0


Article

J. Mech. Des. 2000;122(4):357-358. doi:10.1115/1.1320064.
Commentary by Dr. Valentin Fuster

TECHNICAL PAPERS

J. Mech. Des. 1999;122(4):359-370. doi:10.1115/1.1289637.

Functional models represent a form independent blueprint of a product. As with any blueprint or schematic, a consistent language or coding system is required to ensure others can read it. This paper introduces such a design language, called a functional basis, where product function is characterized in a verb-object (function-flow) format. The set of functions and flows is intended to comprehensively describe the mechanical design space. Clear definitions are provided for each function and flow. The functional basis is compared to previous functional representations and is shown to subsume these attempts as well as offer a more consistent classification scheme. Applications to the areas of product architecture development, function structure generation, and design information archival and transmittal are discussed. [S1050-0472(00)00704-2]

Commentary by Dr. Valentin Fuster
J. Mech. Des. 1999;122(4):371-376. doi:10.1115/1.1315299.

This paper presents a general graph grammar methodology for structure synthesis of mechanisms. Much of current mechanism design is based on a systematic method popularized by Freudenstein, Mruthyunjaya, and Tsai (among others). A graph grammar is a more natural expression for a method that relies on algebraic abstractions of graph theoretic principles. Our proposed grammar rules add vertices and loops to a start graph to obtain desired structural requirements. A grammar adaptation of an existing linear time algorithm for the detection of isomorphism is presented. Also presented is a specialized grammar for the structure synthesis of Epicyclic Gear Trains. A valid graph grammar for structure synthesis of mechanisms enables both the eventual automation of general atlas construction and atlas construction for customized mechanism classes. [S1050-0472(00)01904-8]

Commentary by Dr. Valentin Fuster
J. Mech. Des. 2000;122(4):377-384. doi:10.1115/1.1315592.

A wide range of formal methods have been devised and used for idea generation in conceptual design. Experimental evidence is needed to support claims regarding the effectiveness of these methods in promoting idea generation in engineering design. Towards that goal this paper presents a set of effectiveness metrics experimental methods, data collection and analysis techniques. Statistically based Design of Experiments (DOE) principles were used in developing the guidelines. Four classes of operating variables were considered to characterize the design problem and the environment. The effectiveness metrics proposed are based on outcome and consists of the quantity, quality, novelty, and variety of ideas generated. Two experimental approaches have been developed. In the Direct Method, the influence of the type of design problem and various parameters related to the procedure of an idea generation method is measured by using the method in its entirety. In the Indirect Method, each idea generation method is decomposed into key components and its overall effectiveness is predicted by experimentally studying the effectiveness of its components and their mutual interactions. [S1050-0472(00)02004-3]

Commentary by Dr. Valentin Fuster
J. Mech. Des. 1999;122(4):385-394. doi:10.1115/1.1290247.

In robust design, it is important not only to achieve robust design objectives but also to maintain the robustness of design feasibility under the effect of variations (or uncertainties). However, the evaluation of feasibility robustness is often a computationally intensive process. Simplified approaches in existing robust design applications may lead to either over-conservative or infeasible design solutions. In this paper, several feasibility-modeling techniques for robust optimization are examined. These methods are classified into two categories: methods that require probability and statistical analyses and methods that do not. Using illustrative examples, the effectiveness of each method is compared in terms of its efficiency and accuracy. Constructive recommendations are made to employ different techniques under different circumstances. Under the framework of probabilistic optimization, we propose to use a most probable point (MPP) based importance sampling method, a method rooted in the field of reliability analysis, for evaluating the feasibility robustness. The advantages of this approach are discussed. Though our discussions are centered on robust design, the principles presented are also applicable for general probabilistic optimization problems. The practical significance of this work also lies in the development of efficient feasibility evaluation methods that can support quality engineering practice, such as the Six Sigma approach that is being widely used in American industry. [S1050-0472(00)00904-1]

Commentary by Dr. Valentin Fuster
J. Mech. Des. 2000;122(4):395-402. doi:10.1115/1.1320441.

