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Designers are continuously challenged by complexity, as well as by the excessive instantiation and execution times of models, particularly in the context of integrated product and materials design. In order to manage these challenges, a systematic strategy for evaluating and selecting models is presented in this paper. The systematic strategy is based on value-of-information for design decision making. It consists of a (i) process performance indicator (PPI) to quantify the impact of model refinement from a decision-centric perspective and (ii) a method involving model evaluation. Using this method, a least complex but valid model is evaluated, and, only if necessary, gradually refined it until the most appropriate one is selected. The systematic approach is particularly well suited for integrated product and materials design, and all other scenarios where the perfect knowledge of the true system behavior and bounds of error are not available throughout the design space. The proposed strategy is applied to the design of photonic crystal waveguides for use in a next-generation optoelectronic communication system. In this paper, it is shown that the systematic strategy based on the PPI is useful for evaluating and selecting models particularly when accuracy of the prediction or the associated error bounds are not known. [DOI: 10.1115/1.4002751] Keywords: value-of-information, process design, complexity management, model selection, optoelectronic communication, photonic crystal waveguides

This paper presents a metamorphic kinematic pair extracted from origami folds in the context of mechanisms, its evolved metamorphic chain, and the novel metamorphic parallel mechanism. This paper starts from the generic issues of topological representation for metamorphic mechanism, leading to unified elementary matrix operation for presentation of topological variation. Phase matrix and augmented adjacency matrix are developed to present the topological state and geometry of metamorphic mechanism in an evolutionary, process. The metamorphic kinematic pair has the ability of changing mobility to generate different motion patterns based on mobility change correlated with the link annex induced topological phase change. This paper then investigates topological variation of the metamorphic chain and the topological subphases are enumerated in accordance with structure evolution. Using the metamorphic chain as chain-legs, a multiloop metamorphic mechanism with ability of performing phase change and orientation switch is constructed. The disposition of constraints and geometric constraints induced bifurcated motion are analyzed based on screw theory. The topological variation of the metamorphic parallel mechanism is addressed and the foldability is verified by physical device. [DOI: 10.1115/1.4002691]

This paper presents the design and realization of a multimobile robot system joint locomotion (JL)-2, which features not only a docking and 3D posture-adjusting capability between three robots but also a multifunctional docking gripper. By combining a parallel mechanism and a cam gripper together, this paper develops a docking manipulator, which endows each robot with a simple but forceful grasping capability. Furthermore, the docking manipulator can overcome the possible aligning errors between two robots and interconnect them. A motorized spherical joint will be formed between two docked robots, which will enhance the locomotion flexibility of the whole system. The docking mechanism is discussed in detail, including the docking procedure and analyses of self-aligning ability. A series of experiments not only testify the basic performances of JL-2 but also reveal the limits of current prototype, e.g., the overconstraint connecting pattern, the unbalanced self-aligning performance, etc. [DOI: l0.1115/1.4002719]

In this paper, we report on a multistable linear actuation mechanism articulated with electroactive polymer actuators, widely known as artificial muscles. These actuators, which can operate both in wet and dry media under as small as 1.0 V potential difference, are fundamentally cantilever beams made of two electroactive polymer layers (polypyrrole) and a passive polyvinylidene fluoride substrate in between the electroactive layers. The mechanism considered is kinematically analogous to a four-bar mechanism with revolute-prismatic-revolute-prismatic pairs, converting the bending displacement of a polymer actuator into a rectilinear movement of an output point. The topology of the mechanism resembles that of bistable mechanisms operating under the buckling effect. However, the mechanism proposed in this paper can have many stable positions depending on the input voltage. After demonstrating the feasibility of the actuation concept using kinematic and finite element analyses of the mechanism, experiments were conducted on a real mechanism articulated with a multiple number (2, 4, or 8) of electroactive polymer actuators, which had dimensions of 12 X 2 X O.17 [mm.sup.3]. The numerical and experimental results demonstrate that the angular displacement of the artificial muscles is accurately transformed into a rectilinear motion by the proposed mechanism. The higher the input voltage, the larger the rectilinear displacement. This study suggests that this multistable linear actuation mechanism can be used as a programmable switch and/or a pump in microeleetromechanical systems (MEMS) by adjusting the input voltage and scaling down the mechanism further. [DOI: 10.1115/1.4002661]

This paper presents the use of a mathematical model in updating a decision maker's belief before selecting a product/system concept and demonstrates a procedure to calculate the maximum monetary value of such a model in terms of the expected value of information. Acquiring information about uncertainty and updating belief according to the new information is an important step in concept selection. However, obtaining additional information can be considered beneficial only if the acquisition cost is less than the benefit. In this paper, a mathematical model is used as an information source that predicts outcomes of an uncertainty. The prediction, however, is imperfect information because the model is constructed based on simplifying assumptions. Thus, the expected value of imperfect information needs to be calculated in order to evaluate the tradeoff between the accuracy and the cost of model prediction (information). The construction and analysis of a mathematical model, the calculation of the expected value of information (model prediction) and updating the belief based on the model prediction are illustrated using a concept selection for a public project. [DOI: 10.1115/1.4001974] Keywords: concept selection, updating belief mathematical model, expected value of information

The proper orthogonal decomposition method has been employed to extract the important field signatures of random field observed in an engineering product or process. Our preliminary study found that the coefficients of the signatures are statistically uncorrelated but may be dependent. To this point, the statistical dependence of the coefficients has been ignored in the random field characterization for probability analysis and design. This paper thus proposes an effective random field characterization method that can account for the statistical dependence among the coefficients for probability analysis and design. The proposed approach has two technical contributions. The first contribution is the development of a natural approximation scheme of random field while preserving prescribed approximation accuracy. The coefficients of the signatures can be modeled as random field variables, and their statistical properties are identified using the chi-square goodness-of-fit test. Then, as the paper's second technical contribution, the Rosenblatt transformation is employed to transform the statistically dependent random field variables into statistically independent random field variables. The number of the transformation sequences exponentially increases as the number of random field variables becomes large. It was found that improper selection of a transformation sequence among many may introduce high nonlinearity into system responses, which may result in inaccuracy in probability analysis and design. Hence, this paper proposes a novel procedure of determining an optimal sequence of the Rosenblatt transformation that introduces the least degree of nonlinearity into the system response. The proposed random field characterization can be integrated with any advanced probability analysis method, such as the eigenvector dimension reduction method or polynomial chaos expansion method. Three structural examples, including a microelectromechanical system bistable mechanism, are used to demonstrate the effectiveness of the proposed approach. The results show that the statistical dependence in the random field characterization cannot be neglected during probability analysis and design. Moreover, it is shown that the proposed random field approach is very accurate and efficient. [DOI: 10.1115/1.4002293] Keywords: random field, proper orthogonal decomposition, probability analysis and design, eigenvector dimension reduction

