bluuebunny/crossref_metadata_2025 huggingface dataset:
Optimum Design of Crown Brakes
Authors: Elbella A. , Seireg A.
Published: June 2008

The use of crown brakes with heat input from both the inner and outer surfaces has been suggested as a means of improving the performance of frictional brakes. This paper presents an algorithm for the design of the optimal thermal load sharing and configuration of the rotor for brakes with different ratios of inner and outer radius. Several illustrative examples are considered and the results show that significant improvement in the performance and weight of the brake rotor can be achieved by this approach.
Optimality and Constrained Derivatives in Two-Level Design Optimization
Authors: Azarm S. , Li W.-C.
Published: June 2008

The objective of this paper is twofold. First, an optimality test is presented to show that the optimality conditions for a separable two-level design optimization problem before and after its decomposition are the same. Second, based on identification of active constraints and exploitation of problem structure, a simple approach for calculating the gradient of a “second-level” problem is presented. This gradient is an important piece of information which is needed for solution of two-level design optimization problems. Three examples are given to demonstrate applications of the approach.
A Study on Jumping-Over-Teeth Phenomenon in Roller Chain Drive
Authors: Yixing Wang , Zhifeng Zheng , Guangyi Zhang
Published: June 2008

This paper introduces the experimental device used in the research of the jumping-over-teeth in the roller chain drive, describes the differences and the similarities between the jumping-over-teeth at the driving sprocket and at the driven sprocket, analyzes the likelihood of this phenomenon occurring at the driven sprocket, and presents pictures of the two kinds of jumping-over-teeth and the curve diagram of the chain link tension during the experiment. In addition, the paper also provides the formula of the ultimate service load for the roller chain drive without jumping-over-teeth.
Influence of Gear Tooth Geometry on Tooth Stress of External and Internal Gears
Authors: von Eiff H. , Hirschmann K. H. , Lechner G.
Published: June 2008

Type and geometry of the cutter influence the generated fillet in a gear tooth. Thus optimization of the cutter dimensions is an important step in minimizing gear stress. Gear tooth geometry of external and internal involute gears can be described by the same equations, if we apply the following rule: The number of teeth is positive in external gears and negative in internal gears; the rack has an infinite number of teeth. We demonstrate that both gear geometry and tooth stress, i.e., the location of maximum tangential stress, the amount of tooth stress and the stress concentration factor, change continuously from external to internal gears. The results obtained by FEM computations are verified by photoelastic experiments. Data for calculation of gears, especially internal gears, are presented and discussed.
Optimum Tooth Flank Corrections for Helical Gears
Authors: Weck M. , Mauer G.
Published: June 2008

Growing requirements on the running behavior and the load carrying capacity of heavy-duty gears and furthermore, the expanding techniques in the field of gear manufacturing are demanding suitable designing methods for tooth flank corrections. In order to calculate these corrections the spatial stress and deformation state in the mesh is determined based on the finite element method. Calculated examples of corrected helical gears show that even simple geometric modifications of the flanks which do not require advanced manufacturing methods can improve the gear characteristics so that an increased transferable power and a reduction in noise emission can be expected.
The Compliance of Solid, Wide-Faced Spur Gears
Authors: Steward J. H.
Published: June 2008

In this paper, the requirements for an accurate 3D model of the tooth contact-line load distribution in real spur gears are summarized. The theoretical results (obtained by F.E.M.) for the point load compliance of wide-faced spur gear teeth are set out. These values compare well with experimental data obtained from tests on a large spur gear (18 mm module, 18 teeth).
Formulation of a Laminated Shell Theory Incorporating Embedded Distributed Actuators
Authors: Jia J. , Rogers C. A.
Published: June 2008

Smart materials have created new paradigms for structural design by introducing new concepts for vibration, damage, and structural control. Shape memory alloy reinforced composites are some of the newest and most versatile of this category of novel materials. They have shown tremendous versatility to adaptively and actively tailor mechanical and physical properties of structures and to perform shape and damage control. Moreover, the have generated new concepts for acoustic and vibration control. However, the unique behavior of the shape memory alloy fibers used as active elements within the composite also poses some difficult and interesting problems for describing the mechanical behavior of SMA reinforced structures. This paper will describe the formulation of a generalized laminate shell theory that incorporates embedded distributed actuators, i.e., shape memory alloy fibers or piezoelectric films. The theories consider the nonlinear strain-temperature-stress coupling for shape memory alloy actuators and the simplifications for analyzing piezoelectric actuators. Some of the computational difficulties of predicting the behavior of SMA reinforced shells will be discussed.
Nonlinear Viscoelastic Modelling of the Fiber-Matrix Interphase in Composite Materials
Authors: Sancaktar E. , Zhang P.
Published: June 2008