Snap-fit design has always been more of an art instead of an engineering activity. Research in this area focuses on generating finite element models for predicting the performance of snap-fit features. Such research typically uses fixed-end conditions at the base of the snap-fit feature. Often this is an unrealistic assumption, because snap-fits are usually molded on plastic parts with significant flexibility. The performance of snap-fits can be significantly influenced by this additional flexibility. To predict this performance of snap-fits it often becomes necessary to analyze the entire part, which can be a costly and time consuming process. There is no general methodology in the open literature to incorporate base-part flexibility into the design of snap-fit features. Existing work in this area is inaccurate and limited to certain base-part and snap-fit topologies. This paper proposes a new methodology called structural abstraction for incorporating base-part flexibility into snap-fit feature models. This methodology abstracts base-parts as spring elements with various stiffnesses. The underlying theory and the relevant relationships are developed and the approach is validated using several test cases. Independence of the approach to both base-part and snap-fit topologies is established and shown to be a major advantage of this technique. Use of this methodology will improve snap-fit analysis and give a more accurate estimation of retention strength. It is shown that in certain cases the improvement in accuracy over conventional finite element models of snap-fits can be as high as 70 percent. [S1050-0472(00)02504-6]

Commentary by Dr. Valentin Fuster
J. Mech. Des. 1998;122(4):403-410. doi:10.1115/1.1320820.

Many companies develop a market strategy built around a family of products. These companies regularly add new product variations to the family in order to meet changing market needs or to attract a broader customer base. Although the core functionality remains essentially unchanged across the products within a family, new functions, feature combinations and technologies are incorporated into each new product. If allowed to grow unchecked, these component variations, commonly referred to as “complexity”, can result in a loss of productivity or quality. The challenge lies in an effective management of product variations in the design studio and on the manufacturing floor. The key is to minimize non-value added variations across models within a product family without limiting customer choices. In this paper we discuss the factors that contribute to product complexity in general, and present an objective measure, called the Product Line Commonality Index, to capture the level of component commonality in a product family. Through our Walkman case study, we present a simple yet powerful method of benchmarking product families1 . This method gauges the family’s ability to share parts effectively (modularity) and to reduce the total number of parts (multi-functionality). [S1050-0472(00)02704-5]

Commentary by Dr. Valentin Fuster
J. Mech. Des. 1999;122(4):411-418. doi:10.1115/1.1311788.

This paper presents an approach wherein product design is viewed as a selection process with two main stages: design alternative generation and design alternative evaluation. The focus of this paper is mainly on a design alternative evaluation model in that designer’s preferences, customers’ preferences, and market competition are accounted for in order to select the best possible design. In the model, uncertainties in the product design life, market size and its yearly change, cost and its yearly change, price, and discount rate are considered. Product design selection of a cordless screwdriver is used as a demonstration example. However, the emphasis in the example is on the approach, and not on the details per se. [S1050-0472(00)01504-X]

Commentary by Dr. Valentin Fuster
J. Mech. Des. 1998;122(4):419-425. doi:10.1115/1.1289021.

The presented paper utilizes the basic theory of the envelope surface in differential geometry to investigate the undercutting line, the contact boundary line and the limit normal point of conjugate surfaces in gearing. It is proved that (1) the edges of regression of the envelope surfaces are the undercutting line and the contact boundary line in theory of gearing respectively, and (2) the limit normal point is the common tangent point of the two edges of regression of the conjugate surfaces. New equations for the undercutting line, the contact boundary line and the limit normal point of the conjugate surfaces are developed based on the definition of the edges of regression. Numerical examples are taken for illustration of the above-mentioned concepts and equations. [S1050-0472(00)00104-5]

Topics: Equations
Commentary by Dr. Valentin Fuster
J. Mech. Des. 1999;122(4):426-430. doi:10.1115/1.1319159.

