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EDITORIAL

J. Mech. Des. 2003;125(3):413-415. doi:10.1115/1.1610008.
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Commentary by Dr. Valentin Fuster

TECHNICAL PAPERS

J. Mech. Des. 2003;125(3):416-427. doi:10.1115/1.1582877.

Heterogeneous objects are composed of different constituent materials. In these objects, material properties from different constituent materials are synthesized into one part. Therefore, heterogeneous objects can offer new material properties and functionalities. The task of modeling material heterogeneity (composition variation) is a critical issue in the design and fabrication of such heterogeneous objects. Existing methods cannot efficiently model the material heterogeneity due to the lack of an effective mechanism to control the large number of degrees of freedom for the specification of heterogeneous objects. In this research, we provide a new approach for designing heterogeneous objects. The idea is that designers indirectly control the material distribution through the boundary conditions of a virtual diffusion problem in the solid, rather than directly in the native CAD (B-spline) representation for the distribution. We show how the diffusion problem can be solved using the B-spline shape function, with the results mapping directly to a volumetric B-Spline representation of the material distribution. We also extend this method to material property manipulation and time dependent heterogeneous object modeling. Implementation and examples, such as a turbine blade design and prosthesis design, are also presented. They demonstrate that the physics based B-spline modeling method is a convenient, intuitive, and efficient way to model object heterogeneity.

Commentary by Dr. Valentin Fuster
J. Mech. Des. 2003;125(3):428-433. doi:10.1115/1.1587745.

Virtual reality (VR) technology provides a human-computer interface that allows participants to interact naturally with digital objects which are represented as three-dimensional images that occupy positions in a three-dimensional world. Related to problems of engineering design and manufacturing, this new technology offers engineers the ability to work with computer models in a three-dimensional, immersive environment. This paper describes a virtual reality application where the results of a discrete event simulation of a manufacturing cell are integrated with a virtual model of the cell to produce a virtual environment. The program described in this paper, the VRFactory, combines results from a commercial discrete event simulation program, SLAM II, with a virtual environment. This allows the user to investigate, using three-dimensional computer models, how various changes to the manufacturing cell affect part production. This investigation is performed while immersed in a computer-generated three-dimensional representation of the cell. Existing discrete event programming software allows only two-dimensional views of the factory as the parts progress through the simulation. Parts are shown only as primitive geometric shapes on the computer monitor and instantaneously move from one station to the next. The virtual environment implementation of the SLAM II results allows users to experience the simulation in a fully immersive three-dimensional digital environment. The virtual environment used here is a CAVE™-like projection screen-based facility called the C2, which is located at Iowa State University. This paper describes the creation of the VR model of the manufacturing cell, the animation of the environment and the implementation of the results of the discrete event simulation.

Commentary by Dr. Valentin Fuster
J. Mech. Des. 2003;125(3):434-442. doi:10.1115/1.1586309.

This paper describes a robust and versatile method based on graph embedding for reconstructing a solid model from a wireframe model. The robustness and versatility of the conventional methods are limited in that: (1) most of them are heuristic and thus less robust, and (2) the rest, deterministic ones, can handle only small class of wireframes. Unlike the conventional methods, our approach is deterministic and covers a larger class of wireframes that are topologically 2-connected planar multigraphs. The class includes wireframes that can be interpreted as a closed two-manifold in multiple ways. The proposed algorithm consists of three steps: (1) all topological solutions are exhaustively generated using triconnected component decomposition; (2) the surface geometries for all the topological solutions are generated; and (3) the solutions are pruned down to geometrically valid ones. We also show the algorithm is extendable to the class of general planar multigraphs. The approach is characterized by generating the complete set of topological solutions without referring to the geometry of the wireframe, which makes the process free from geometric errors and instabilities. The algorithm is also fast, because even when there are many topological solutions, the total number of different faces is very small. The proposed approach provides a method for easy and intuitive geometric modeling as well as a conversion tool for legacy wireframes.

