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TECHNICAL PAPERS

J. Mech. Des. 1998;123(3):313-321. doi:10.1115/1.1371774.

Product development firms continually struggle to simultaneously keep product cost low while increasing product quality. This paper focuses on variation and its impact on the quality-failure costs—scrap, rework, extra labor, customer dissatisfaction, and product returns. In many cases, reducing quality failures requires an increase in product cost. Balancing these two costs is challenging because perfect information about process variability is rarely, if ever, available. As a result of process variation uncertainty, there is no clear optimal solution to the quality-failure cost/unit cost tradeoff. The author has observed that companies take one of two approaches to this dilemma: optimistic or pessimistic. The optimistic approach risks high rework costs to ensure the lowest cost product. On the other hand, the pessimistic approach forgoes potential unit cost reductions to avoid any quality failure. This paper presents a utility theory model of decision making under process capability uncertainty. This model is used to describe why either approach can be optimal depending on the organization, market, and product characteristics. In addition, information value theory is applied to explain the relative value of process capability information and variation reduction in the two approaches. The paper uses a frequently encountered design scenario to demonstrate the approach. In addition, a variety of other examples from industry are used to describe how the theory can be applied.

Commentary by Dr. Valentin Fuster
J. Mech. Des. 2001;123(3):322-329. doi:10.1115/1.1372705.

The automation concept is being applied to many areas as the automation system in the manufacturing field works more efficiently. Automation of the design process is also very important for the reduction of the entire engineering cost, and can be achieved by an excellent design process and software development. Design axioms have been announced as a general theoretical framework for all design fields. Application of the design axioms is investigated, and automation is obtained by computer programs. The design process can be analyzed and newly defined to satisfy the axioms. A software system can be designed according to the newly defined design process. In this research, a conventional design process for a TV glass design has been improved by an axiomatic approach, and a software system is designed for the automation of the design process. It is found that the conventional process is coupled, and the coupling causes inefficiencies. A new process is established by the application of axioms. A software design is conducted based on the new process and software development is carried out according to the software design. The developed software is exploited well in the real design.

Commentary by Dr. Valentin Fuster
J. Mech. Des. 1999;123(3):330-336. doi:10.1115/1.1371478.

This paper presents an integrated approach to the layout generation of 3D rectagonal objects and wiring area estimation. Problems of this type are encountered in various component layout tasks such as the space-efficient placement of electronic components in automobiles. The goal is to achieve high packing densities and fitting of objects in predefined design spaces while satisfying spatial constraints. The layout problem is formulated as mixed integer linear program and can be solved either by a branch&bound procedure or heuristically. The wiring area estimation is integrated in the problem formulation on the basis of a number of explicit wiring variants for each cable.

Commentary by Dr. Valentin Fuster
J. Mech. Des. 1999;123(3):337-345. doi:10.1115/1.1377282.

To address the conflicting requirements between holding specified surface quality and decreasing build time in layered manufacturing, we present a feature-based fabrication methodology whereby the curvature effects are localized within each decomposed volume. However, staircase interaction between the boundaries of the decomposed neighboring volumes creates geometric incompatibility for deposition, which further results in undesired material properties. This paper proposes a novel concept, feature interaction volume, to eliminate the staircase interaction. Based on this concept, a feature based volume decomposition algorithm is developed. This algorithm enables each decomposed volume to be fabricated independently and compatibly. Implementation and example results are also presented.

Commentary by Dr. Valentin Fuster
J. Mech. Des. 2000;123(3):346-352. doi:10.1115/1.1372190.

The paper presents an analytical approach to corner-filleted flexure hinges. Closed- form solutions are derived for the in-plane compliance factors. It is demonstrated that the corner-filleted flexure hinge spans a domain delimited by the simple beam and the right circular flexure hinge. A comparison that is made with the right circular flexure hinges indicates that the corner-filleted flexures are more bending-compliant and induce lower stresses but are less precise in rotation. The finite element simulation and experimental results confirmed the model predictions.

Commentary by Dr. Valentin Fuster
J. Mech. Des. 1999;123(3):353-358. doi:10.1115/1.1374197.