This paper investigates, via numerical simulations, the finite displacements of all the known Bennett-based 6R overconstrained linkages: Goldberg’s 6R, variant Goldberg 6R, Waldron’s hybrid 6R, and Wohlhart’s hybrid 6R linkages. An investigation of the finite displacements of nine distinct linkages reveals that every Bennett-based 6R linkage, except for the isomerization of Wohlhart’s hybrid linkage, inherits the linear properties of the Bennett mechanism. The relative finite displacement screws of some non-adjacent links of these linkages form screw systems of the second order. Thirty-one screw systems are reported in this paper. [S1050-0472(00)02204-2]

Commentary by Dr. Valentin Fuster
J. Mech. Des. 1999;122(4):431-438. doi:10.1115/1.1290395.

The displacement analysis problem for planar and spatial mechanisms can be written as a system of multivariate polynomial equations. Elimination theory based on resultants and polynomial continuation are some of the methods that have been used to solve this problem. This paper presents a new approach to displacement analysis using the reduced Gröbner basis form of a system of equations under degree lexicographic (dlex) term ordering of its monomials and Sylvester’s Dialytic elimination method. Using the Gröbner-Sylvester hybrid approach, a finitely solvable system of equations F is transformed into its reduced Gröbner basis G using dlex term ordering. Next, using the entire or a subset of the set of generators in G, the Sylvester’s matrix is assembled. The vanishing of the resultant, given as the determinant of Sylvester’s matrix, yields the necessary condition for polynomials in G (as well as F) to have a common factor. The proposed approach appears to provide a systematic and rational procedure to the problem discussed by Roth, dealing with the generation of (additional) equations for constructing the Sylvester’s matrix. Three examples illustrating the applicability of the proposed approach to displacement analysis of planar and spatial mechanisms are presented. The first and second examples address the forward displacement analysis of the general 6-6 Stewart mechanism and the 6-6 Stewart platform, whereas the third example deals with the determination of the I/O polynomial of an 8-link 1-DOF mechanism that does not contain any 4-link loop. [S1050-0472(00)01204-6]

Commentary by Dr. Valentin Fuster
J. Mech. Des. 1999;122(4):439-446. doi:10.1115/1.1311612.

The structural characteristics associated with parallel manipulators are investigated. Using these characteristics a class of 3 degree-of-freedom parallel manipulators are enumerated. Several parallel manipulators with only translational degrees of freedom are identified and the 3-UPU parallel manipulator is chosen for design analysis and optimization. The kinematics of this 3-UPU parallel manipulator is studied. Two geometric conditions that lead to pure translational motion of the moving platform are described. Due to the simple kinematic structure, the inverse kinematics yields two equal and opposite limb lengths whereas the direct kinematics produces two possible manipulator postures with one being the mirror image of the other. The Jacobian matrix is derived and several singular conditions are discussed. Furthermore the conditions for existence of an isotropic point within the workspace are discussed and equations to compute the isotropic configurations of a 3-UPU manipulator are derived. Finally, we undertake architecture optimization and show that certain values of design variables maximize the global condition index of the 3-UPU manipulator. [S1050-0472(00)01404-5]

Commentary by Dr. Valentin Fuster
J. Mech. Des. 1998;122(4):447-456. doi:10.1115/1.1289388.

An optimization approach to computing the boundaries of the workspaces of planar manipulators is presented. This numerical method consists of finding a suitable radiating point in the output coordinate space and then determining the points of intersection of a representative pencil of rays, emanating from the radiating point, with the boundary of the accessible set. This is done by application of a novel constrained optimization approach that has the considerable advantage that it may easily be automated. The method is illustrated by its application to two planar mechanisms, namely a planar Stewart platform and a planar redundantly controlled serial manipulator. In addition to the exterior boundaries of the workspace, interior curves that represent configurations at which controllability and mobility may be limited, are also mapped. The optimization methodology, implemented here for the planar case, may readily be extended to spatial Stewart platforms. [S1050-0472(00)00304-4]

Commentary by Dr. Valentin Fuster
J. Mech. Des. 1998;122(4):457-463. doi:10.1115/1.1289139.

