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### Editorial

J. Mech. Des. 2008;130(11):110201-110201-1. doi:10.1115/1.3005146.
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Recycling used resources for reuse is always good, except when it comes to our own research work. Republishing our own research should be done with extreme caution.

Commentary by Dr. Valentin Fuster

### Research Papers: Design Theory and Methodology

J. Mech. Des. 2008;130(11):111101-111101-10. doi:10.1115/1.2976455.

This paper presents a decision-analytic system concept selection for a public project. In the proposed approach, the decision-maker (engineer) chooses a system concept and requests a budget for building the system. The unique customer (government) decides whether to approve the project but also has the option to cancel the project if the cost of the project exceeds the budget. Thus, at the time of system concept selection, the cost of the system, the government’s criterion to approve the project, and its criterion to continue/cancel the project when the cost exceeds the budget are modeled as uncertainties. To model the uncertainty of project continuation, the engineer assumes that the government’s criterion to continue/cancel the project is a linear combination of its initial criterion to approve the project and the budget. By analyzing the government’s option to cancel the project, the engineer can optimize his or her choice of a system concept (technology and target system requirements) and budget.

Commentary by Dr. Valentin Fuster
J. Mech. Des. 2008;130(11):111102-111102-14. doi:10.1115/1.2976446.

Product upgrade, achieved through the improvement of the functionality of reused or remanufactured products, is often accepted as an effective way to attain a competitive reutilization. Design for upgradability (DFU) is a tool that primarily focuses on enhancing a product’s functional as well as physical fitness for ease of upgrade. This paper presents the development of a novel approach and its implementation algorithm for a systematic design of product upgradability. The framework of this approach consists of two major phases––modeling and optimization. Fuzzy logic is used as a tool to facilitate the modeling of a product’s upgradability based on its technical characteristics and the reutilization mode. In the optimization phase, a new DFU optimization program is developed by using genetic algorithm techniques. The objective of a product’s DFU optimization is defined so as to configure/redesign a product for the maximal level of upgradability with minimal associated costs and violations of engineering, economic, and environmental constraints. A case study on a solar heating system is presented to demonstrate the application of the proposed DFU algorithm and its effectiveness in generating optimal configurations for the system, which are reflected as significant improvements in the system’s upgradability, cost efficiency, and overall functionality.

Commentary by Dr. Valentin Fuster

### Research Papers: Design Automation

J. Mech. Des. 2008;130(11):111401-111401-9. doi:10.1115/1.2976449.

Computational models with variable fidelity have been widely used in engineering design. To alleviate the computational burden, surrogate models are used for optimization without directly invoking expensive high-fidelity simulations. In this work, a model fusion technique based on the Bayesian–Gaussian process modeling is employed to construct cheap surrogate models to integrate information from both low-fidelity and high-fidelity models, while the interpolation uncertainty of the surrogate model due to the lack of sufficient high-fidelity simulations is quantified. In contrast to space filling, the sequential sampling of a high-fidelity simulation model in our proposed framework is objective-oriented, aiming for improving a design objective. Strategy based on periodical switching criteria is studied, which is shown to be effective in guiding the sequential sampling of a high-fidelity model toward improving a design objective as well as reducing the interpolation uncertainty. A design confidence metric is proposed as the stopping criterion to facilitate design decision making against the interpolation uncertainty. Examples are provided to illustrate the key ideas and features of model fusion, sequential sampling, and design confidence—the three key elements in the proposed variable-fidelity optimization framework.

Commentary by Dr. Valentin Fuster

### Research Papers: Mechanisms and Robotics

J. Mech. Des. 2008;130(11):112301-112301-9. doi:10.1115/1.2976444.

This paper deals with the problem of synthesizing smooth piecewise rational spherical motions of an object that satisfies the kinematic constraints imposed by a spherical robot arm with revolute joints. This paper brings together the kinematics of spherical robot arms and recently developed freeform rational motions to study the problem of synthesizing constrained rational motions for Cartesian motion planning. The kinematic constraints under consideration are workspace related constraints that limit the orientation of the end link of robot arms. This paper extends our previous work on synthesis of rational motions under the kinematic constraints of planar robot arms. Using quaternion kinematics of spherical arms, it is shown that the problem of synthesizing the Cartesian rational motion of a 2R arm can be reduced to that of circular interpolation in two separate planes. Furthermore, the problem of synthesizing the Cartesian rational motion of a spherical 3R arm can be reduced to that of constrained spline interpolation in two separate planes. We present algorithms for the generation of $C1$ and $C2$ continuous rational motion of spherical 2R and 3R robot arms.