Previously, we have shown that, to realize an arbitrary spatial stiffness matrix, spring components that couple the translational and rotational behavior along/about an axis are required. We showed that, three such coupled components and three uncoupled components are sufficient to realize any full-rank spatial stiffness matrix and that, for some spatial stiffness matrices, three coupled components are necessary. In this paper, we show how to identify the minimum number of components that provide the translational-rotational coupling required to realize an arbitrarily specified spatial stiffness matrix. We establish a classification of spatial stiffness matrices based on this number which we refer to as the “degree of translational–rotational coupling” (DTRC). We show that the DTRC of a stiffness matrix is uniquely determined by the spatial stiffness mapping and is obtained by evaluating the eigenstiffnesses of the spatial stiffness matrix. The topological properties of each class are identified. In addition, the relationships between the DTRC and other properties identified in previous investigations of spatial stiffness behavior are discussed.

Topics: Stiffness
Commentary by Dr. Valentin Fuster
J. Mech. Des. 1999;123(3):359-366. doi:10.1115/1.1370977.

The dimensional synthesis of a spatial two revolute jointed dyad for path following tasks with applications to coupled serial chain mechanisms is presented. The precision point synthesis equations obtained using the rotation matrix approach form a rank-deficient linear system in the link-vector components. The nullspace of this rank-deficient linear system is derived analytically and interpreted geometrically. The nullspace vectors lead to the specification of additional constraints via the so-called auxiliary equations and to the solution of the linear system of equations. The geometry also allows the derivation of a closed form solution for the three design position problem. Finally, optimal path following by coupled R-R dyads is achieved by optimization over the free choice variables.

Topics: Chain , Design , Equations , Rotation
Commentary by Dr. Valentin Fuster
J. Mech. Des. 1998;123(3):367-374. doi:10.1115/1.1374198.

This paper presents the concept of underactuation applied to grippers and mechanical hands. The main objective of this work is the kinematic analysis and design of underactuated mechanisms. First, the kinematic and static modeling of these mechanisms is addressed and a general kinetostatic model is proposed. Then, a two-degree-of-freedom underactuated gripper based on a five-bar planar mechanism is studied in order to illustrate the usefulness of the model in a context of analysis and design.

Commentary by Dr. Valentin Fuster
J. Mech. Des. 2000;123(3):375-381. doi:10.1115/1.1370976.

This paper introduces several new types of parallel mechanisms with prismatic actuators whose degree of freedom is dependent on a constraining passive leg connecting the base and the platform. A general kinetostatic model is established for the analysis of the structural rigidity and accuracy of this family of mechanisms. The geometric model of this class of mechanisms is first introduced. Then, a lumped kinetostatic model is proposed in order to account for joint and link compliances. Additionally, the inverse kinematics and velocity equations are given for both rigid-link and flexible-link mechanisms. Finally, a few examples are given to illustrate the results.

Commentary by Dr. Valentin Fuster
J. Mech. Des. 2000;123(3):382-387. doi:10.1115/1.1372192.

This paper presents a general method for the analysis of any planar mechanism consisting of rigid links connected by revolute joints. The method combines a complex plane formulation [1] with the Dixon determinant procedure of Nielsen and Roth [2]. The result is simple to derive and implement, so in addition to providing numerical solutions, the approach facilitates analytical explorations. The procedure leads to a generalized eigenvalue problem of minimal size. Both input/output problems and the derivation of tracing curve equations are addressed, as is the extension of the method to treat slider joints.

Commentary by Dr. Valentin Fuster
J. Mech. Des. 1999;123(3):388-394. doi:10.1115/1.1370978.

A new approach to the synthesis of planar linkage mechanisms with approximate velocity constraints is proposed. The paper presents the first closed-form complex-number dyad solution to the ground pivot specification problem for two precision positions with velocity specified at one of the positions. The solution is then manipulated in order to add approximate velocity constraints to design methods for two exact positions and an unlimited number of approximate positions. The approximate position and velocity constraints facilitate more realistic representation of design objectives. Solution spaces are presented using two-dimensional ground-pivot maps. Computer implementation of the proposed methodologies would allow designers with little or no knowledge of the synthesis techniques to interactively explore maps of solutions for four-bar motion generation.

Commentary by Dr. Valentin Fuster
J. Mech. Des. 1999;123(3):395-401. doi:10.1115/1.1374196.

A model is presented in which the oscillations, and the forces thus produced, in a chain drive, working at moderate and high speed, can be calculated. Since the outer system affects the result it has been necessary to include this in the model. The mass of the chain is included in the model and both the gravitational forces and the inertia forces in the chain are taken into account. The elasticity in the links is included. The sprockets are connected by two spans, both of which have to be included in the model to fulfill the equilibrium equations for the rollers in contact with the sprockets. The position of the chain is given by the geometric conditions as well as the equilibrium condition. On the slack side a chain tensioner is used to reduce the transverse oscillation, which occur at higher speeds.