Commentary by Dr. Valentin Fuster
J. Mech. Des. 2003;125(3):443-451. doi:10.1115/1.1587749.

The development of solid modeling to represent the geometry of designed parts and the development of parametric modeling to control the size and shape have had significant impacts on the efficiency and speed of the design process. Designers now rely on parametric solid modeling, but often are frustrated by a problem that unpredictably causes their sketches to become twisted, contorted, or take an unexpected shape. Mathematically, this problem, known as the “multiple solution problem” occurs because the dimensions and geometric constraints yield a set of non-linear equations with many roots. In practice, this situation occurs because the dimensioning and geometric constraint information given in a CAD model is not sufficient to unambiguously and flexibly specify which configuration the user desires. This paper first establishes that only explicit, independent solution selection declarations can provide a flexible mechanism that is sufficient for all situations. The paper then describes the systematic derivation of a set of “solution selector” types by considering the occurrences of multiple solutions in combinations of mutually constrained geometric entities. The result is a set of eleven basic solution selector types and two derived types that incorporate topological information. In particular, one derived type “concave/convex” is user-oriented and may prove to be particularly useful.

Commentary by Dr. Valentin Fuster
J. Mech. Des. 2003;125(3):452-463. doi:10.1115/1.1582879.

This paper presents a method that systematically decomposes product geometry into a set of components considering the structural stiffness of the end product. A structure is represented as a graph of its topology, and the optimal decomposition is obtained by combining FEM analyses with a Genetic Algorithm. As the first case study, the side frame of a passenger car is decomposed for the minimum distortion of the front door panel geometry. As the second case study, the under body frame of a passenger car is decomposed for the minimum frame distortion. In both case studies, spot-weld joints are considered as joining methods, where each joint, which may contain multiple weld spots, is modeled as a torsional spring. First, the rates of the torsional springs are treated as constant values obtained in the literature. Second, they are treated as design variables within realistic bounds. By allowing the change in the joint rates, it is demonstrated that the optimal decomposition can achieve the smaller distortion with less amount of joint stiffness (hence less welding spots), than the optimal decomposition with the typical joint rates available in the literature.

Commentary by Dr. Valentin Fuster
J. Mech. Des. 2003;125(3):464-473. doi:10.1115/1.1587746.

This paper presents a method of assembly synthesis focused on the in-process adjustability, where assembly synthesis is defined as the decomposition of the end product design prior to the detailed component design phase. Focusing on the effect of joint configurations on dimensional integrity of complex assemblies, the method recursively decomposes a product configuration and assigns joint configurations according to simple rules, in order to achieve a designed dimensional adjustability and non-forced fit. The rules employed during the decomposition process are drawn from the previous works of assembly design. An augmented AND/OR graph is utilized to represent a process of assembly synthesis with the corresponding assembly sequences, and the algorithm for generating the AND/OR graph is discussed. The method is applied to two dimensional skeletons of products without moving parts at very early stage of the design process. The relation of the assembly synthesis to Datum Flow Chain [1] is discussed. It is also shown that each final design from the assembly synthesis defines its own Datum Flow Chain.

Commentary by Dr. Valentin Fuster
J. Mech. Des. 2003;125(3):474-480. doi:10.1115/1.1582501.

Target cascading is a key challenge in the early product development stages of large complex artifacts: how to propagate the desirable top level design specifications (or targets) to appropriate specifications for the various subsystems and components in a consistent and efficient manner. Consistency means that all parts of the designed system should work well together, while efficiency means that the process itself should avoid iterations at later stages, which are costly in time and resources. In the present article target cascading is formalized by a process modeled as a multilevel optimal design problem. Design targets are cascaded down to lower levels using partitioning of the original problem into a hierarchical set of subproblems. For each design problem at a given level, an optimization problem is formulated to minimize deviations from the propagated targets and thus achieve intersystem compatibility. A coordination strategy links all subproblem decisions so that the overall system performance targets are met. The process is illustrated with an explicit analytical problem and a simple automotive chassis design model that demonstrates how the process can be applied in practice.