Predictive modeling can be a valuable tool for systems designers, allowing them to capture and reuse knowledge from a set of observed dam related to their system. An important challenge associated with predictive modeling is that of describing the domain over which model predictions are valid. This is necessary to avoid extrapolating beyond the original data, particularly when designers use predictive models in concert with optimizers or other computational routines that search a model's input space automatically. The general problem of domain description is complicated by the characteristics of observational data sets, which can contain small numbers of samples, can have nonlinear associations among the variables, can be nonconvex, and can occur in disjoint clusters. Support vector machine (SVM) techniques, developed originally in the machine learning community, offer a solution to this problem. This paper is a description of a kernel-based SVM approach that yields a formal mathematical description of the valid input domain of a predictive model. The approach also provides for cluster analysis, which can lead to improved model accuracy through the decomposition of a data set into multiple subsets that designers can model independently. This paper includes a mathematical presentation of kernel-based SVM methods, an explanation of the procedure for applying the approach to predictive modeling problems, and illustrative examples for applying and using the approach in systems design. [DOI: 10.1115/1.4002151]

This paper presents a method for assessing the quality of a progressive design process by measuring the profitability of the product that the process generates. The proposed approach uses separations, a type of problem decomposition, to model progressive design processes. The subproblems in the separations correspond roughly to phases in the progressive design processes. The proposed method simulates the choices of a bounded rational designer for each subproblem using different search algorithms. This paper presents a simple two-variable problem to help describe the approach and then applies the approach to assess motor design processes. Different types and versions of these search processes are considered to determine if the results are robust to the decision-making model. The results indicate that well-designed progressive design processes are the best way to generate profitable product designs. Methods for assessing the quality of engineering design processes can be used to guide improvements to engineering design processes and generate more valuable products. [DOI: 10.1115/1.4001902]

In this paper, a reliability sensitivity analysis methodology for the kinematic accuracy of rack-and-pinion steering linkages (RPSLs) is developed. The direct linearization method is applied to obtain the kinematic accuracy errors of planar linkages due to link-length variations. The RPSL widely used in many types of vehicles is chosen as an example to propose an analytical model for reliability analysis of the kinematic accuracy of planar linkages. Furthermore, reliability sensitivity analysis of planar linkages, which is the main focus of this paper, is used w compute the reliability sensitivity of the kinematic accuracy of steering linkages with respect to the statistical parameters (e.g., mean, standard deviation, or higher moments) of the basic errors of random variables. Finally, the practicality and efficiency of the proposed method are demonstrated by a numerical example. [DOI: 10.1115/1.4001901] Keywords: uncertainty analysis, reliability sensitivity, mechanism, steering linkage, kinematic accuracy

This paper employs control techniques to analyze kinematic relationships via block diagrams for planetary gear systems. The revealed tangent-velocity equations at each contact point of the mechanical gearsets are utilized to plot the block diagrams. Then, the concepts of feedback and feedforward strategies are adopted to illustrate speed-reduction and increasing functions in kinematics with sensitivity analysis. The structural difference between unusual planetary gears and common ones is also explained based on the characteristic equation of feedback strategies for structural constraints in terms of stability conditions. A cam-controlled planetary gear is further illustrated for the constraint and kinematic analysis by using the block diagram technique and characteristic equation, and the computational simulations for the sensitivity and the motion output of this planetary gear are obtained. Through the correspondence between control and kinematics, this paper provides a guide for engineers in various fields to easily understand the function of mechanical design. [DOI: 10.1115/1.4001598] Keywords: signal flow graph, block diagram, planetary gear, epicyclic gearset, cam-controlled, kinematic, feedback, feedforward, characteristic equation, cam-controlled planetary gear

This paper presents a methodology toward designing, analyzing, and optimizing piezoelectric interdigitated microactuators using multiphysics finite element analysis. The models used in this paper were based on a circularly interdigitated design that takes advantage of primarily the d33 electromechanical piezoelectric constant coefficient. Because of the symmetric nature of the devices, a small number of 2D axisymmetric parametric models were developed to characterize the behavior of the diaphragms. The parametric models offered a large range of possible results from a very small number of models. The variations in the design parameters and their effects on deflection were captured using these models. The models also showed that several of the design parameters were naturally coupled. Discrete models were then used to capture the variations in the key design parameters during fabrication. The numerical models correlate well to the maximum deflection of the experimental devices. [DOI: 10.1115/1.4001596] Keywords: microactuators, piezoelectric, modeling

This paper describes an approach to automate the design for sheet metal parts that satisfy multiple objective functions such as material cost and manufacturability. Unlike commercial software tools such as PRO/SHEETMETAL, which aids the user in finalizing and determining the sequence of manufacturing operations for a specified component, our approach starts with spatial constraints in order to create the component geometries and helps the designer design. While there is an infinite set of parts that can feasibly be generated with sheet metal, it is difficult to define this space systematically. To solve this problem, we have created 108 design rules that have been developed for five basic sheet metal operations: slitting, notching, shearing, bending, and punching. A recipe of the operations for a final optimal design is then presented to the manufacturing engineers thus saving them time and cost. The technique revealed in this paper represents candidate solutions as a graph of nodes and arcs where each node is a rectangular patch of sheet metal, and modifications are progressively made to the sheet to maintain the parts manufacturability. This paper also discusses a new topological optimization technique to solve graph-based engineering design problems by decoupling parameters and topology changes. This paper presents topological and parametric tune and prune ([(TP).sup.2]) as a topology optimization method that has been developed specifically for domains representable by a graph grammar schema. The method is stochastic and incorporates distinct phases for modifying the topologies and modifying parameters stored within topologies. Thus far, with abovementioned sheet metal problem, [(TP).sup.2] had proven better than genetic algorithm in terms of the quality, of solutions and time taken to acquire them. [DOI: 10.1115/1.4001409] Keywords: sheet metal, graph, rule-based systems, topology, graph transformation, grammar, optimization, parametric tuning, design automation