In this paper we present a novel method for approximating a finite set of n spatial locations with n spherical orientations. This is accomplished by determining a design sphere and the associated orientations on this design sphere which are nearest the n spatial locations. The design sphere and the orientations on it are optimized such that the sum of the distances between each spatial location and its approximating spherical orientation is minimized. The result is a design sphere and n spherical orientations which best approximate a set of n spatial locations. In addition, we include a modification to the method which enables the designer to require that one of the n desired spatial locations be exactly preserved. This method for approximating spatial locations with spherical orientations is directly applicable to the synthesis of spherical mechanisms for motion generation. Here we demonstrate the utility of the method for motion generation task specification in spherical mechanism design. [S1050-0472(00)00204-X]

Topics: Design , Mechanisms , Motion
Commentary by Dr. Valentin Fuster
J. Mech. Des. 1999;122(4):464-471. doi:10.1115/1.1290394.

This paper presents a closed-form approach, based on the theory of resultants, for deriving the coupler curve equation of 16 8-link mechanisms. The solution approach entails successive elimination of problem unknowns to reduce a multivariate system of 8 equations in 9 unknowns into a single bivariate equation. This bivariate equation is the coupler curve equation of the mechanism under consideration. Three theorems, which summarize key coupler curve characteristics, are outlined. The computational procedure is illustrated through two numerical examples. The first example addresses in detail some of the problems associated with the conversion of transcendental loop equations into an algebraic form using tangent half-angle substitutions. An extension of the proposed approach to the determination of degrees of input-output (I/O) polynomials and coupler curves for a general n-link mechanism is also presented. [S1050-0472(00)01104-1]

Commentary by Dr. Valentin Fuster
J. Mech. Des. 1998;122(4):472-478. doi:10.1115/1.1289770.

An efficient and systematic methodology for the topological synthesis of admissible fractionated geared differential mechanisms is presented. Based on the extension of the 2-dof automotive gear differential, it is shown that a fractionated geared differential mechanism can be decomposed into a main component and an input component. Characteristics of these two components are laid out, and the atlases of admissible input and main components are identified from the existing atlases of non-fractionated geared kinematic chains. With a systematic procedure to choose input and main components and select admissible connecting links, fractionated geared differential mechanisms with three and four input/output links are generated accordingly. [S1050-0472(00)00804-7]

Topics: Mechanisms , Gears , Equations
Commentary by Dr. Valentin Fuster
J. Mech. Des. 1998;122(4):479-483. doi:10.1115/1.1313826.

In this paper, the concept of kinematic fractionation is introduced for epicyclic gear trains (EGTs) which contains structural fractionation as a degenerate case. With the concept of kinematic fractionation, kinematically independent group(s) embedded in an EGT can be identified. A composition list, which depicts the links and the link connection in the associated group, is used to determine the type of fractionation. It is found that most previously enumerated structurally non-fractionated EGTs in the literature are kinematically fractionated. It is shown that a structurally non-fractionated EGT may be kinematically fractionated while a structurally fractionated EGT must be kinematically fractionated. The concept of kinematic fractionation can lead to efficient topological analysis of EGTs with physical comprehension. [S1050-0472(00)01604-4]

Commentary by Dr. Valentin Fuster
J. Mech. Des. 1999;122(4):484-488. doi:10.1115/1.1314867.

Proper modeling of joint clearance is of great importance in the analysis and design of multibody mechanical systems. The clearance may be due to wear or imperfection in manufacturing. When there is no lubricant in the clearance, solid-to-solid contact occurs. The impulse due to contact between the links is transmitted throughout the system. The presence of a lubricant avoids such contact, as the hydrodynamic forces developed by the lubricant film support the loads acting on the bodies and prevent the bodies from coming into contact. In this paper, an analysis of revolute joint clearances in multibody mechanical systems with and without lubricant is presented. Squeeze as well as viscous effects are considered utilizing the hydrodynamic theory of lubrication in long bearings. Unlike the traditional machine design approach, the instantaneous lubricant forces are the unknown and evaluated in terms of the known geometrical position and velocity of the journal and bearing. In the case of analysis of a joint clearance with no lubricant, a modified Hertzian relation is used to model the impact or contact between the journal and bearing, which includes a hysteresis damping term to account for the energy dissipation during impact. The methodology is applied for the analysis of a slider-crank mechanism having a clearance in the piston pin. The simulations are carried out with and without lubricant and the results are compared. It is shown that the lubricant results in a steady motion with fewer peaks in the required cranking moment for the system. [S1050-0472(00)01804-3]

Commentary by Dr. Valentin Fuster
J. Mech. Des. 1999;122(4):489-497. doi:10.1115/1.1319160.