A nonlinear viscoelastic analysis of the carbon fiber-thermoset (or thermoplastic) matrix interphase is presented. The second order nonlinear partial differential equation governing the state of stress at the fiber-matrix interphase is solved by using an iterative scheme involving successive differentiation and Taylor expansions to satisfy the boundary conditions. Additional iteration is used for the case with nonlinear viscoelastic matrix material. The results reveal that the thickness and material properties of the interphase have strong influence in reducing the shear stress magnitudes and distribution along the fiber. The analysis and results provide valuable insight into the application and interpretation of the single fiber tension (fragmentation) test procedure and the design of “tailored interphases.”
On the Geometry of Geared 5-Bar Motion
Authors: Gibson C. G. , Marsh D.
Published: June 2008

A new approach is adopted to study the geometry of the coupler curves associated to geared 5-bar motion. The key idea is to think of a configuration of the mechanism as a point in a higher - dimensional configuration space; the family of all configurations is then represented by an algebraic curve in that space. Coupler curves appear naturally as projections of this curve, so their properties can be deduced by projection, independent of any explicit knowledge of their equations.
Topological Analysis of Single-Degree-of-Freedom Planetary Gear Trains
Authors: Olson D. G. , Erdman A. G. , Riley D. R.
Published: June 2008

Graph theory has been demonstrated by many researchers to be useful during the conceptual phase of mechanism design. For the particular class of mechanisms known as planetary gear trains, the graph representation has been used primarily for “topological synthesis,” the enumeration of kinematic chains satisfying the requirements for planetary gear trains. The subsequent “topological analysis” steps resulting in the specification of ground, input, and output links, have received very little attention in the literature, perhaps because the conventional graph representation for topological analysis, and utilizes a new graph representation which enables these steps to be performed in a straightforward manner. It is shown that among the thirteen distinct displacement graphs representing planetary geared kinematic chains with five links and one degree-of-freedom, only four distinct planetary gear trains result after assigning the ground, input, and output links subject to meaningful topological requirements.
Performance Evaluation of Four-Bar Linkages for Rigid-Body Guidance Based on Generalized Coupler Curves
Authors: Angeles J. , Ma O.
Published: June 2008

The concept of generalized coupler curves of linkages is introduced in this paper. Using this concept, the study of path generation and rigid-body guidance can be done within the same framework for analysis, synthesis and optimization of linkages. Moreover, a unified method of performance evaluation for rigid-body guidance is presented, that is applicable to four-bar linkages of any type, as long as the linkages have quadratic input-output or input-coupler functions. The method is an extension of the performance-evaluation method for path generation introduced in a previous paper. That method is based on the usual coupler curves, and hence, is only applicable to path-generation problems. The present method is based on generalized coupler curves, and is, thus, applicable to the problems of both path-generation and rigid-body guidance. It is oriented towards the iterative optimization of rigid-body-guidance tasks with four-bar linkages, and hence, considers numerical complexity as a determining issue. Numerical examples in which the method is applied to a planar four-bar linkage and a spherical four-bar linkage are included.
An Integrated System for Design of Mechanisms by an Expert System—Domes: Applications
Authors: Yang B. , Datseris P. , Datta U. , Kowalski J.
Published: June 2008

Two mechanism design problems are tested through the developed expert system DOMES (Design Of Mechanism by an Expert System) to check its performance. The two problems are Variable Stroke Piston Engine design by Freudenstein and Maki [16] and Robot Gripper design by Datseris and Palm [19]. The results from these two applications indicate that the automated techniques effectively identify all previously obtained solutions via manual techniques. Additional solutions are also identified and several errors of the manual process are detected. The developed methodologies and software of DOMES appear to perform a complete and unbiased search of all possible candidate designs and are not prone to the errors of the manual process.
Rotatability Laws for N-Bar Kinematic Chains and Their Proof
Authors: Ting Kwun-Lon , Liu Yung-Way
Published: June 2008