Computational tools such as finite element analysis and simulation are widely used in engineering, but they are mostly used for design analysis and validation. If these tools can be integrated for design optimization, it will undoubtedly enhance a manufacturer's competitiveness. Such integration, however, faces three main challenges: (1) high computational expense of simulation, (2) the simulation process being a black-box function, and (3) design problems being high dimensional. In the past two decades, metamodeling has been intensively developed to deal with expensive black-box functions, and has achieved success for low dimensional design problems. But when high dimensionality is also present in design, which is often found in practice, there lacks of a practical method to deal with the so-called high dimensional, expensive, and black-box (HEB) problems. This paper proposes the first metamodel of its kind to tackle the HEB problem. This paper integrates the radial basis function with high dimensional model representation into a new model, RBF-HDMR. The developed RBF-HDMR model offers' an explicit function expression, and can reveal (1) the contribution of each design variable, (2) inherent linearity/nonlinearity with respect to input variables, and (3) correlation relationships among input variables. An accompanying algorithm to construct the RBF-HDMR has also been developed. The model and the algorithm fundamentally change the exponentially growing computation cost to be polynomial. Testing and comparison confirm the efficiency and capability of RBF-HDMR for HEB problems. [DOI: 10.1115/1.4001597] Keywords: response surface, metamodel, large-scale, high dimension, design optimization, simulation-based design

This work focuses on the multi-objective optimization of a compliant-mechanism accelerometer. The design objective is to maximize the sensitivity of the accelerometer in its sensing direction, while minimizing its sensitivity in all other directions. In addition, this work proposes a novel compliant hinge intended to reduce the stress concentration in compliant mechanisms. The paper starts with a brief description of the new compliant hinge, the Lame-shaped hinge, followed by the formulation of the aposteriori multi-objective optimization of the compliant accelerometer. By using the normalized constrained method, an even distribution of the Pareto frontier is found. The paper also provides several optimum solutions on a Pareto plot, as well as the CAD model of the selected solution. [DOI: 10.1115/1.4001002]

Reverse engineering, defined as extracting information about a product from the product itself, is a common industry practice for gaining insight into innovative products. Both the original designer and those reverse engineering the original design can benefit from estimating the time and barrier to reverse engineer a product. This paper presents a set of metrics and parameters that can be used to calculate the barrier to reverse engineer any product, as well as the time required to do so. To the original designer, these numerical representations of the barrier and time can be used to strategically identify and improve product characteristics so as to increase the difficulty and time to reverse engineer them. As the metrics and parameters developed in this paper are quantitative in nature, they can also be used in conjunction with numerical optimization techniques, thereby enabling products to be developed with a maximum reverse engineering barrier and time--at a minimum development cost. On the other hand, these quantitative measures enable competitors who reverse engineer original designs to focus their efforts on products that will result in the greatest return on investment. [DOI: 10.1115/1.4001347] Keywords: reverse engineering, barrier to reverse engineering, product imitation, hardware imitation, time estimation, Ohm's law

Environmental protection legislation, consumer interest in 'green' products, a trend toward corporate responsibility and recognition of the potential profitability of salvaging operations, has resulted in increased interest in product take back. However, the cost effectiveness of product take-back operations is hampered by many factors, including the high cost of disassembly and a widely varying feedstock of dissimilar products. Two types of decisions, must be made, how to carry out the disassembly process in the most efficient. manner to 'mine' the value-added that is still embedded in the product, and then how to best utilize that value-added once it is recovered. This paper presents a method for making those decisions. The concept of a transition matrix is integrated with mixed integer linear programming to determine the extent to which products should be disassembled and simultaneously determine the optimal end-of-life (EOL) strategy for each resultant component or subassembly: The main contribution of this paper is the simultaneous consideration of selective disassembly multiple products, and the value added that remains in each component or subassembly. Shared disassembly operations and capacity limits are considered. An example using two cell phone products illustrates application of the model. The obtained results demonstrate the most economical level of disassembly for each cell phone and the best EOL options for each resultant module. In addition, the cell phone example shows that sharing disassembly operations between different products makes disassembly more cost effective compared with the case in which each product is disassembled separately. [DOI: 10.1115/1.4001207]

This paper proposes a new type of double-crowned helical gear that can be continuously cut on a modern Cartesian-type hypoid generator with two face-hobbing head cutters and circular-arc cutter blades. The gear tooth flank is double crowned with a cycloidal curve in the longitudinal direction and a circular arc in the profile direction. To gauge the sensitivity of the transmission errors and contact patterns resulting from various assembly errors, this paper applies a tooth contact analysis technique and presents several numerical examples that show the benefit of the proposed double-crowned helical gear set. In contrast to a conventional helical involute gear, the tooth bearing and transmission error of the proposed gear set are both controllable and insensitive to gear-set assembly error. [DOI: 10.1115/1.4001214] Keywords: helical gears, face-hobbing method, cycloidal, tooth contact analysis

The purpose of this paper is to propose a pair of external and internal spiral bevel gears with double circular-arc in the nutation drive. Based on the movement of nutation, this paper develops equations of the tooth profiles for the gear set, leading to the mathematical modeling of the spiral bevel gear with a constant helical angle gear alignment curve, enabling the tooth surface to be generated, and permitting the theoretical contacting lines to be produced in light of the meshing function. Simulation and verification are carried out to prove the mathematical equations. Numerical control (NC) simulation of machining the external and internal double circular-arc spiral bevel gears is developed, and the spiral gears were manufactured on a NC milling machine. The prototype of the nutation drive is illustrated in the case study at the end of this paper. [DOI: 10.1115/1.4001003] Keywords: double circular-arc, spiral bevel gear, tooth profile, mathematical modeling, gear machining

This paper proposes a procedure for obtaining the load distribution in a four contact-point slewing bearing considering the effect of the structure's elasticity. The uneven stiffness of the rings and the supporting structures creates a variation with respect to the results obtained with a rigid model. It is necessary to evaluate the effect of the elasticity on the increase in the contact forces in order to be able to design the slewing bearing and the structures involved in the connection. Depending on the shape of the structures, the contact force value obtained on the most loaded rolling element is different. The evaluation of this maximum force at extreme loads is essential to design the structures joined to the bearing rings. The new elastic model presented in this paper is highly nonlinear so iterative loops are needed in order to obtain a satisfactory solution. At the same time a finite element model (FEM) has been created for the global model, having also represented the rolling elements and their contact with the raceways. The results obtained using the FEM have been correlated with the results of the new procedure. [DOI: 10.1115/1.4000834] Keywords: slewing bearing, stiffness, contact angle, FEM