Analysis of frictional impact in a multibody mechanical system requires a friction model capable of correct detection of all possible impact modes such as sliding, sticking, and reverse sliding. Conventional methods for frictional impact analysis have either shown energy gain or not developed for jointed mechanical system, and especially not for closed-chain multibody systems. This paper presents a general formulation for the analysis of impact problems with friction in both open- and closed-loop multibody mechanical systems. Poisson’s hypothesis is used for the definition of the coefficient of restitution, and thus the energy gains inherent with the use of Newton’s hypothesis are avoided. A canonical form of the system equations of motion using Cartesian coordinates and Cartesian momenta is utilized. The canonical momentum-balance equations are formulated and solved for the change in the system Cartesian momenta using an extension of Routh’s graphical method for the normal and tangential impulses. The velocity jumps are calculated by balancing the accumulated system momenta during the contact period. The formulation is shown to recognize all modes of impact; i.e., sliding, sticking, and reverse sliding. The impact problems are classified into seven types, and based on the pre-impact system configuration and velocities, expressions for the normal and tangential impulses are derived for each impact type. Examples including the tip of a double pendulum impacting the ground with some experimental verification, and the impact of the rear wheel and suspension system of an automobile executing a very stiff bump are analyzed with the developed formulation. [S1050-0472(00)02304-7]

Commentary by Dr. Valentin Fuster
J. Mech. Des. 1999;122(4):498-507. doi:10.1115/1.1289636.

Many flexible multibody applications are characterized by high inertia forces and motion discontinuities. Because of these characteristics, problems can be encountered when large displacement finite element formulations are used in the simulation of flexible multibody systems. In this investigation, the performance of two different large displacement finite element formulations in the analysis of flexible multibody systems is investigated. These are the incremental corotational procedure proposed in an earlier article (Rankin, C. C., and Brogan, F. A., 1986, ASME J. Pressure Vessel Technol., 108 , pp. 165–174) and the non-incremental absolute nodal coordinate formulation recently proposed (Shabana, A. A., 1998, Dynamics of Multibody Systems, 2nd ed., Cambridge University Press, Cambridge). It is demonstrated in this investigation that the limitation resulting from the use of the infinitesmal nodal rotations in the incremental corotational procedure can lead to simulation problems even when simple flexible multibody applications are considered. The absolute nodal coordinate formulation, on the other hand, does not employ infinitesimal or finite rotation coordinates and leads to a constant mass matrix. Despite the fact that the absolute nodal coordinate formulation leads to a non-linear expression for the elastic forces, the results presented in this study, surprisingly, demonstrate that such a formulation is efficient in static problems as compared to the incremental corotational procedure. The excellent performance of the absolute nodal coordinate formulation in static and dynamic problems can be attributed to the fact that such a formulation does not employ rotations and leads to exact representation of the rigid body motion of the finite element. [S1050-0472(00)00604-8]

Commentary by Dr. Valentin Fuster
J. Mech. Des. 1999;122(4):508-514. doi:10.1115/1.1320819.

A model was used, where the total gear mesh stiffness was approximated by two constant stiffness levels, in order to analyze the influence of the contact ratio on the dynamic response of spur gears. Due to the stiffness variation there is parametric excitation of the transmission error, which generally causes tooth separation at certain critical rotational speeds. The present paper discloses a method to analytically calculate which contact ratio to use in order to avoid tooth separation near a specific critical rotational speed. [S1050-0472(00)02604-0]

Commentary by Dr. Valentin Fuster
J. Mech. Des. 2000;122(4):515-522. doi:10.1115/1.1320821.