This paper presents a thorough proof and adds valuable insight into the theorems [1] concerning the mobility of planar N-bar linkages. The paper includes four parts: the assemblability, the revolvability between two links, the full rotatability, and the classification. The proof is based on the assemblability condition of N-bar linkages and the revolvability condition of an angle. Examples are also provided to further clarify the use of these theorems. In these theorems, Grashof’s Law becomes a very special case.
Sensitivity Distribution in the Synthesis Solution Space of Four-Bar Linkages
Authors: Faik S. , Erdman A. G.
Published: June 2008

This paper describes the sensitivity to tolerances of four-bar linkage link angles in terms of two nondimensional quantities σ and τ. The traces of these quantities are then plotted in the (λ1, λ3, λ4) space thus allowing the designer to synthesize a fourbar linkage with a prescribed sensitivity value and predict the tolerance required to achieve a certain accuracy on link angles.
Development of a New Geneva Mechanism With Improved Kinematic Characteristics
Authors: Fenton R. G. , Zhang Y. , Xu J.
Published: June 2008

A Geneva wheel with curved slots is proposed as an intermittent rotary motion generating mechanism. The proposed mechanism has vastly improved kinematic characteristics. Changing the slot shape from a straight radial line to a curved line results in the elimination of shock loading at the beginning and end of the motion cycles and reduces the wheel peak velocity and peak acceleration values, making this new mechanism well suited for high speed applications. In addition, the designer can freely select the dwell to motion time ratio of the wheel. Furthermore, this paper presents a great improvement to the design of a curve slotted Geneva wheel, by introducing an offset to the curved slot. The offsetting technique, which does not alter the kinematic characteristics of the mechanism, modifies the shape of the slot. A suitable offset can yield a curved slot acceptable for practical applications. This development provides an important tool for designing a simple, practical and reliable intermittent motion generating mechanism with excellent kinematic characteristics.
Modeling, Simulation, and Modal Analysis of a Hydraulic Valve Lifter With Oil Compressibility Effects
Authors: Hatch C. T. , Pisano A. P.
Published: June 2008

A two-degree-of-freedom (2-DOF), analytical model of a hydraulic valve lifter is derived. Special features of the model include the effects of bulk oil compressibility, multimode behavior due to plunger check valve modeling, and provision for the inclusion of third and fourth body displacements to aid in the use of the model in extended, multi-DOF systems. It is shown that motion of the lifter plunger and body must satisfy a coupled system of third-order, nonlinear differential equations of motion. It is also shown that the special cases of zero oil compressibility and/or 1-DOF motion of lifter plunger can be obtained from the general third-order equations. For the case of zero oil compressibility, using Newtonian fluid assumptions, the equations of motion are shown to reduce to a system of second-order, linear differential equations. The differential equations are numerically integrated in five scenarios designed to test various aspects of the model. A modal analysis of the 2-DOF, compressible model with an external contact spring is performed and is shown to be in excellent agreement with simulation results.
Identification and Minimization of Deviations of Real Gear Tooth Surfaces
Authors: Litvin F. L. , Zhang Yi , Kieffer J. , Handschuh R. F.
Published: June 2008

The authors propose an approach that uses coordinate measurements of the real surface to: (a) determine the real applied machine-tool settings, (b) determine the deviations of the real surface from the theoretical one, (c) minimize the deviations by correction of the machine-tool settings, and (d) represent the real surface analytically in the same Gaussian coordinates as the theoretical one.
Four-Bar Path Generation Synthesis by a Continuation Method
Authors: Subbian T. , Flugrad D. R.
Published: June 2008

A different approach for the synthesis of four-bar planar path generating mechanisms is presented. A continuation method is used to solve the system of nonlinear equations derived for the path generating problem. A brief description of the method is provided followed by the development of equations representing the four-bar linkage. The implementation of the method for five position path generation is discussed in detail and the solutions for two examples are presented.
Simulation of Planar Dynamic Mechanical Systems With Changing Topologies—Part 1: Characterization and Prediction of the Kinematic Constraint Changes
Authors: Gilmore B. J. , Cipra R. J.
Published: June 2008