Commentary by Dr. Valentin Fuster
J. Mech. Des. 2008;130(11):112302-112302-9. doi:10.1115/1.2976447.

This contribution presents new considerations on the theory of type synthesis of fully parallel platforms. These considerations prove that the theory of type synthesis of fully parallel platforms can be dealt with by analyzing two types of fully parallel platforms, where the displacements of the moving platform generate a subgroup of the Euclidean group, $SE(3)$, including in this type, 6DOF parallel platforms and lower mobility platforms or, more precisely, parallel platforms where the displacements of the moving platforms generate only a subset of the Euclidean group. The theory is based on an analysis of the subsets and subgroups of the Euclidean group, $SE(3)$, and their intersections. The contribution shows that the different types of parallel platforms are determined by the intersections of the subgroups or subsets, of the Euclidean group, generated by the serial connecting chains or limbs of the parallel platform. From an analysis of the intersections of subgroups and subsets of the Euclidean group, this contribution presents three possibilities for the type synthesis of fully parallel platforms where the displacements of the moving platform generate a subgroup of the Euclidean group, and two possibilities for the type synthesis of fully parallel platforms where the displacements of the moving platforms generate only a subset of the Euclidean group. An example is provided for each one of these possibilities. Thus, once these possible types of synthesis are elucidated, the type synthesis of fully parallel platforms is just reduced to the synthesis of the serial connecting chains or limbs that generate the required subgroups or subsets of the Euclidean group.

Commentary by Dr. Valentin Fuster
J. Mech. Des. 2008;130(11):112303-112303-8. doi:10.1115/1.2976450.

So far, in the derivation of the singularity equations of Gough–Stewart platforms, all researchers defined the mobile frame by making its origin coincide with the considered point on the platform. One problem can be that the obtained singularity equation contains too many geometric parameters and is not convenient for singularity analysis, especially not convenient for geometric optimization. Another problem can be that the obtained singularity equation cannot be used directly in practice. To solve these problems, this work presents a new approach to derive the singularity equation of the Gough–Stewart platform. The main point is that the origin of the mobile frame is separated from the considered point and chosen to coincide with a special point on the platform in order to minimize the geometric parameters defining the platform. Similarly, by defining a proper fixed frame, the geometric parameters defining the base can also be minimized. In this way, no matter which practical point of the platform is chosen as the considered point, the obtained singularity equation contains only a minimal set of geometric parameters and becomes a solid foundation for the geometric optimization based on singularity analysis.

Commentary by Dr. Valentin Fuster
J. Mech. Des. 2008;130(11):112304-112304-8. doi:10.1115/1.2976452.

The maximal singularity-free workspace of parallel mechanisms is a desirable criterion in robot design. However, for a 6DOF parallel mechanism, it is very difficult to find an analytic method to determine the maximal singularity-free workspace around a prescribed point for a given orientation. Hence, a numerical algorithm is presented in this paper to compute the maximal singularity-free workspace as well as the corresponding leg length ranges of the Gough–Stewart platform. This algorithm is based on the relationship between the maximal singularity-free workspace and the singularity surface. Case studies with different orientations are performed to demonstrate the presented algorithm. The obtained results can be applied to the geometric design or parameter (leg length) setup of this type of parallel robots.

Commentary by Dr. Valentin Fuster
J. Mech. Des. 2008;130(11):112305-112305-9. doi:10.1115/1.2976790.

This paper presents the problem formulation and design of compliant grip-and-move manipulators. Each manipulator is composed of two identical path generating compliant mechanisms such that it can grip an object and convey it from one point to another. The integration of both gripping and moving behaviors within a simple mechanism is accomplished by the use of compliant mechanisms, which generate paths that are symmetric. The automated synthesis of these symmetric path generating mechanisms is by a structural topology optimization approach. The problem of topology optimization of continuum structures is solved using a multiobjective genetic algorithm coupled with a morphological representation of geometry that efficiently defines the variable structural geometry upon a finite element grid. A graph-theoretic chromosome encoding together with compatible crossover and mutation operators are then applied to form an effective evolutionary optimization procedure. Two designs have been created and are presented in this paper, and some concluding remarks and future work are put forward.