Topics: Design
Commentary by Dr. Valentin Fuster
J. Mech. Des. 2003;125(3):481-489. doi:10.1115/1.1586308.

Target cascading in product development is a systematic effort to propagate the desired top-level system design targets to appropriate specifications for subsystems and components in a consistent and efficient manner. If analysis models are available to represent the consequences of the relevant design decisions, analytical target cascading can be formalized as a hierarchical multilevel optimization problem. The article demonstrates this complex modeling and solution process in the chassis design of a sport-utility vehicle. Ride quality and handling targets are cascaded down to systems and subsystems utilizing suspension, tire, and spring analysis models. Potential incompatibilities among targets and constraints throughout the entire system can be uncovered and the trade-offs involved in achieving system targets under different design scenarios can be quantified.

Topics: Design , Vehicles , Springs
Commentary by Dr. Valentin Fuster
J. Mech. Des. 2003;125(3):490-497. doi:10.1115/1.1587156.

In this paper, we present the importance of using a single criterion approach to Decision-Based Design (DBD) by examining the limitations of multicriteria approaches. We propose in this paper an approach to DBD as an enhancement to Hazelrigg’s DBD framework that utilizes the economic benefit to the producer as the single criterion in alternative selection. The technique of Discrete Choice Analysis (DCA) is introduced for constructing a product demand model, which is crucial for the evaluation of both profit and production cost. An academic universal motor design problem illustrates the proposed DBD approach. It appears that DBD, when applied correctly, is capable of unambiguously selecting the preferred alternative in a rigorous manner. Open research issues related to implementing the DBD approach are raised. The focus of our study is on demonstrating the approach rather than the design results per se.

Topics: Design , Modeling
Commentary by Dr. Valentin Fuster
J. Mech. Des. 2003;125(3):498-508. doi:10.1115/1.1582500.

This paper broadly discusses aspects of the novel Rotary Vane Engine (RVE). It also considers, in detail, the geometrical structure of work unit and the entire engine. The rigorous mathematical description of work unit and torque transmission mechanism are presented for a first time in literature. Although the RVE is a simple structure possessing a small number of moving parts, it is this property that provides the RVE with an important advantage when compared to a usual reciprocating engine. The main idea is to use noncircular gears in torque transmission mechanism together with Kauertz-Virmel work unit. It is found that the rotary engine can produce almost constant angular velocity of the flywheel, which would result in an efficient and smooth performance.

Commentary by Dr. Valentin Fuster
J. Mech. Des. 2003;125(3):509-517. doi:10.1115/1.1588344.

Torsional oscillations in mechanical power transmission systems are a significant source of dynamic loads which are harmful to the system performance. The effects can cause a drive shaft to become unstable and self-destructive at critical speeds. This research focuses on dynamic analysis of a nonlinear torsional flexible coupling with elastic links. The equations of motion are derived by means of Lagrange’s equation. These equations are used to obtain the quasi-static performance of torque vs. angular displacement at constant rotational velocity. An exact solution is also found for the phase-plane representation for free oscillation torque. The fluctuation ratios of input velocity vs. output velocity of the system are obtained for determining the system performance. The results of the analyses of steady running and transient oscillation performance are applied to the determination of optimum proportions of the couplings. Results are compared with those of rigid-link couplings to show the influence of elasticity of the link on dynamic behavior of the system.

Commentary by Dr. Valentin Fuster
J. Mech. Des. 2003;125(3):518-526. doi:10.1115/1.1586936.