Due to changes in the kinematic constraints, many mechanical systems are described by discontinuous equations of motion. This paper addresses those changes in the kinematic constraints which are caused by planar bodies contacting and separating. A strategy to automatically predict and detect the kinematic constraint changes, which are functions of the system dynamics, is presented in Part 1. The strategy employs the concepts of point to line contact kinematic constraints, force closure, and ray firing together with the information provided by the rigid bodies’ boundary descriptions, state variables, and reaction forces to characterize the kinematic constraint changes. Since the strategy automatically predicts and detects constraint changes, it is capable of simulating mechanical systems with unpredictable or unforessen changes in topology. Part 2 presents the implementation of the characterizations into a simulation strategy and presents examples.
Simulation of Planar Dynamic Mechanical Systems With Changing Topologies—Part 2: Implementation Strategy and Simulation Results for Example Dynamic Systems
Authors: Gilmore B. J. , Cipra R. J.
Published: June 2008

Part 2 presents a technique which uses the general point to line kinematic constraint equation presented in part 1 coupled with an incidence matrix to automatically reformulate the kinematic constraint equations between contacting or separating rigid bodies and solve the resulting dynamic equations of motion. The automatic determination of system connectivity coupled with impulse-momentum theory enables the strategy to handle impact between rigid bodies in line contact or between rigid bodies in topologically complex systems. The characterizations of the changes in the kinematic constraints, as described by Part 1, are combined with the incidence matrix and impact analysis to form an automatic dynamic simulation strategy. The strategy automatically predicts, detects, and determines the changes in the system topology and then reformulates the equations of motion without the user specifying the kinematic constraint changes and resulting system topology. The simulation results of two example systems are presented. The examples illustrate the effect the boundaries have on a system’s motion and show that the only connectivity data required by the strategy is the initial system topology.
The Determination of the Probabilistic Properties of Velocities and Accelerations in Kinematic Chains With Uncertainty
Authors: Lee S. J. , Gilmore B. J.
Published: June 2008

A probabilistic model and methods to determine the means and variances of the velocity and acceleration within stochastically-defined planar pin jointed kinematic chains are presented. The presented model considers the effect of tolerances on link length and radial clearance and uncertainty of pin location as a net effect on the link’s effective length. The determination of the mean values and variances of the output variables requires the calculation of sensitivities of secondary variables with respect to the random variables. It is shown that this computation is straightforward and can be accomplished by a conventional kinematic analysis package. Thus, the concepts of tolerance and clearance have been captured by the model and analysis. The only input data is the nominal linkage model and statistical information. The “effective link length” model is shown to be applicable to both analytical solution and Monte Carlo simulation. The results from both methods are compared. This paper solves the higher-order kinematics problem for the probabilistic design analysis of stochastically defined mechanisms.
The Roseville Bomb Disaster Simulated Train Braking System Tests and Boxcar Wood Floor Ignition Experiments
Authors: Ross B. , Parikh P. G.
Published: June 2008

A massive chain of property damaging explosions involving an ammunition train occurred at the railroad yard, Roseville, California. The train had pulled into the yard after a night trip of some 100 miles across Donner Summit and down the extended Norden-Roseville grade. Physical evidence confirmed that first explosions were centered at a DODX type boxcar loaded with 250 lb. bombs. Further, bomb cook-off detonation tests established that the triggering bomb blast was not a result of shock loads but rather derived from an engulfing fire initiated in the boxcar wood plank floor under influence of extended heavy braking action on the mountain grade. It was also suspected that high friction composition brake shoes were fitted on the car as replacements for cast iron shoes but the brake mechanical linkage lever ratios had not been modified as required. Results of a comprehensive research program are presented within context of the explosion event, and include analytical computer simulation of train descent profiles on mountain grades through full scale dynamometer tests with actual rail wheels and ultimately more scientific scaled wood floor ignition experiments in the laboratory. The thermal response of a simulated DODX boxcar wood floor was studied through experiments, full scale at a rail wheel dynamometer test facility, and in the laboratory. Certain input data for the wood floor ignition test program were measured on an actual boxcar joined with a freight train consist in transit down the Norden-Roseville grade. Two series of scaled wood ignition experiments were conducted on simulated DODX boxcar floors. Objectives of these tests were to determine: Influence of a cooling air stream on the ignition behavior of radiantly heated wood surfaces, and effectiveness of DODX (stand-off) and AAR (flush) type spark shields in preventing ignition of wood surfaces under radiant heating. It was found that for radiant heat flux levels representative of high friction composition shoes under severe train braking conditions, low speed airflow (wind) exerts a dramatic influence on the wood ignition time. For example, average ignition time for a simulated boxcar floor at a heat flux level of 0.4 cal/cm2sec was determined to be 15.6 min. with a 5 mph wind as compared to 3.6 min. with no wind. In the spark shield effectiveness tests, conducted at heat flux levels representative of cast iron shoes under severe braking conditions, the DODX (stand-off) type spark shield failed to prevent spontaneous flaming ignition of a wood surface directly above it. Under identical conditions, no flaming ignition was encountered with the AAR (flush) type spark shield.
Hybrid (Symbolic-Numerical) Optimization in Mechanism Design for the Elimination of Redundant Constraints
Authors: Hoeltzel D. A. , Chieng Wei-Hua
Published: June 2008