Commentary by Dr. Valentin Fuster

### Research Papers: Power Transmissions and Gearing

J. Mech. Des. 2008;130(11):112601-112601-10. doi:10.1115/1.2976453.

In the lapping process of hypoid gears, a gear set is run at varying operating positions and under a light load in order to lap the complete tooth surface. Because of the rolling and sliding motion inherent to hypoid gears, the lapping compound acts as an abrasive and refines the tooth surface to achieve smoothness in rolling action and produce high quality gear sets. In this paper, the lapping process is reproduced using advanced modeling tools such as gear tooth vectorial simulation for the tooth surfaces and reverse engineering to analyze the tooth contact pattern of existing gear sets. Test gear sets are measured using a coordinate measurement machine prior to a special lapping cycle where the position of the gear sets on the lapper does not change, and then are remeasured after lapping in order to establish how much and where material was removed. A wear constant named “wear coefficient” specific to the lapping compound is then calculated. Based on the obtained wear coefficient value, an algorithm for simulating the lapping process is presented. Gear sets lapped on the production line at AAM are used for simulation case studies. Initial results show significant scattering of tooth distortion from tooth to tooth and from gear set to gear set, which makes the simulation process difficult. However, it is possible to predict a confidence range within which actual lapping should fall, thereby opening the door to the optimization of the lapping process.

Topics: Wear , Grinding , Gears , Errors , Simulation
Commentary by Dr. Valentin Fuster
J. Mech. Des. 2008;130(11):112602-112602-8. doi:10.1115/1.2976454.

This paper presents a new systematic method for identifying the values of the machine-tool settings required to obtain flank form modifications in hypoid gears. The problem is given a nonlinear least-squares formulation, and it is solved by the Levenberg–Marquardt method with a trust-region strategy. To test the method, the same ease-off topography was obtained by means of very different sets of machine-tool settings, including a set of only kinematic parameters and a highly redundant set of 17 parameters. In all cases, the goal was achieved in a few iterations, with residual errors well below machining tolerances and, even more importantly, with realistic values of all parameters. Therefore, significant improvements in practical gear design can be achieved by employing the overall proposed procedure.

Commentary by Dr. Valentin Fuster
J. Mech. Des. 2008;130(11):112603-112603-10. doi:10.1115/1.2976802.

The infinitely variable transmissions (IVTs) allow the transmission ratio to vary with continuity, offering the possibility of also reaching zero values for the transmission ratio and the motion inversion. In this paper an original infinitely variable transmission system is described (MG-IVT). MG-IVT is made up of the coupling of a continuously variable transmission, a planetary gear train, and two ordinary transmissions with a constant transmission ratio. By means of two frontal clutches, the MG-IVT is allowed to get two different configurations. The main purpose is to get the configurations that make the optimal efficiency of the transmission at different transmission ratios. Kinetic characteristics of single component devices are obtained, and the MG-IVT system’s performance is determined by considering how the efficiency of the component devices change as a function of operating conditions. The advantages of the MG-IVT are therefore shown in terms of power and efficiency in comparison to the traditional IVT.

Commentary by Dr. Valentin Fuster
J. Mech. Des. 2008;130(11):112604-112604-8. doi:10.1115/1.2978342.

In this paper, a theoretical and experimental investigation on an innovative cycloidal speed reducer is presented. The typical cycloid drive has a planet wheel, the profile of which is the internal offset of an epitrochoid meshing with cylindrical rollers connected to the case. This reducer, on the contrary, has an external ring gear, the transverse profile of which is the external offset of an epitrochoid and engages with the planet wheel by means of cylindrical rollers. This paper investigates the structural characteristics and the kinematic principles of this type of reducer. A theoretical approach based on the theory of gearing (following Litvin’s approach) is developed and compared to a development of Blanche and Yang’s approach. Furthermore, a simplified procedure to calculate the force distribution on cycloid drive elements, its power losses, and theoretical mechanical efficiency is presented. The effects of design parameters on the values of forces are studied for an optimal design of this type of reducer. The theoretical model is tuned on the basis of the results of tests made on purpose. The mechanical efficiency dependency on speed and torque is described. The main aim of this work is to tune a theoretical model in order to predict the operating behavior of the cycloid drive and to improve its design procedure.

Commentary by Dr. Valentin Fuster

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