A model based upon a finite element procedure is introduced for analyzing the influence of tooth friction on spur and helical gear dynamics. The equations of motion are solved by combining a time-step integration method with several iterative algorithms aimed at satisfying normal and tangential contact conditions. Comparisons between simulated and measured quasi-static bearing forces are satisfactory and largely validate the theoretical developments. Results also reveal the potentially significant contribution of tooth friction to gear vibration and noise. Simulations are then extended to high speeds and the interest of considering both transmission error and tooth friction excitations to achieve silent gears is discussed. [S1050-0472(00)02804-X]

Commentary by Dr. Valentin Fuster
J. Mech. Des. 1999;122(4):523-528. doi:10.1115/1.1290248.

This paper presents a systematic model for the design and analysis of toroidal traction drive continuously variable transmissions (CVT). The contacts between the input disk, the roller and the output disk of the traction drive are formulated using the classical Hertzian contact theory. The traction force and side slip force occurring in CVT operation are modelled based on the elasto-hydrodynammic theory and are correlated to the traction drive geometric and kinematic parameters. The model allows for the quantitative analysis of traction drive operation under various torque inputs and over the desired ratio range. [S1050-0472(00)01004-7]

Topics: Force , Rollers , Traction , Disks
Commentary by Dr. Valentin Fuster
J. Mech. Des. 1998;122(4):529-535. doi:10.1115/1.1289390.

A new approach for the computerized simulation of load distribution in mismatched hypoid gears with point contact is presented. The load distribution calculation is based on the bending and shearing deflections of gear teeth, on the local contact deformations of the mating surfaces, on gear body bending and torsion, on the deflections of the supporting shafts, and on the manufacturing and alignment errors of the mating members. The tooth deflections of the pinion and gear teeth are calculated by FEM, and the tooth contact is treated in a special way: it is assumed that the point contact under load spreads over a surface along the “potential” contact line, which line is made up of the points of the mating tooth surfaces in which the separations of these surfaces are minimal, instead of assuming an elliptical contact pattern. The system of governing equations is solved by approximations and by using the successive-over-relaxation method. The corresponding computer program is developed. The calculations, performed by this program, show that in the case of hypoid gears, the new approach gives a more realistic contact pattern and contact pressure than the usually assumed and applied elliptical contact approach, especially for the tooth pairs contacting on the toe and on the heel of teeth, and in the case of load distribution calculations made in misaligned gear pairs. By using this program the influence of design data on load distribution parameters is investigated and discussed. [S1050-0472(00)00504-3]

Commentary by Dr. Valentin Fuster
J. Mech. Des. 1999;122(4):536-542. doi:10.1115/1.1311611.

In this paper a method for the design of new rotor profiles for high-sealing lobe pump is presented. The objective of this research is to improve the sealing property of lobe pumps by designing chamber profile conforming rotors. The deviation function method is adopted for the design. The resultant rotors are trapping-free and have C1 continuity. A design procedure for rotor generation is also developed. A sealing index is defined to evaluate the sealing property of lobe pumps. Our results show that it is possible to design many new rotor profiles that have better sealing property than conventional involute rotors. [S1050-0472(00)01304-0]

Commentary by Dr. Valentin Fuster
J. Mech. Des. 1998;122(4):543-552. doi:10.1115/1.1288217.

This paper proposes a systematic synthesis method for twin-screw rotor profiles for compressors. Both “original generating curves” and “generated curves” are distributed on each rotor profile, and all the geometric parameters of these curves can be determined with satisfying the conditions of continuity in tangency by given only several specific parameter values. The contact lines on rotor surfaces and the blowhole area calculation are also presented. Three cases of optimization problems are shown in this paper and both contact-line length and blowhole area are reduced when letting the contact-line length be the object function with a constraint of blowhole area. [S1050-0472(00)01103-X]

Commentary by Dr. Valentin Fuster
J. Mech. Des. 1999;122(4):553-559. doi:10.1115/1.1313827.