Both experimental investigation and finite element analysis were conducted to explore the mechanisms for the early stage self-loosening of bolted joints under transverse cyclic loading. The nuts were glued to the bolts using a strong thread locker in the self-loosening experiments to ensure that no backing-off of the nut occurred. Depending on the loading magnitude, the clamping force reduction ranged from 10% to more than 40% of the initial preload after 200 loading cycles. Three-dimensional elastic-plastic finite element analysis was conducted with the implementation of an advanced cyclic plasticity model. The finite element results revealed that the local cyclic plasticity occurring near the roots of the engaged threads resulted in cyclic strain ratcheting. The localized cyclic plastic deformation caused the stresses to redistribute in the bolt, and the result was the gradual loss of clamping force with loading cycles. The finite element results agreed with the experimental observations quantitatively. When the two clamped plates started to slip and the slip displacement was controlled, both experiments and finite element simulations suggested that the friction between the clamped plates has an insignificant influence on the early stage self-loosening.

Commentary by Dr. Valentin Fuster
J. Mech. Des. 2003;125(3):527-532. doi:10.1115/1.1567312.

By means of comparing results from finite element analysis and photoelasticity, the salient characteristics of a finite element model of a nut and bolt have been established. A number of two-dimensional and three-dimensional models were created with varying levels of complexity, and the results were compared with photoelastic results. It was found that both two-dimensional and three-dimensional models could produce accurate results provided the nut thread run-out and friction were modeled accurately. When using two-dimensional models, a number of models representing different positions around the helix of the thread were created to obtain more data for the stress distribution. This approach was found to work well and to be economical.

Commentary by Dr. Valentin Fuster
J. Mech. Des. 2003;125(3):533-539. doi:10.1115/1.1565082.

Welded cylindrical containers are susceptible to stress corrosion cracking (SCC) in the closure-weld area. An induction coil heating technique may be used to relieve the residual stresses in the closure-weld. This technique involves localized heating of the material by the surrounding coils. The material is then cooled to room temperature by quenching. A two-dimensional axisymmetric finite element model is developed to study the effects of induction coil heating and subsequent quenching. The finite element results are validated through an experimental test. The container design is tuned to maximize the compressive stress from the outer surface to a depth that is equal to the long-term general corrosion rate of the container material multiplied by the desired container lifetime. The problem is subject to several geometrical and stress constraints. Two different solution methods are implemented for this purpose. First, an off-the-shelf optimization software is used. The results however were unsatisfactory because of the highly nonlinear nature of the problem. The paper proposes a novel alternative: the Successive Heuristic Quadratic Approximation (SHQA) technique. This algorithm combines successive quadratic approximation with an adaptive random search within varying search space. SHQA promises to be a suitable search method for computationally intensive, highly nonlinear problems.

Commentary by Dr. Valentin Fuster
J. Mech. Des. 2003;125(3):540-544. doi:10.1115/1.1564572.

The stress-life (S-N) method along with the Palmgren-Miner cumulative damage theory is the simplest and the most commonly used fatigue life prediction technique. Its main advantage is that the material properties needed are easy to collect and life calculation is simple. However under many variable amplitude loading conditions, life predictions have been found to be unreliable. Various modifications have been proposed to the Palmgren-Miner theory, but they have not lead to more reliable life predictions. In this paper, a two-stage cumulative damage model will be developed and validated. This model divides fatigue life into two phases—a crack initiation phase and a crack propagation phase. It will be shown that the proposed method results in greatly improved life prediction capabilities. Also, the proposed method retains the simplicity of the S-N based approach in that the material data is still relatively simple to generate and the calculations are straightforward.

Commentary by Dr. Valentin Fuster
J. Mech. Des. 2003;125(3):545-551. doi:10.1115/1.1582499.

The high degree of automation of Solid Freeform Fabrication (SFF) processing and its ability to create geometrically complex parts to precise dimensions provide it with a unique potential for low volume production of rapid tooling and functional components. A factor of significant importance in the above applications is the capability of producing components with adequate mechanical performance (e.g., stiffness and strength). This paper introduces a strategy for optimizing the design of Fused-Deposition Acrylonitrile-Butadiene-Styrene (FD-ABS; P400) components for stiffness and strength under a given set of loading conditions. In this strategy, a mathematical model of the structural system is linked to an approximate minimization algorithm to find the settings of select manufacturing parameters, which optimize the mechanical performance of the component. The methodology is demonstrated by maximizing the load carrying capacity of a two-section cantilevered FD-ABS beam.