This paper proposes a single-loop system reliability-based design optimization (SRBDO) approach using the recently developed matrix-based system reliability (MSR) method. A single-loop method was employed to eliminate the inner-loop of SRBDO that evaluates probabilistic constraints. The MSR method enables us to compute the system failure probability and its parameter sensitivities efficiently and accurately through convenient matrix calculations. The SRBDO/MSR approach proposed in this paper is applicable to general systems including series, parallel, cut-set, and link-set system events. After a brief overview on SRBDO algorithms and the MSR method, the SRBDO/MSR approach is introduced and demonstrated by three numerical examples. The first example deals with the optimal design of a combustion engine, in which the failure is described as a series system event. In the second example, the cross-sectional areas of the members of a statically indeterminate truss structure are determined for minimum total weight with a constraint on the probability of collapse. In the third example, the redistribution of the loads caused by member failures is considered for the truss system in the second example. The results based on different optimization approaches are compared for further investigation. Monte Carlo simulation is performed in each example to confirm the accuracy of the system failure probability computed by the MSR method. [DOI: 10.1115/1.4000483] Keywords: computer-aided design, design optimization, reliability in design, risk-based design, systems engineering, uncertainty analysis

This study contributes to the development of a systematic methodology for the torque and power-flow analyses of multi-input multi-output (MIMO) epicyclic gear mechanisms (EGMs) with or without reaction link based on the concept of fundamental circuit. The studies on power-flow analysis of EGMs are mostly done in the context of efficiency formulations. In the opinion of the authors, the design process of the MIMO mechanism involves not only finding the configuration that provides the correct velocity ratios but also meeting other kinematic requirements and ensuring that the two inputs have a mutually constructive nature. To demonstrate the analysis, a new motor/generator integrated hybrid transmission design is used to show how the torque acting on each link of an epicyclic gear train (EGT) can be systematically solved in terms of input torque(s) and/or controlled output torque. This paper presents a unification of kinematic and torque balance approaches for the analysis of MIMO epicyclic-type transmission trains. The results presented are meant to deepen the knowledge as to how and why a MIMO epicyclic-type transmission should operate in a certain way under the given conditions. In the process, this paper explores the theoretical bases of operation of the Toyota Hybrid System and the root cause of some confusion in the field of EGTs. [DOI: 10.1115/1.4000644]

Nonlinear springs enhance the performance of many applications including prosthetics, microelectromechanical systems devices, and vibration absorption systems. This paper describes a comprehensive approach to developing compliant elements of prescribed nonlinear stiffness. It presents a generalized methodology for designing a single planar nonlinear spring for a prescribed load-displacement function. The spring's load-range, displacement-range, and nonlinear behavior are matched using this methodology, while also addressing stress, material, stability, and space constraints. Scaling guidelines are included within the optimization to relax the constraints on the solution space. Given the nonlinear nature of the spring designs, this paper further investigates their function in new configurations. Compliant structures with customized elastic properties are constructed by exploiting symmetry and by arranging nonlinear springs in series and/or in parallel. Scaling guidelines are used to meet new design specifications. The guidelines allow adjustment of load-range, displacement-range, material, and the overall footprint while preserving the spring's nonlinear behavior without violating stress constraints. Various examples are provided throughout the paper to demonstrate the implementation and merit of these design approaches. [DOI: 10.1115/1.4000595] Keywords: compliant mechanism, nonlinear spring, spring synthesis, geometric nonlinearity, nonlinear stiffness

Gerotor performance is influenced by sealing properties, area efficiency, contact stress, and outlet pressure. This paper uses the hypotrochoidal curve to generate the gerotor profile, and adopts the curvature difference method to assess the sealing property and predict the stress on the rotor profile. Numerical examples show that this method can successfully estimate and forecast the rotor sealing and the Hertz stress variation. For confirmation, these results are proved by theoretical stress calculations and software simulations. This paper also presents the results of sealing performance, stress variation, area efficiency, and outlet pressure for various geometrical design parameters. These results can serve as a pump performance reference, assisting designers wishing to create a better gerotor pump. Keywords: gerotor, curvature difference, sealing property, contact stress [DOI: 10.1115/1.4000484]

Thermally conductive filled polymers enable the creation of multifunctional structures that offer both anchoring points for the embedded actuators, as well as heat-dissipation functions, in order to facilitate the miniaturization of devices. However, there are two important challenges in creating these structures: (1) sufficient thermal management to prevent failure of the actuator and (2) the ability of the actuator to survive the manufacturing process. This paper describes a systematic approach for design of multifunctional structures with embedded heat-generating components using an in-mold assembly process to address these challenges. For the first challenge, the development of appropriate thermal models is presented along with incorporation of in-mold assembly process constraints in the optimization process. For the second challenge, a simulation of the molding process is presented and demonstrated to enable the determination of processing conditions ensuring survival of the in-mold assembly process for the embedded actuator. Thus, the design methodology described in this paper was utilized to concurrently optimize the choice of material size of the structure, and processing conditions in order to demonstrate the feasibility of creating multifunctional structures from thermally conductive polymers by embedding actuators through an in-mold assembly process. [DOI: 10.1115/1.4000239]

This paper presents a new paradigm of system reliability prediction that enables the use of evolving, insufficient, and subjective data sets. The data sets can be acquired from expert knowledge, customer survey, inspection and testing, and field data throughout a product life-cycle. In order to handle such data sets, this research integrates probability encoding methods to a Bayesian updating mechanism. The integrated tool is called Bayesian Information Toolkit. Subsequently, Bayesian Reliability Toolkit is presented by incorporating reliability analysis to the Bayesian updating mechanism. A generic definition of Bayesian reliability is introduced as a function of a predefined confidence level This paper also finds that there is no data-sequence effect on the updating results. It is demonstrated that the proposed Bayesian reliability analysis can predict the reliability of door closing performance in a vehicle body-door subsystem, where available data sets are insufficient, subjective, and evolving. [DOI: 10.1115/1.4000251]

A circular surface with a fixed radius can be swept out by moving a circle with its center following a curve, which acts as the spine curve. Based on a system of Euclidean invariants, the paper identifies those circular surfaces taking lines of curvature as generating circles and further explores the properties of the principal curvatures and Gaussian curvature of the tangent circular surfaces. The paper then applies the study to mechanism analysis by proving the necessary and sufficient condition for a circular surface to be generated by a serially connected C'R, HR, or RR mechanism, where C' joint can be visualized as a special H joint with a variable pitch of one degree of freedom. Following the analysis, this paper reveals for the first time the relationship between the invariants of a circular surface and the commonly used D-H parameters of C'R, HR, and RR mechanisms. [DOI: 10.1115/1.3212679] Keywords: circular surface, lines of curvature, Euclidean invariants, mechanisms, kinematics, differential geometry, robotics, workspace