In this research, the diameter of the shaft within an axial-piston swash-plate type hydrostatic pump is considered from a stress point of view. To analyze the loading of the shaft, the components within the pump are studied using a force and torque diagram and it is shown that the loads are applied differently for three main sections of the shaft. From the force and torque diagram, the actual shaft loads are determined based upon the geometry of the pump and the working pressure of the hydraulic system. Using well-accepted machine design practices, governing equations for the shaft diameter are produced for the various regions of loading along the shaft. These equations consider both bending and torsional stresses on the outer surface of the shaft. Results for the required shaft diameter are then computed for a typical pump design and compared to the geometry of an actual shaft. It is noted that stress concentrations can significantly alter these results and that the required shaft diameter can be reduced by applying the proper heat treatments and increasing the shaft strength. Finally, the designer is cautioned regarding the deflection difficulties that can arise when the shaft diameter is reduced too much. [S1050-0472(00)01704-9]

Commentary by Dr. Valentin Fuster
J. Mech. Des. 1998;122(4):560-566. doi:10.1115/1.1319158.

This paper demonstrates the automatic design synthesis of continuum structures by the process of topology/shape optimization. The problem is solved as a discrete optimization problem using the genetic algorithm (GA). Past efforts using this approach have not been very effective due to the lack of an appropriate structural geometric representation which is highly essential to the success of the evolutionary processes of the GA. Based on the morphology of living creatures, a representation scheme has been developed using arrangements of skeleton and ‘flesh’ to define structural geometry. This scheme facilitates the transmission of topological and shape characteristics across generations in the evolutionary process, and will not render any structurally invalid designs. Good results are illustrated using this scheme to design a compliant mechanism and a cantilever beam. [S1050-0472(00)02104-8]

Commentary by Dr. Valentin Fuster
J. Mech. Des. 1999;122(4):567-574. doi:10.1115/1.1319319.

Mechanical parts are modeled as (predominantly rigid) solid shapes that may move in space in order to function, be manufactured (for example, machine or be machined), and be assembled or disassembled. While it is clear that such mechanical shapes are greatly influenced by collision, interference, containment, and contact constraints through prescribed motions, the motion itself is usually not part of these shape models. This in turn leads to proliferation of computational methods for modeling and analysis of various motion-related constraints. We show that all motion-related constraints can be formulated and applied within the same computational framework that treats motion as an integral part of the model. Our approach relies on two computational utilities. The first one is the unsweep operation which, given an arbitrary n-dimensional subset of Euclidean space E and a general motion M, returns the largest subset of E that remains inside E under M. The second modeling utility is a disjoint decomposition of space induced by the operations of unsweep and the standard set operations. The proposed approach subsumes and unifies the traditional sweep-based modeling of moving parts, and provides improved computational support for mechanical shape design. [S1050-0472(00)02404-1]

Topics: Motion
Commentary by Dr. Valentin Fuster
J. Mech. Des. 1998;122(4):575-582. doi:10.1115/1.1289389.

Models of the dynamics of multibody systems generally result in a set of differential-algebraic equations (DAE). State-space methods for solving the DAE of motion are based on reduction of the DAE to ordinary differential equations (ODE), by means of local parameterizations of the constraint manifold that must be often modified during a simulation. In this paper it is shown that, for vehicle multibody systems, generalized coordinates that are dual to suspension and/or control forces in the model are independent for the entire range of motion of the system. Therefore, these additional coordinates, together with Cartesian coordinates describing the position and orientation of the chassis, form a set of globally independent coordinates. In addition to the immediate advantage of avoiding the computationally expensive redefinition of local parameterization in a state-space formulation, the existence of globally independent coordinates leads to efficient algorithms for recovery of dependent generalized coordinates. A topology based approach to identify efficient computational sequences is presented. Numerical examples with realistic vehicle handling models demonstrate the improved performance of the proposed approach, relative to the conventional Cartesian coordinate formulation, yielding real-time for vehicle simulation. [S1050-0472(00)00404-9]

Commentary by Dr. Valentin Fuster

BOOK REVIEWS

J. Mech. Des. 2000;122(4):583. doi:10.1115/1.1334346.
FREE TO VIEW
Abstract
Topics: Design , Mechanisms
Commentary by Dr. Valentin Fuster
J. Mech. Des. 2000;122(4):583. doi:10.1115/1.1334345.
FREE TO VIEW
Abstract
Topics: Linkages , Design

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In