Commentary by Dr. Valentin Fuster
J. Mech. Des. 2003;125(3):552-556. doi:10.1115/1.1588345.

The aim of this paper is to find out a computational procedure for the kinematic and dynamic analysis of a mechanism with multiple loops having motion spaces of a Lie algebra or Lie algebras. The basis of a motion space of the loop is determined such that it consists of passive joints axes in a loop, and a basis of a wrench space is determined to be its dual basis. The analysis of a closed loop mechanism can be done by selecting loop-cut-joints and computing values of wrenches acting on these joints from the condition that virtual works of passive joints are zero. By expressing these wrenches in the coordinate vectors on the dual bases, the concise analysis procedure can be obtained. Because a formulation for the analysis is developed based on the bases consisting of passive joint axes and their dual bases, the computational procedure can be applied to a mechanism with any Lie algebras.

Commentary by Dr. Valentin Fuster
J. Mech. Des. 2003;125(3):557-563. doi:10.1115/1.1588343.

The analysis of the workspace singularities is one of the fundamental aspects in the design of parallel robots. The architecture singularities are generally studied analysing the local properties of the Jacobian matrix. Nevertheless, for limited-DOF parallel robots, there is a category of singularities (constraint or constructive singularities), relating to the constraint force transmission, which are not described by this matrix. This paper deals with a general approach to the analysis of these singularities, used in the synthesis of a Linear Delta robot to suitably modify its geometry, remarkably improving the structural behavior. Details and numerical results are provided.

Topics: Force , Robots
Commentary by Dr. Valentin Fuster
J. Mech. Des. 2003;125(3):564-572. doi:10.1115/1.1582876.

This investigation deals with singularity analysis of parallel manipulators and their instantaneous behavior while in or close to a singular configuration. The method presented utilizes line geometry tools and screw theory to describe a manipulator in a given position. Then, this description is used to obtain the closest linear complex, presented by its screw coordinates, to the set of governing lines of the manipulator. The linear complex axis and pitch provide additional information and a better physical understanding of the type of singularity and the motion the manipulator tends to perform in a singular point and in its neighborhood. Examples of Hunt’s, Fichter’s and 3-UPU singularities, along with a few selected examples taken from Merlet’s work [1], are presented and analyzed using this method.

Commentary by Dr. Valentin Fuster
J. Mech. Des. 2003;125(3):573-581. doi:10.1115/1.1582878.

This paper presents the results of a detailed study of the singular configurations of 3-DOF planar parallel mechanisms with three identical legs. Only prismatic and revolute joints are considered. From the point of view of singularity analysis, there are ten different architectures. All of them are examined in a compact and systematic manner using planar screw theory. The nature of each possible singular configuration is discussed and the singularity loci for a constant orientation of the mobile platform are obtained. For some architectures, simplified designs with easy to determine singularities are identified.

Commentary by Dr. Valentin Fuster
J. Mech. Des. 2003;125(3):582-592. doi:10.1115/1.1587748.