This paper illustrates the power and versatility of the convex programming framework for optimal spline synthesis that was developed in a companion paper (Demeulenaere, Pipeleers, De Caigny, Swevers, De Schutter, and Vandenberghe, 2009, 'Optimal Spines for Rigid Motion Systems: A Convex Programming Framework', ASME J. Mech. Des., 131, p. 101005.). Two case studies concerning rigid motion systems illustrate the ability of the framework to improve upon recent (2005) literature results: (i) a numerical optimization study concerning kinematic optimization of uniform quintic splines for cam systems and (ii) an analytical study concerning time optimal quartic splines for motion systems driven by servomotors and subject to kinematic constraints. In a third study, the versatility of the framework is illustrated by generating time optimal and time-energy optimal motions for a rigid servomotor driven system under torque constraints. Based on these three case studies, the convex programming framework of the companion paper is extended with the following generic aspects: (i) a bisection to generate time optimal motions, (ii) a direct expression of the upper and lower bounds on motor torque, and (iii) a convex quadratic energy objective function for servomotor driven systems. [DOI: 10.1115/1.3201991]

This paper focuses on the synthesis of an independent suspension that can guide the wheel to track a straight line when moving up (jounce) and down (rebound). With displacement subgroups, it first synthesizes a rigid body guidance mechanism and verifies the result through screw theory. To simplify and optimize the loads of each kinematic chain of the knuckle, it investigates the static equations and ultimately synthesizes a symmetric redundant-constraint suspension structure, which could not only eliminate the shambling shocks induced by the jumping of wheels but also decrease the abrasion of tires. Theoretically, only one pair of noncoplanar kinematic chains is necessary to realize straight line guidance. However, a second pair of noncoplanar kinematic chains is particularly utilized to improve the load status of the links. Because of the redundant constraints induced by the suspension structures, the whole weight can be significantly reduced compared with the initial one. ADAMS simulations with a set of real parameters indicate that the rear suspension mechanism proposed in this paper can guide the wheel to follow a rectilinear locus during jounce and rebound. Therefore, this kind of independent suspension can improve the ride and handling properties of advanced vehicles. [DOI: 10.1115/1.3179153] Keywords: vehicle, suspension, rectilinear motion, rigid body guidance mechanism, synthesis

The act of creating a new product, system, or process is an innovation; the result of excogitation, study and experimentation. It is an inductive and/or deductive process. The inductive process involves studying systems that exist, for example, in nature, patents and products, and inducing from the behavior of these systems elemental features for innovating novel products. The deductive process involves deducing such aspects from hypothetical concepts and situations where systems or products could exist. By the application of a combined inductive and deductive approach, this paper reports on a methodology for the creation of innovative products with a broader functional repertoire than traditional designs. This breed of innovative products is coined as transformers, transforming into different configurations or according to different states. Current design theory lacks a systematic methodology for the creation of products that have the ability to transform. This paper identifies analogies in nature, patents, and products along with hypothesizing the existence of such products in different environments and situations. Transformation design principles are extracted by studying key design features and functional elements that make up a transforming product. These principles are defined and categorized according to their roles in general transformations. The principles and categorizations are then validated and applied to conceptualize transforming products as part of an innovative design process. [DOI: 10.1115/1.3125205] Keywords: design principles, transformational design, design transformation theory, inductive research, deductive research

Successful realization of a flapping wing micro-air vehicle (MAV) requires development of a light weight drive mechanism that can convert the continuous rotary motion of the motor into oscillatory flapping motion of the wings. The drive mechanism should have low weight to maximize the payload and battery capacity. It should also have high power transmission efficiency to maximize the operational range and to minimize weight of the motor. In order to make flapping wing MAVs attractive in search, rescue, and recovery efforts, they should be disposable from the cost point of view. Injection molded compliant drive mechanisms are an attractive design option because of manufacturing scalability and reduction in the number of parts. However, realizing compliant drive mechanism using injection molding requires use of multipiece multigate molds. Molding process constraints need to be considered during the design stage to successfully realize the drive mechanism. This paper describes an approach for determining the drive mechanism shape and size that meets both the design and molding requirements. The novel aspects of this work include (1) minimizing the number of mold pieces and (2) the use of sacrificial shape elements to reduce the impact of the weld-lines on the structural performance. The design generated by the approach described in this paper was utilized to realize an operational flapping wing MAV. [DOI: 10.1115/1.3116258]

The present paper describes the analytical solution of position kinematics for a three degree-of-freedom parallel manipulator. It also provides a numeric example of workspace calculation and a procedure for its optimization. The manipulator consists of a base and a moving platform connected to the base by three identical legs; each leg is provided with a PPS chain, where P designates an actuated prismatic pair, P stands for a passive prismatic pair, and S a spherical pair. The direct analysis yields a nonlinear system with eight solutions at the most. The inverse analysis is solved in three relevant cases: (i) the orientation of the moving platform is given, (ii) the position of a reference point of the moving platform is given, and (iii) two rotations (pointing) and one translation (focusing) are given. In the present paper it is proved that case (i) yields an inverse singularity condition of the mechanism; case (ii) provides a nonlinear system with four distinct solutions at the most; case (iii) allows the finding of some geometrical configurations of the actuated pairs for minimizing parasitic movements in the case of a pointing/focusing operation of the manipulator. [DOI: 10.1115/1.3116257]

A three-dimensional wide curve is a spatial curve with variable cross sections. This paper introduces a geometric optimization method for spatial compliant mechanisms by using three-dimensional wide curves. In this paper, every material connection in a spatial compliant mechanism is represented by a three-dimensional wide curve and the whole spatial compliant mechanism is modeled as a set of connected three-dimensional wide curves. The geometric optimization of a spatial compliant mechanism is considered as the generation and optimal selection of the control parameters of the corresponding three-dimensional parametric wide curves. The deformation and performance of spatial compliant mechanisms are evaluated by the isoparametric degenerate-continuum nonlinear finite element procedure. The problem-dependent objectives are optimized and the practical constraints are imposed during the optimization process. The optimization problem is solved by the MATLAB constrained nonlinear programming algorithm. [DOI: 10.1115/1.3086792]