Commentary by Dr. Valentin Fuster
J. Mech. Des. 1999;123(3):402-407. doi:10.1115/1.1377016.

The instantaneous variation of pressure loads acting on the rotors of positive displacement rotary blowers may produce vibrations and noise that in some case produce the failure of the machine and of the piping. In a previous paper the authors determined the pressure loads acting on the rotors, starting from the geometry of the chambers that are formed during the rotor meshing and the thermodynamic transformation of the working fluid. The calculation of the loads has been made in a quasi-static manner. In this paper the model has been improved by taking into account the effects due to a closed volume chamber at the discharge. This assumption better reproduces the real cases and allows the researchers to perform more efficient calculations and more reliable predictions.

Commentary by Dr. Valentin Fuster
J. Mech. Des. 2000;123(3):408-415. doi:10.1115/1.1371477.

Effect of flexibility of an internal gear on the quasi-static behavior of a planetary gear set is investigated. A state-of-the-art finite elements/semi-analytical nonlinear contact mechanics formulation is employed to model a typical automotive automatic transmission planetary unit. The model considers each gear as deformable bodies and meshes them to predict loads, stresses and deformations of the gears. Actual support and spline conditions are included in the model. The rim thickness of the internal gear is varied relative to the tooth height and gear deflections and bending stresses are quantified as a function of rim thickness. Influence of rim thickness on the load sharing amongst the planets is also investigated with and without floating sun gear condition. The results are discussed in detail and guidelines regarding the design of a planetary internal gear are presented.

Commentary by Dr. Valentin Fuster
J. Mech. Des. 2000;123(3):416-421. doi:10.1115/1.1377281.

The geometry of a gear pair depends on the center distance and the included angle between the two axes of rotation along with the axial positions of the toe and heel (face width). During operation, loads can cause the gear system components to deflect such that the relative position and orientation between the gear elements change. This paper illustrates how certain gear body displacements are used to specify a gear pair’s geometric parameters that can improve contact during mesh. An illustrative example involving cylindrical gear elements is presented to demonstrate the procedure.

Topics: Gears , Deflection , Rotation
Commentary by Dr. Valentin Fuster
J. Mech. Des. 1999;123(3):422-430. doi:10.1115/1.1349420.

The early detection of failures in geared systems is an important industrial problem which has still to be addressed from both an experimental and theoretical viewpoint. The proposed paper combines some extensive numerical simulations of a single stage geared unit with localized tooth faults and the use of several detection techniques whose performances are compared and critically assessed. A model aimed at simulating the contributions of local tooth defects such as spalling to the gear dynamic behavior is set up. The pinion and the gear of a pair are assimilated to two rigid cylinders with all six degrees of freedom connected by a series of springs which represent gear body and gear tooth compliances on the base plane. Classical shaft finite elements including torsional, flexural and axial displacements can be superimposed to the gear element together with some lumped stiffnesses, masses, inertias, [[ellipsis]] which account for the load machines, bearings and couplings. Tooth defects are modeled by a distribution of normal deviations over a zone which can be located anywhere on the active tooth flanks. Among the numerous available signal processing techniques used in vibration monitoring, cepstrum analysis is sensitive, reliable and it can be adapted to complex geared system with several meshes. From an analytical analysis of the equations of motion, two complementary detection techniques based upon acceleration power cepstrum are proposed. The equations of motion and the contact problem between mating flanks are simultaneously solved by coupling an implicit time-step integration scheme and a unilateral normal contact algorithm. The results of the numerical simulations are used as a data base for the proposed detection techniques. The combined influence of the defect location, depth and extent is analyzed for two examples of spur and helical gears with various profile modifications and the effectiveness of the two complementary detection methods is discussed before some conclusions are drawn.

Commentary by Dr. Valentin Fuster
J. Mech. Des. 2000;123(3):431-435. doi:10.1115/1.1370496.

It has long been recognized that the fatigue life of a component can be divided into a crack initiation phase and a crack propagation phase, but researchers have typically ignored one phase or the other in their analytical models. Even in the stress-life method of life prediction, which implicitly includes both phases, no distinction is made between the initiation and propagation phases. In this paper a methodology for generating initiation and propagation S-N curves will be outlined. It will be shown that for components like gears, both phases represent significant portions of total life. It will also be shown that gear bending fatigue lives for variable amplitude load tests are better predicted by a two-stage linear damage theory compared to the commonly used Miner’s total life linear damage theory.