Hybrid optimization, a new approach to design optimization employing both symbolic reasoning and algorithmic analysis, has been applied to the design of kinematic pairs in mechanisms. This hybrid design methodology provides a three-step systematic approach for (1) combining the degrees-of-freedom found in simple, lower kinematic pairs to obtain more complex but robust higher pairs, (2) judging inappropriately assigned joints for the elimination of redundant kinematic constraints and harmful mobilities, and (3) assisting nonexpert designers in applying nonlinear programming algorithms for detailed numerical design optimization of kinematic pairs. An example taken from the design of a spatial mechanism, specifically a universal joint, is presented and serves to demonstrate the utility of this procedure for detailed hybrid design optimization of kinematic pairs in mechanisms.
Symbolic Closed-Form Modeling and Linearization of Multibody Systems Subject to Control
Authors: Lieh Junghsen , Haque Imtiaz-ul
Published: June 2008

Symbolic closed-form equation formulation and linearization for constrained multibody systems subject to control are presented. The formulation is based on the principle of virtual work. The algorithm is recursive, automatically eliminates the constraint forces and redundant coordinates, and generates the nonlinear or linear dynamic equations in closed-form. It is derived with respect to principal body coordinates and a moving reference frame that allows one to generate the dynamic equations for multibody systems moving along curved track or road. The output equations may be either in syntactically correct FORTRAN form or in the form as derived by hand. A procedure that simplifies the trigonometric expressions, linearizes the geometric nonlinearities, and converts the linearized equations in state-space form is included. Several examples have been used to validate the procedure. Included is a simulation using a seven-DOF automobile ride model with active suspensions.
Comparison of Hypotrochoidal and Epitrochoidal Gerotors
Authors: Beard J. E. , Hall A. S. , Soedel W.
Published: June 2008

The planar rotary mechanisms, by virtue of its volume changing ability can be used as a pump, engine, or compressor. Most of the types of rotary mechanisms used today, from the Wankel rotary engine to the gerotor pump, are based on epitrochoidal generation and its conjugate shape. This paper presents a very general mathematical relationship for a generating arc traveling on a hypotrochoidal path and also compares the flow rate, pocket displacement, and compression ratios of the hypotrochoidal and epitrochoidal generated profiles.
Unified Spherical Curvature Theory of Point-, Plane-, and Circle-Paths
Authors: Ting Kwun-Lon , Bunduwongse Ruj
Published: June 2008

This paper presents a unified treatment on the spherical curvature theory of point-, plane-, and circle-, paths or direct and inverse kinematics. It features the use of spherical inverse Euler-Savary equation to identify the kinematic loci such as return cone, double cusp axes, center-axis cone, and Burmester center axes. These results are then applied to the curvature theory of plane-path or circle-path to identify return plane, center plane, Ball’s plane, and Burmester plane. It explains satisfactorily the duality between point- and plant-paths.
A Recursive Formulation for Real-Time Dynamic Simulation of Mechanical Systems
Authors: Bae Dae-Sung , Hwang Ruoh-Shih , Haug Edward J.
Published: June 2008