Although researchers desire to evaluate system reliability accurately and efficiently over the years, little progress has been made on system reliability analysis. Up to now, bound methods for system reliability prediction have been dominant. However, two primary challenges are as follows: (1) Most numerical methods cannot effectively evaluate the probabilities of the second (or higher)--order joint failure events with high efficiency and accuracy, which are needed for system reliability evaluation and (2) there is no unique system reliability approximation formula, which can be evaluated efficiently with commonly used reliability methods. Thus, this paper proposes the complementary intersection (CI) event, which enables us to develop the complementary intersection method (CIM) for system reliability analysis. The CIM expresses the system reliability in terms of the probabilities of the CI events and allows the use of commonly used reliability, methods for evaluating the probabilities of the second-order (or higher) joint failure events efficiently. To facilitate system reliability analysis for large-scale systems, the CI-matrix can be built to store the probabilities of the first- and second-order CI events. In this paper, three different numerical solvers for reliability analysis will be used to construct the CI-matrix numerically: first-order reliability method, second-order reliability method, and eigenvector dimension reduction (EDR) method. Three examples will be employed to demonstrate that the CIM with the EDR method outperforms other methods for system reliability analysis in terms of efficiency, and accuracy. [DOI: 10.1115/1.3086794]

A continuous protein synthesis formulation based on the design principles applied to topology optimization problems is proposed in this paper. In contrast to conventional continuous protein design methods, the power law (PL) protein design formulation proposed in this paper can handle any number of residue types to accomplish the goal of protein synthesis, and hence provides a general continuous formulation for protein synthesis. Moreover, a discrete sequence with minimum energy can be determined by the PL design method as it inherits the feature of material penalization used in designing a structural topology; Since a continuous optimization method is implemented to solve the PL design formulation, the entire design process is more efficient and robust than conventional design methods employing stochastic or enumerative search methods. The performance of the proposed PL design formulation is explored by designing simple lattice protein models, for which an exhaustive search can be carried out to identify a sequence with minimum energy. We used residue probabilities as an initial guess for the design optimization to enhance the capability and efficiency of the PL design formulation. The comparison with the exchange replica method indicates that the PL design method is millions of times more efficient than the conventional stochastic protein design method. [DOI: 10.1115/1.3086790] Keywords: protein sequence design, deterministic optimization, inverse folding, artificial power law, topology optimization

This paper presents a vector method for measuring rigid body motion from marker coordinates, including both finite and infinitesimal displacement analyses. The common approach to solving the finite displacement problem involves the determination of a rotation matrix, which leads to a nonlinear problem. On the contrary, infinitesimal displacement analysis is a linear problem that can be easily solved. In this paper we take advantage of the linearity of infinitesimal displacement analysis to formulate the equations of finite displacements as a generalization of Rodrigues' formula when more than three points are used. First, for solving the velocity problem, we propose a simple method based on a mechanical analogy that uses the equations that relate linear and angular momenta to linear and angular velocities, respectively. This approach leads to explicit linear expressions for infinitesimal displacement analysis. These linear equations can be generalized for the study of finite displacements by using an intermediate body whose points are the midpoint of each pair of homologous points at the initial and final positions. This kind of transformation turns the field of finite displacements into a skew-symmetric field that satisfies the same equations obtained for the velocity analysis. Then, simple closed-form expressions for the angular displacement, translation, and position of finite screw axis are presented. Finally, we analyze the relationship between finite and infinitesimal displacements, and propose vector closed-form expressions based on derivatives or integrals, respectively. These equations allow us to make one of both analyses and to obtain the other by means of integration or differentiation. An experiment is presented in order to demonstrate the usefulness of this method. The results show that the use of a set of markers with redundant information (n >3) allows a good accuracy of measurement of kinematic variables. [DOI: 10.1115/1.3066468] Keywords: kinematics, finite displacement analysis, screw axis

A team's design--the structuring of its resources and flows of knowledge--is an important element determining its effectiveness. An essential element in achieving a team's problem-solving potential is the role that interdependence, in both the task and the organization, plays in determining the dynamic and emergent system-level properties of the organization. In this paper, we present a computational platform for experimentally investigating the influence of informational dependencies found in the design of a complex system for exploring their role in determining system behaviors and performance. The approach presented in this paper is a multiagent simulation of the conceptual design of space mission plans by Team X, an advanced project design group at NASA's Jet Propulsion Laboratory. The algorithm is composed of rich descriptive models of both the team-types and timing of interactions, collaborative methods, sequencing, rates of convergence- and the task-primary variables, their behaviors and relations, and the approaches used to resolve them. The objective is to create an environment of interaction representative of that found in actual design sessions. Better understanding how the dynamics arising from organizational and domain interdependencies impact an organization's ability to effectively resolve its task should lead to the development of guidelines for better coping with task complexities, suggest ways to better design organizations, as well as suggest ways for improving the search for innovative solutions. [DOI: 10.1115/1.3066501]

Taguchi optimization or robust design is an effective way to balance rigorous statistical testing and compressed time schedules when engineering a product design. In an effort to define the specifications of the parameters that will eventually control the product output, it is necessary to first identify those parameters that will most likely have the greatest effect on the performance of the system. Once the parameters have been narrowed down, it is then the job of the testing to identify the levels of each parameter to ensure robust performance of the system. Without the efficiencies of the designed experiments described as robust design, it would be impossible within the constraints of a tight design schedule to properly optimize a system design for reliable performance. The usefulness of the Taguchi optimization is especially important when a design will be subjected to a wide variety of noises. It is for this reason that Taguchi techniques fit well in the world of paper handling product design. This paper discusses how these techniques were used to optimize a production printer finishing module. It steps through the process from identifying the parameters and setting up the test to the additional evaluation of parameters to meet the design constraints of the physical hardware. [DOI: 10.1115/1.3042162] Keywords: robust design, Taguchi optimization, parameter design, compound noise, orthogonal array, outer noise array, confirmation testing

This paper addresses the problem of certifying the performance of a precision flexure-based mechanism design with respect to the given constraints. Due to the stringent requirements associated with flexure-based precision mechanisms, it is necessary to be able to evaluate and certify the performance at the design stage, taking into account the possible sources of errors such as fabrication tolerances and the modeling inaccuracies in flexure joints. An interval-based method is proposed to certify whether various constraints are satisfied for all points within a required workspace. Unlike the finite-element methods that are commonly used today to evaluate a design, where material properties are used for evaluation on a point-to-point sampling basis, the proposed technique offers a wide range of versatility in the design criteria to be evaluated and the results are true for all continuous values within the certified range of the workspace. This paper takes a pedagogical approach in presenting the interval-based methodologies and the implementation on a planar 3revolute-revolute-revolute (RRR) parallel flexure-based manipulator. [DOI: 10.1115/1.3042151]