Commentary by Dr. Valentin Fuster
J. Mech. Des. 1999;123(3):436-446. doi:10.1115/1.1372191.

In this paper, a new type of a clutch by the name of the variable torque clutch with skewed rollers is first introduced and second investigated both theoretically and experimentally. It is comprised of an inner and an outer race that are each in spatial line contact with the crossed axis cylindrical rollers. Torque transmission is delivered by a slipping induced between the rollers and the races due to skewing the rollers. The equations of the race surfaces are derived and the geometrical properties are analyzed. Based on the kinematic analysis, a roller-wedge model is proposed for this clutch in order to visualize the motion at the tangency of the rollers and the races. By assuming the linear distribution of the contact force along the spatial contact line, the transmitted torque capacity and kinematic characteristics can be evaluated properly from the solution of a set of nonlinear equilibrium equations. Several prototypes of this clutch are manufactured and measured to show the validity of this design idea and the theoretical results. The computational results are found to coincide with the experimental data. In addition, the influences of the design parameters on the fundamental characteristics are discussed in detail.

Commentary by Dr. Valentin Fuster
J. Mech. Des. 2000;123(3):447-455. doi:10.1115/1.1371775.

Many axial-piston pumps utilize a swash plate for regulating discharge flow. In this research, the required control and containment forces are examined for a cradle-mounted, transverse-actuated swash plate. These forces are described in closed-form for providing the designer with information that is necessary for sizing these critical components within the pump. In this research, it is shown that improper design of the containment device will cause the swash plate to dislocate itself from the cradle. In general, it is noted that this failure mode is severe and that it may even cause catastrophic failure of the pump. In summary, a design criterion is presented which describes the limits of successful operation during both high and low-pressure conditions. Design and operational changes are suggested for improving the adequacy of the swash-plate containment design.

Commentary by Dr. Valentin Fuster
J. Mech. Des. 2000;123(3):456-463. doi:10.1115/1.1371476.

Rotary shouldered connections (RSC), used in the oil and gas industries, are probably the most stressed components of the drill string because they are subjected both to make-up torque and to axial and bending loads. Since loads can vary and can result in fatigue crack initiation and propagation, there is often severe damage to the first threads engaged. Such damage leads to shoulder load reduction and discontinuity in the drill string. Once we know the geometric dimensions and the materials of the pin and box elements composing the RSCs, API standards make it possible to evaluate the working limits of RSCs when they are subjected to make-up torque, torsion and tension. It is not, however, possible to establish the stress state of the connection for extreme working limits. The aim of this paper is to propose a numerical procedure, confirmed by full-scale experimental tests, which enables the evaluation both of the working limits, combined make-up and axial tensile loads, and of the stress state of RSCs for any load condition and, in particular, when RSCs are subjected to extreme combinations of make-up, torsion and axial tensile loads.

Commentary by Dr. Valentin Fuster

TECHNICAL BRIEFS

J. Mech. Des. 1999;123(3):464-468. doi:10.1115/1.1376396.

The pseudo-rigid-body model concept allows compliant mechanisms to be analyzed using well-known rigid-body kinematics. This paper presents a pseudo-rigid-body model for initially curved pinned-pinned segments that undergo large, nonlinear deflections. The model approximates the segment as three rigid members joined by pin joints. Torsional springs placed at the joints model the segment’s stiffness. This model has been validated by fabricating several such segments from a variety of different materials. Testing of the force-deflection behavior of these segments verified the accuracy of the model.

Commentary by Dr. Valentin Fuster
J. Mech. Des. 1999;123(3):468-472. doi:10.1115/1.1376397.

The aim of this paper is a detailed analysis of a particular mechanism with variable piston stroke. This crank mechanism is presently applied to metering pumps, because it allows the piston stroke to be adjusted in length and permits the pump flow to be changed also during the pump functioning. The following analysis shows the different characteristics of piston motions obtainable by changing the ratios among the mechanism rod lengths.

Topics: Pistons , Motion

BOOK REVIEW

J. Mech. Des. 2001;123(3):473. doi:10.1115/1.1403435.
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Commentary by Dr. Valentin Fuster

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