A new recursive algorithm for real-time dynamic simulation of mechanical systems with closed kinematic loops is presented. State vector kinematic relations that represent translational and rotational motion are defined to simplify the formulation and to relieve computational burden. Recursive equations of motion are first derived for a single loop multi-body system. Faster than real-time performance is demonstrated for a closed loop manipulator, using an Alliant FX/8 multiprocessor. The algorithm is extended to multi-loop, multi-body systems for parallel processing real-time simulation in companion papers [1, 2] where performance of the algorithm on a shared memory multi-processor is compared with that achieved with other dynamic simulation algorithms.
Optimization of Dynamic Forces in Mechanical Hands
Authors: Nahon M. A. , Angeles J.
Published: June 2008

Mechanical hands have become of greater interest in robotics due to the advantages they offer over conventional grippers in tasks requiring dextrous manipulation. However, mechanical hands also tend to be more complex in construction and require more sophisticated analysis to determine the forces in the system. A mechanical hand can be described as a kinematic chain with time-varying topology which becomes redundantly actuated when an object is grasped. When this occurs, care must be exercised to avoid crushing the object or generating excessive forces within the mechanism. In the present work, this problem is formulated as a constrained quadratic optimization problem. The forces to be minimized form the objective, the dynamic equations of motion form the equality constraints, and the finger-object contacts yield the inequality constraints. The quadratic-programming approach is shown to be advantageous due to its ability to minimize “internal forces.” A technique is proposed for smoothing the discontinuities in the force solution which occur when the topology changes.
A Mathematical Model for the Tooth Geometry of Circular-Cut Spiral Bevel Gears
Authors: Fong Z. H. , Tsay Chung-Biau
Published: June 2008

A complete tooth geometry of the circular-cut spiral bevel gears has been mathematically modeled. The mathematical model has been divided into several independent modules, each representing an individual kinematic relation or tool-setting, with examples included. A comparison with the spiraloid model has also been made in this paper. The mathematical model can be applied to simulate and calculate the tooth profiles for the Duplex Method, Helical Duplex Method, Formate Method, and Modified Roll Method for circular-cut spiral bevel gears. It can also be applied to the computer numerical controlled (CNC) machining, computer-aided finite element stress analysis, and tooth contact analysis (TCA) for the spiral bevel gear.
Effect of Tooth Contact and Gear Dimensions on Transmission Errors of Loaded Hypoid Gears
Authors: Sugimoto M. , Maruyama N. , Nakayama A. , Hitomi N.
Published: June 2008

The effect of the tooth contact and alignment error of the hypoid gear assembly on transmission error was investigated with a new measuring apparatus which can measure the transmission errors of loaded hypoid gears assembled into a final drive unit. Measurements indicate that transmission error predictions made with the TCA and LTCA — analytical tools developed by Gleason Works for a no-load and loaded state, respectively — have sufficient accuracy when actual data on the gear tooth surface and alignment error of the gear assembly are used in the calculations. A systematic examination has also been made of the effects of tooth contact and gear assembly alignment error on transmission error on the basis of the LTCA calculations. It was found that the transmission errors relative to the applied load varied not only according to the tooth contact but also the no-load transmission error of the gears. This relationship was also examined by taking into account the effects of the gear dimensions. It was confirmed through calculation and experiment that a small module design was effective in reducing transmission error.
Field Effects in Fatigue Crack Initiation: Long Life Fatigue Strength
Authors: Sheppard S. D.
Published: June 2008

This work is focused on explaining observed fatigue crack initiation behavior in notched members in terms of the stress state in a finite volume at the notch root. In principle, this is no different than the work of several other researchers. What is different is the manner in which the stress fields were predicted; namely using the finite element method. By using this approach, no approximations were necessary as to the form of the stress field at the notch root. This implies that this approach is extendable to complex geometries and to the finite life regime where plastic flow is expected at the notch root.
An Alternative to the Weibull Function for Some Cases
Authors: Neville D. J. , Kennedy J. B.
Published: June 2008

Doubt about the applicability of the Weibull function has been expressed by various workers, some of whom have suggested modifications to the Weibull function. Such modifications usually involve more parameters than the original Weibull function being thus much more flexible and thereby, in some cases, providing a good fit if the numerous (up to six) parameters can be estimated. These functions are not valid as asymptotic extreme-value distribution functions and thus represent a departure from the so-called weak-link principle. A fundamental problem with the Weibull approach, the lack of statistical independence of volume elements, will be briefly discussed. For cases where failure is caused by sharp defects a new extreme-value (weakest-link) function has been developed on the basis of the mechanics of the near-tip regions of such defects. The new function has only two statistical parameters which can be measured easily from plots, graphically or by least-squares fitting. Several large sets of data, fracture toughness, and fracture stress from several different materials will be shown, to which the new function provides a much better fit than the Weibull function.
A Knowledge Based Dwell Mechanism Assistant Designer
Authors: Rosen D. , Riley D. , Erdman A.
Published: June 2008

