data, which is a desired characteristic of validation metric. In this paper, the concept of area metric is extended to a new metric, namely interval area metric, for single-site model validation with limited experimental data. The kernel of the proposed metric is defining two boundary distribution functions based on Dvoretzky–Kiefer–Wolfowitz inequality, so as to provide an interval at a given confidence level, which covers the true cumulative distribution function (CDF) of physical observations. Based on this interval area metric, the validity of a model can be quantitatively measured with the specific confidence level in association with consideration of the lack of experiment information. The new metric is examined and compared with the existing metrics through numerical case studies to demonstrate its validity and discover its properties. Furthermore, an engineering example is provided to illustrate the effectiveness of the proposed metric in practical satellite structure engineering application.

Commentary by Dr. Valentin Fuster

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

J. Mech. Des. 2018;140(6):062301-062301-9. doi:10.1115/1.4039449.

This paper addresses the assembly strategy capable of deriving a family of overconstrained mechanisms systematically. The modular approach is proposed. It treats the topological synthesis of overconstrained mechanisms as a systematical derivation rather than a random search. The result indicates that a family of overconstrained mechanisms can be constructed by combining legitimate modules. A spatial four-bar linkage containing two revolute joints (R) and two prismatic joints (P) is selected as the source-module for the purpose of demonstration. All mechanisms discovered in this paper were modeled and animated with computer-aided design (CAD) software and their mobility were validated with input–output equations as well as computer simulations. The assembly strategy can serve as a self-contained library of overconstrained mechanisms.

Commentary by Dr. Valentin Fuster
J. Mech. Des. 2018;140(6):062302-062302-11. doi:10.1115/1.4039388.

The umbrella linkage is one of the most classical deployable mechanisms. This paper concentrates on topological structural design of a family of umbrella-shaped deployable mechanisms based on new two-layer and two-loop spatial linkage units. First, deployable units are developed systematically from two-layer and two-loop linkage with four revolute pair (4R) coupling chains. Then, mobile connection modes of the deployable units are established based on the conditions of one degree-of-freedom (DOF) and structural symmetry. Finally, umbrella-shaped deployable mechanisms are constructed based on the developed deployable units and the established mobile connection modes. Like umbrellas, the designed deployable mechanisms can be actuated in a simple and reliable way, and those mechanisms have good potential applications in the fields of architecture, manufacturing, space exploration, and recreation.

Commentary by Dr. Valentin Fuster
J. Mech. Des. 2018;140(6):062303-062303-10. doi:10.1115/1.4039852.

Lamina emergent compliant mechanisms (including origami-adapted compliant mechanisms) are mechanical devices that can be fabricated from a planar material (a lamina) and have motion that emerges out of the fabrication plane. Lamina emergent compliant mechanisms often exhibit undesirable parasitic motions due to the planar fabrication constraint. This work introduces a type of lamina emergent torsion (LET) joint that reduces parasitic motions of lamina emergent mechanisms, and presents equations for modeling parasitic motion of LET joints. The membrane joint also makes possible one-way joints that can ensure origami-based mechanisms emerge from their flat state (a change point) into the desired configuration. Membrane-enhanced LET (M-LET) joints, including one-way surrogate folds, are described here and show promise for use in a wide range of compliant mechanisms and origami-based compliant mechanisms. They are demonstrated as individual joints and in mechanisms such as a kaleidocycle (a 6R Bricard linkage), degree-4 origami vertices (spherical mechanisms), and waterbomb base mechanisms (an 8R multi-degrees-of-freedom origami-based mechanism).

Commentary by Dr. Valentin Fuster

### Research Papers: Design of Direct Contact Systems

J. Mech. Des. 2018;140(6):063301-063301-12. doi:10.1115/1.4039769.

All of the cutting edges on an hourglass worm gear hob have different shapes and spiral angles. If the spiral angles are small, straight flutes are typically adopted. However, for hobs with multiple threads, the absolute values of the negative rake angles on one side of the cutting teeth will greatly affect the cutting performance of the hob if straight flutes are still used. Therefore, spiral flutes are typically adopted to solve this problem. However, no method to determine the spiral flute of an hourglass worm gear hob has been proposed until now. Based on the curved surface generating theory and the hourglass worm forming principle, a method for generating the spiral flute of the planar double enveloping hourglass worm gear hob is proposed in this paper. A mathematical model was built to generate the spiral flute. The rake angles of all cutting teeth of the hob are calculated. The laws of the rake angles of the cutting teeth for four hobs with different threads from one to four threads were analyzed when straight flutes and spiral flutes are adopted. The laws between the value of the negative rake angles of the hob with four threads and the transmission ratio were studied. The most appropriate transmission ratio for generating the spiral flute was obtained. The machining of the spiral flutes was simulated using a virtual manufacturing system, and the results verify the correctness of the method.

Commentary by Dr. Valentin Fuster

### Research Papers: Design of Energy, Fluid, and Power Handing Systems

J. Mech. Des. 2018;140(6):063401-063401-13. doi:10.1115/1.4039451.

Most of the prior design studies on compound split hybrids focused on the selection of optimal configurations through evaluating their performance within the physical design space, i.e., powertrain configurations. However, the authors revealed that using the compound lever for the performance analysis dramatically reduces the design space as redundant configurations exist for a single compound lever design, resulting in computational load reduction. Nevertheless, using the compound lever results in the loss of information required to realize the given configurations as these two configurations are represented by two different sets of variables. The powertrain configuration is defined by two physical design variables, i.e., gear ratios of the two planetary gears. However, the compound lever design is defined by two nonphysical design variables, $α$ and $β$, which are the vertical bar lengths between the output node (vehicle) and the two motor/generators' (MG) nodes. Thus, if the compound lever is used as a design tool, the selected designs should be converted into powertrain configurations. This paper introduces an automatic methodology to generate feasible powertrain configurations for any given compound lever using generic conversion equations that express the relationship between the nonphysical design variables, α and β, and the physical design variables, gear ratios. Conversion maps relating the 252 powertrain configurations to the compound lever design space were generated, and the results confirmed that the compound lever removes the redundancy existing in the physical design space.

Topics: Levers , Design
Commentary by Dr. Valentin Fuster

### Technical Brief

J. Mech. Des. 2018;140(6):064501-064501-6. doi:10.1115/1.4039588.

This paper studies the influence of macrogeometry and material type of spur gears on their torque capacity, reliability, and acquisition cost. The developed model indicates how costly it is to enhance the torque capacity or the reliability of gears. The results are in agreement with the catalog prices of a manufacturer in a wide size range and different modules. The model provides a simple cost estimation tool for multi-objective gear design and optimization.

Commentary by Dr. Valentin Fuster