A 3D multilayer wide curve is a spatial curve with variable cross sections and multiple materials. The performance of multimaterial compliant mechanisms and structures is enhanced by integrating multiple materials into one-piece configurations. This paper introduces a geometric modeling method for spatial multimaterial compliant mechanisms and structures by using 3D multilayer wide curves. Based on the introduced modeling method, a geometric synthesis approach is proposed. In this paper, every connection in a spatial multimaterial compliant mechanism or structure is represented by a 3D multilayer wide curve and the whole compliant mechanism or structure is modeled as a set of connected wide curves. The geometric modeling and synthesis are considered as the generation and optimization of the control parameters of the corresponding 3D multilayer wide curves. The performance of spatial multimaterial compliant mechanisms and structures is evaluated by the isoparametric degenerate-continuum nonlinear finite element procedure. The problem-dependent objectives are optimized and the practical constraints are imposed during the synthesis process. The effectiveness of the proposed geometric modeling and synthesis procedures is verified by the demonstrated examples. [DOI: 10.1115/1.3013355]

The purpose of this paper is to present an efficient methodology for the design of six-speed Ravigneaux-type automatic transmissions based on the concepts of basic gear ratios and speed ratio equations. First, the speed ratio equations of an eight-link two-degree-of-freedom Ravigneaux gear mechanism are derived, which are functions of basic gear ratios. Next, the ranges of the derived speed ratio equations are estimated and classified into three groups to synthesize all possible clutching sequences. Then, a planargraph representation is proposed to arrange the desired clutches for each possible clutching sequence into the Ravigneaux gear mechanism. Finally, the number of teeth of all gears is synthesized from assigning three desired speed ratios by the analytic method presented by Hsu. The result of this paper shows that the eight-link two-degree-of-freedom Ravigneaux gear mechanism could reach six forward speeds at most, and only a particular set of speed ratios is practical for use. [DOI: 10.1115/1.3013346] Keywords: automatic transmission, epicyclic gear mechanism, Ravigneaux, speed ratios

The biological world provides numerous cases for analogy and inspiration. From simple cases such as hook and latch attachments to articulated-wing flying vehicles, nature provides many sources for ideas. Though biological systems provide a wealth of elegant and ingenious approaches to problem solving, there are challenges that prevent designers from leveraging the full insight of the biological world into the designed world. This paper describes how those challenges can be overcome through functional analogy. Through the creation of a function-based repository, designers can find biomimetic solutions by searching the function for which a solution is needed. A biomimetic function-based repository enables learning, practicing, and researching designers to fully leverage the elegance and insight of the biological world. In this paper, we present the initial efforts of functional modeling biological systems and then transferring the principles of the biological system to an engineered system. Four case studies are presented in this paper. These case studies include a biological solution to a problem found in nature and engineered solutions corresponding to the high-level functionality of the biological solution, i.e., a housefly's winged flight and a flapping wing aircraft. The case studies show that unique creative engineered solutions can be generated through functional analogy with nature. [DOI: 10.1115/1.2992062]

One perspective of a design process in the engineering design community is that it is largely a process marked and defined by a series of decisions. The fundamental assumption in most developed design decision support methodologies is that decision makers make rational choices; that is. choices that maximize the payoff for the predicted outcome. Decisions that do not maximize the predicted payoff are termed as mistakes or irrational choices and discarded. However, research in behavioral economics, psychology, and cognitive science has studied the human mind and suggested the notion of 'bounded rationality' to explain decision errors. Bounded rationality refers to the intrinsic inability of human beings to accurately choose 'rational' options prescribed by decision models such as expected utility. This paper extends the notion of bounded rationality within engineering design. Specifically, this paper studies the design of complex systems that require interaction among several different subsystems contributing to the overall product design. For convergent decentralized design problems, rational designers converge to equilibrium solutions that lie at the intersection of their individual rational reaction sets. These equilibrium solutions are usually not Pareto optimal and due to the dynamics of the designers' interaction in collaborative design, it is rarely possible for them to converge to Pareto optimal solutions. However, when models for bounded rationality are introduced into individual designer behavior, it is seen that the converged solutions can improve the resulting solution. Bounded rational decisions within decentralized design are modeled, and the effects of propagating such decisions within a design process are studied. [DOI: 10.1115/1.2988479] Keywords: bounded rationality, multi-objective optimization, decentralized design, game theory

This paper deals with face gear design. The goal is to propose a simple formula for predicting the width of the wheel as a function of the main design parameters. A specific software was used to achieve this goal. This numerical tool is able to simulate the geometry and the quasistatic loaded behavior of a face gear. The statistical method used for analyzing the influence of data is described: The design of experiments leads to a simple regression model taking into account the influential parameters and their couplings. In the last part of this paper, the results of the formulas are compared to those of the software and an optimal design is proposed based on the regression model. [DOI: 10.1115/1.2965606]

This paper addresses the design of a microwrist for needle laparoscopic surgery (needlescopy) using microelectromechanical system technology and an original three degree of freedom, 3D architecture. Advancement in needlescopy drives the development of multi-DOF microtools 1-2 mm in diameter with 3D mobility but standard available fabrication techniques are for 2.5D structures. Thus paper discusses the development steps and design solutions for the realization of the 3D wrist with available technology. A compliant mechanism is used, which is derived from a reference parallel kinematics mechanism architecture with three legs. A singular configuration of increased instantaneous mobility is exploited to achieve the desired 3D mobility. Alternative leg architectures are investigated to obtain satisfactory performance. The legs are fabricated as monolithic compliant structures and assembled to wrist base and end-effector. The definition of the leg geometry revealed a complex task. The steps to obtain the final design satisfying task requirements are detailed. [DOI: 10.1115/1.2965608] Keywords: robotic surgery, needlescopy, parallel mechanisms, compliant mechanisms