A knowledge-based dwell mechanism design program has been developed on the premise that mechanism design can be considered as an example of general mechanical design. The program, called DWELL-ASSIST, was built using a knowledge based system shell, MIDAS, developed to embody a new model of conceptual and preliminary design. Based on required dwell and entire-motion characteristics, plus any designer preferences, DWELL-ASSIST proposes mechanism types and synthesis methods, in the context of prespecified “problem statements,” which the program judges to be compatible with the problem requirements. DWELL-ASSIST can choose from among cam, geared, and linkage mechanisms, and among path curvature, precision-point, optimization, and other specialized synthesis methods in its search for solutions. As a final step, DWELL-ASSIST has the capability of developing these chosen solutions and evaluating them based on problem requirements.
Fourth and Fifth Order Double Burmester Points and the Highest Attainable Order of Straight Lines
Authors: Ting Kwun-Lon , Wang S. C.
Published: June 2008

This paper addresses the problems of fourth and fifth order double Burmester points. It also presents a general treatment to elaborate Mueller’s concepts on the highest attainable order of straight lines. The treatment is made possible with the derivation of a bi-quadratic equation whose four roots representing the four Burmester points in a planar motion. The subjects are complex but the treatment is simple and no complex geometry is involved. The results are general and applicable to any general planar motion rather than limited to four-bar linkages. Simple synthesis techniques are demonstrated in examples and the inverse Euler-Savary equation is introduced as a convenient feature in synthesis.
The Algebraic Classification of the Image Curves of Spherical Four-Bar Motion
Authors: Ge Q. Jeffrey , McCarthy J. M.
Published: June 2008

A rotational displacement of the coupler of a spherical four-bar linkage can be mapped to a point with coordinates given by the Euler parameters of the rotation. The set of rotational movements available to the coupler defines a curve in this three-dimensional projective space (four homogeneous coordinates). In this paper, we determine the generalized eigenvalues and eigenvectors of the pencil of quadrics that pass through this curve and examine their properties. The result is an algebraic classification of the image curves that parallels the well-known classification of spherical four-linkages. In addition, we find that the characteristic polynomial of the system yields Grashof’s criterion for the rotatability of cranks.
Order Rectification for Complex Number Based Burmester Curves
Authors: Chase T. R. , Fang W. E.
Published: June 2008

A new solution to the order rectification problem for a driving dyad of planar mechanisms is presented. The method identifies sections of both Burmester curves where the driving link rotates in a single direction when passing through four precision positions in sequence. The new solution describes desirable regions of the curves in terms of the complex number parameters used to generate the curves, providing a complex number equivalent to available pole based order rectification procedures. The new solution is stated in a summary form that is readily codifiable. An example is presented. The theory underlying the new solution is then developed in detail.
Variable-Ratio Chain Drives With Noncircular Sprockets and Minimum Slack-Theory and Application
Authors: Freudenstein F. , Chen Ching-Kong
Published: June 2008

The theory has been developed for the design of a new mechanical component: variable-ratio chain drives with noncircular sprockets and minimum slack. The theory is based on a kinematic correspondence between noncircular chain drives and noncircular gears. This in turn permits the development of an algorithm for minimizing chain slack. The theory is applicable to a wide range of mechanical equipment, including bicycles and nonuniform motion transmissions involving band drives, tape drives, and timing belts. Such drives may or may not require a tensioner, but if they do, tensioner displacement will be minimal. Numerical examples illustrate applications to the design of an optimum bicycle configuration and a harmonic-motion generator.
Kinematic Displacement Analysis of a Double-Cardan-Joint Driveline
Authors: Fischer I. S. , Paul R. N.
Published: June 2008