Metal forming press is one of the most commonly used manufacturing machines. Every day, millions of parts are produced by metal forming ranging from battery caps to automotive body panels. Therefore, even a small improvement may add to significant corporative gain. Currently, the metal forming presses can be divided into two categories: mechanical presses and hydraulic presses. The former is fast (high speed presses may reach up to several thousand shots per minute) and energy efficient (the large flywheel eases the impulsive force), but lacks flexibility. On the other hand, the hydraulic presses are flexible (their motions can be programmed) and accurate, but are expensive to build and to operate. Recently, there are mechanical presses driven by servomotors. They could perform as flexible as hydraulic presses with high speed. Nevertheless, they are even more expensive to build and to operate. This paper introduces a new design of mechanical press whose performances are programmable, including the trajectory and the velocity of the stroke, and yet, it is relatively inexpensive to build and to operate. The key idea of the new design is a 2-degree-of-freedom seven-bar linkage mechanism driven by a large constant speed motor and a small servomotor. First, the kinetics and kinematics of the design are presented including the feasibility conditions, mechanical advantage, as well as the torque and power distribution between the two motors. Next, a number of simulation results are given. The design (parameter) optimization is also carried out using Genetic Algorithm (GA). Based on computer simulation, it is shown that the new design is indeed very attractive.

Commentary by Dr. Valentin Fuster
J. Mech. Des. 2003;125(3):593-601. doi:10.1115/1.1582502.

Traditionally, cam-follower systems are designed by assuming a constant camshaft speed. Nevertheless, all cam-follower systems, especially high-speed systems, exhibit some camshaft speed fluctuation (despite the presence of a flywheel) which causes the follower motions to be inaccurate. This paper therefore proposes a novel design procedure that explicitly takes into account the camshaft speed variation. The design procedure assumes that (i) the cam-follower system is conservative and (ii) all forces are inertial. The design procedure is based on a single design choice, i.e., the amount of camshaft speed variation, and yields (i) cams that compensate for the inertial dynamics for any period of motion and (ii) a camshaft flywheel whose (small) inertia is independent of the period of motion. A design example shows that the cams designed in this way offer the following advantages, even for non-conservative, non-purely inertial cam-follower systems: (i) more accurate camshaft motion despite a smaller flywheel, (ii) lower motor torques, (iii) more accurate follower motions, with fewer undesired harmonics, and (iv) a camshaft motion spectrum that is easily and robustly predictable.

Commentary by Dr. Valentin Fuster
J. Mech. Des. 2003;125(3):602-608. doi:10.1115/1.1587157.

This paper, after a rigorous proof of the formulas originally proposed by Radzimovsky, demonstrates the numerical equivalence of the different approaches available for computing the mechanical efficiency of two degrees-of-freedom (d.o.f.) epicyclic gear trains. The paper includes also a discussion on the redundancy of data required by some formulas.

Commentary by Dr. Valentin Fuster
J. Mech. Des. 2003;125(3):609-619. doi:10.1115/1.1596242.

Optimal design of a multi-speed gearbox involves different types of decision variables and objectives. Due to lack of efficient classical optimization techniques, such problems are usually decomposed into tractable subproblems and solved. Moreover, in most cases the explicit mathematical expressions of the problem formulation is exploited to arrive at the optimal solutions. In this paper, we demonstrate the use of a multi-objective evolutionary algorithm, which is capable of solving the original problem involving mixed discrete and real-valued parameters and more than one objectives, and is capable of finding multiple nondominated solutions in a single simulation run. On a number of instantiations of the gearbox design problem having different complexities, the efficacy of NSGA-II in handling different types of decision variables, constraints, and multiple objectives are demonstrated. A highlight of the suggested procedure is that a post-optimal investigation of the obtained solutions allows a designer to discover important design principles which are otherwise difficult to obtain using other means.

Commentary by Dr. Valentin Fuster
J. Mech. Des. 2003;125(3):620-624. doi:10.1115/1.1596241.

This paper presents an approach to reduce the effect of the backlash nonlinearity in systems with relative cyclic motion. A compensation approach is developed to calculate a modified course of input motion for a desired velocity profile in systems with known backlash. The modified input trajectory contains accelerating and decelerating motion features to traverse the backlash area in minimal time. The method was proved with a dc-motor driven gear train. Results show that the output motion delay could be remarkably reduced. The time to overcome the backlash gap depends upon the desired velocity and the amount of backlash introduced to the system. Time savings between 43% and 74% could be measured with the utilized experimental setup. The proposed velocity compensation method is most efficient for low operating speeds and large mounting allowance between gears.