The joint velocity jump for redundant robots in the presence of locked-joint failures is discussed in this paper. First, the analytical formula of the optimal joint velocity with minimum jump is derived, and its specific expressions for both all joint failure and certain single joint failure are presented. Then, the jump difference between the minimum jump solution and the least-norm velocity solution is mathematically analyzed, and the influence factors on this difference are also discussed. Based on this formula, a new fault tolerant algorithm with the minimum jump is proposed. Finally, simulation examples are implemented with a planar 3R robot and a 4R spatial robot, and an experimental study is also done. Study results indicate that the new algorithm proposed in this paper is well suited for real time implementation, and can further reduce the joint velocity jump thereby improving the motion stability of redundant robots in fault tolerant operations. Also, the fewer the possible failed joints are, the more obvious the effect of this new algorithm becomes. [DOI: 10.1115/1.2943302]

Displacement-amplifying compliant mechanisms (DaCMs) reported in literature are widely used for actuator applications. This paper considers them for sensor applications that rely on displacement measurement, and proposes methods to evaluate and design such mechanisms. The motivation of this work is to increase the sensitivity of a micro-machined capacitive accelerometer and a minute mechanical force sensor using DaCMs. A lumped spring-mass-lever (SML) model, which effectively captures the effects of appending a DaCM to a sensor, is introduced. This model is a generalization of the ubiquitously used spring-mass model for the case of an elastic body that has two points of interest--an input and an output. The SML model is shown to be useful in not only evaluating the suitability of an existing DaCM for a new application but also for designing a new DaCM. With the help of this model, we compare a number of DaCMs from literature and identify those that nearly meet the primary problem specifications. To obtain improved designs that also meet the secondary specifications, topology and size-optimization methods are used. For the two applications considered in this paper, we obtain a few new DaCM topologies, which are added to the catalog of DaCMs for future use. The spring-mass-lever model, the evaluation and design methods, and the catalog of DaCMs presented here are useful in other sensor and actuator applications. [DOI: 10.1115/1.2965599]

This paper uses the concept of bisecting linear line complex of the two position theory in kinematics to present a geometric foundation for finite displacement screw systems, with an emphasis on incompletely specified displacement of points. It is shown that the bisecting linear line complex arising from the finite displacement of points is subject to a reciprocal condition if a specific definition of pitch of finite screws is used. The screw systems of finite displacements are then characterized in terms of intersections of bisecting linear line complexes. The line varieties corresponding to the two-system and four-system associated with finite displacements of two points and a point, respectively, are illustrated. This paper demonstrates that the bisecting .linear line complex provides a geometric framework for studying finite and infinitesimal kinematics. [DOI: 10.1115/1.2965362]

Many engineering systems are required to operate under changing operating conditions. A special class of systems called adaptive systems has been proposed in the literature to achieve high performance under changing environments. Adaptive systems acquire this powerful feature by allowing their design configurations to change with operating conditions. In the optimization of the adaptive systems, designers are often required to select (i) adaptive and (ii) nonadaptive (or fixed) design variables of the design configuration. Generally, the selection of these variables and the optimization of adaptive systems are performed sequentially, thus being a source of suboptimality. In this paper, we propose the Selection-Integrated Optimization (SIO) methodology, which integrates the two key processes: (1) the selection of the adaptive and fixed design variables and (2) the optimization of the adaptive system, thereby eliminating a significant source of suboptimality from adaptive system optimization problems. A major challenge to integrating these two key processes is the selection of appropriate fixed and adaptive design variables, which is discrete in nature. We propose the Variable-Segregating Mapping-Function (VSMF), which overcomes this challenge by progressively approximating the discreteness in the design variable selection process. This simple yet effective approach allows the SIO methodology to integrate the selection and optimization processes and helps avoid one significant source of suboptimality from the optimization procedure. The SIO methodology finds its applications in a variety of other engineering fields, such as product family optimization. However, in this paper, we limit the scope of our discussion to adaptive system optimization. The effectiveness of the SIO methodology is demonstrated by designing a new air-conditioning system called Active Building Envelope (ABE) system. [DOI: 10.1115/1.2965365]

Bolted bearing connections are one of the most important connections in some industrial structures, and manufacturers are always looking for a quick calculation model for a safe design. In this context, all the analytical and numerical models reduce the global study to the study of the most critical sector. Therefore, the main inputs for these models are the maximal equivalent contact load and the corresponding contact angle. Thus, a load distribution calculation model that takes all the important parameters, such as the stiffness of the supporting structure and the variation in the contact angle, into consideration is needed. This paper presents a 3D finite element (FE) simplified analysis of load distribution and contact angle variation in a slewing ball bearing. The key element of this methodology, which is based on the Hertz theory, is modeling the rolling elements under compression by nonlinear traction springs between the centers of curvature of the raceways. The contact zones are modeled by rigid shells to avoid numerical singularities. Each raceway curvature center is coupled to the corresponding contact zone by rigid shells. The main contribution of this method is not only the evaluation of the contact loads with a relatively reduced calculation time but also the variation in the contact angle from the deformed coordinates of the curvature centers. Results are presented for several loading cases: axial loading, turnover moment, and a combined loading of axial force and turnover moment. The influence of the most important parameters such as the contact angle, the stiffness of the bearings, and the supporting structure is discussed. Finally, a preliminary experimental validation is conducted on a standard ball bearing. The results presented in this paper seem encouraging. The FE study shows an important influence of several parameters and a good correlation with experimental results. Consequently, this model can be extended to other types of slewing bearings such as roller bearings. Moreover, it can be implemented in complex industrial structures such as cranes and lifting devices to determine the corresponding load distributions and contact angles and, consequently, the most critical sector. [DOI: 10.111511.2918915] Keywords: slewing bearing, Hertz theory, load distribution, contact angle, nonlinear spring

This paper presents results of a comprehensive experimental and theoretical study to determine the influence of certain key factors in planetary transmissions on gear stresses and planetary load sharing. A series of tests are conducted on a family of planetary gear sets, and strains are recorded at various locations on the outer diameter and gear tooth fillet of the ring gear. Pinion position errors are introduced as a representative key manufacturing tolerance, and the resultant changes in the planetary behavior are observed. The experimental data are compared to the predictions of a state-of-the-art multibody contact analysis model--Gear System Analysis Modules (GSAM). This model is capable of including the influences of a number of system-level variables and quantifying their impact on gear strains. The model predictions are shown to compare well with the measured strain at the ring gear outer diameter and tooth fillet. GSAM predictions of planet load sharing are then used to quantify the influence of tangential pinhole position errors on three-, four-, five-, and six-planet test gear sets. These predictions also agree well with the planet load sharing experiments presented in a companion paper. [DOI: 10.1115/1.2890110]