Commentary by Dr. Valentin Fuster
J. Mech. Des. 2003;125(3):625-631. doi:10.1115/1.1584689.

Spur gears were typically analyzed in the past using two-dimensional (2-D) Finite Element (FE) models. This is not adequate in many cases. A three-dimensional (3-D) FE model of a spur gear system, which accommodates all the gear teeth, the gear bodies, and the two transmission shafts, is developed in this paper using a sub-structuring method. The load between pinion and gear wheel is delivered by elastic frictional contact. The contact problem is solved according to the FE parametric quadratic programming method. The paper presents the shape of the contact region as well as the load distribution along the tooth width and profile. The results show that the transmission shafts have significant effects on the contact conditions including load distribution, contact region, and load deviation. The proposed method also applies to other types of gearing.

Commentary by Dr. Valentin Fuster
J. Mech. Des. 2003;125(3):632-639. doi:10.1115/1.1588346.

The purpose of this paper is to solve the problem of designing a shaving cutter for plunge shaving a topologically modified involute pinion. Application of topologically modified pinion allows noise reduction. Due to the desired topologically modified pinion tooth surface is determined not analytically, and discretely by a grid of points, the problem under consideration cannot be solved by direct application of methods developed in theory of enveloping surfaces. A modified kinematical approach is developed to establish one-to-one correspondence between points that determine tooth surface of a pinion to be machined, and points that determine tooth surface of a shaving cutter to be applied. The developed approach is based on ideas, which could be traced back to publications by E. Buckingham. The following three considerations are essential: a) tooth surface of an initial nonmodified pinion, b) desired deviations of the topologically modified pinion tooth surface relatively to the nonmodified pinion tooth surface, and c) relative motion that shaving cutter performs in gear finishing operation. Consequently, the algorithm, and software for computing coordinates of points, which determine the modified gear-shaving cutter tooth surface is developed.

Commentary by Dr. Valentin Fuster

TECHNICAL BRIEFS

J. Mech. Des. 2003;125(3):640-642. doi:10.1115/1.1564574.

This paper proposes a new method for detection of graph isomorphism using the concept of quadratic form. Graphs/kinematic chains are represented first by quadratic form, and the comparison of two graphs is thus reduced to the comparison of two quadratic form expressions. If both the lengths and the directions of the semiaxes of quadric surfaces, which are characterized by the eigenvalues and eigenvectors, are the same, the associated graphs/kinematic chains are isomorphic. An algorithm is developed based on this idea, and tested for the counter-examples known to other methods.

Commentary by Dr. Valentin Fuster
J. Mech. Des. 2003;125(3):642-646. doi:10.1115/1.1587747.

In this paper, the conical-shaped equivalent model for a bolted joint is considered. In particular, the governing equations for this model are made non-dimensional for the purposes of conducting sensitivity analysis. From this work, a plot of the dimensionless spring-rate of the clamped material is generated for all reasonable designs for which the conical-shaped equivalent model applies. The sensitivity analysis is then used to discuss the relative importance of estimating the proper model and design parameters and a maximum percent of uncertainty in the spring-rate calculation is also presented. It is shown in this discussion that the calculations are quite sensitive to a proper estimation of the cone angle (a model parameter) and that uncertainty within this calculation can range from 5 to 20%.

OBITUARY

J. Mech. Des. 2003;125(3):647-649. doi:10.1115/1.1605768.
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Commentary by Dr. Valentin Fuster

BOOK REVIEWS

J. Mech. Des. 2003;125(3):650. doi:10.1115/1.1605769.
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Abstract
Topics: Machinery , Mechanisms
Commentary by Dr. Valentin Fuster
J. Mech. Des. 2003;125(3):650. doi:10.1115/1.1605770.
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Abstract
Topics: Machinery , Design

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