The input-output displacement relations of two Cardan joints arranged in series on a driveline has been investigated in detail, including the effects of unequal joint angles, the phase angle between the two Cardan joints and also such manufacturing tolerance errors as nonright angle moving link lengths and offset joint axes. A combined Newton-Raphson method and Davidon-Fletcher-Powell optimization algorithm using dual-number coordinate-transformation matrices was employed to perform the analysis. An experiment was conducted to validate the results of the analysis. The apparatus consisted of a double-Cardan-joint driveline whose rotations were measured by optical shaft encoders that were sampled by a computer data-acquisition system. The equipment was arranged so that the phase angle between the joints and the offset angles between the shafts at each of the two joints could be readily varied. The “relative phase angle,” the difference between the phase angle of the two joints and the angle between the planes defined by the input and intermediate and the intermediate and output shafts, was found to be the significant factor. If the offset angles at both Cardan joints are equal, the double-Cardan-joint driveline functions as a constant-velocity coupling when the magnitude of the relative phase angle is zero. If the offset angles at the two Cardan joints are unequal, a condition prevailing in the important front-wheel-drive automobile steering-column application, then fluctuation in output velocity for a constant input velocity is minimized although not eliminated for zero relative phase angle.
A Hybrid Variable Metric Update for the Recursive Quadratic Programming Method
Authors: Beltracchi T. J. , Gabriele G. A.
Published: June 2008

The Recursive Quadratic Programming (RQP) method has become known as one of the most effective and efficient algorithms for solving engineering optimization problems. The RQP method uses variable metric updates to build approximations of the Hessian of the Lagrangian. If the approximation of the Hessian of the Lagrangian converges to the true Hessian of the Lagrangian, then the RQP method converges quadratically. The choice of a variable metric update has a direct effect on the convergence of the Hessian approximation. Most of the research performed with the RQP method uses some modification of the Broyden-Fletcher-Shanno (BFS) variable metric update. This paper describes a hybrid variable metric update that yields good approximations to the Hessian of the Lagrangian. The hybrid update combines the best features of the Symmetric Rank One and BFS updates, but is less sensitive to inexact line searches than the BFS update, and is more stable than the SR1 update. Testing of the method shows that the efficiency of the RQP method is unaffected by the new update but more accurate Hessian approximations are produced. This should increase the accuracy of the solutions obtained with the RQP method, and more importantly, provide more reliable information for post optimality analyses, such as parameter sensitivity studies.
A Modified Game Theory Approach to Multiobjective Optimization
Authors: Rao S. S. , Freiheit T. I.
Published: June 2008

Many mechanical and structural design problems encountered in practice require solutions which balance several conflicting objectives. The vector, scalarization, and trade-off-curve methods have been developed to achieve multiobjective solutions. One of the best known methods for generating a compromise solution, based on the concept of Pareto minimum solution, is the cooperative game theory method since it uses a scalarized approach and has a numerical measure of compromise. However, game theory is hard to automate due to a two step optimization process involved. Hence, in this work, a modification to the game theory is introduced in which the two optimization steps are combined and an algorithm for its implementation is developed. The algorithm is tested on two numerical examples, including one dealing with the probabilistic design of an eighteen speed machine tool gear train. The probabilistic theory necessary for the design of the gear train is also introduced. The examples validate the modified game theory.
Efficient CSG Representations of Two-Dimensional Solids
Authors: Shapiro V. , Vossler D. L.
Published: June 2008

Good methods are known for converting a Constructive Solid Geometry (CSG) representation of a solid into a boundary representation (b-rep) of the solid, but not for performing the inverse conversion, b-rep→CSG, which is the subject of this paper. Important applications of b-rep→CSG conversion arise in solid modeling, image processing, and elsewhere. The problem can be divided into two tasks: (1) finding a set of halfspaces that is necessary and sufficient (but not unique) to represent a given solid, and (2) constructing an efficient CSG representation using those halfspaces. This paper solves the problem for curved planar solids, i.e., r-sets in E2, with or without holes, whose boundary is given by a collection of edges. The edges may be subsets of straight lines or convex curves (i.e., curves which intersect any line in at most two points). We prove a number of results and describe algorithms that have been fully implemented for solids bounded by line segments and circular arcs. Empirical results show that the computed CSG representations are superior to those produced by earlier algorithms, and produce superior three-dimensional CSG representations for mechanical parts defined by contour sweeping. A companion paper generalizes the results to higher dimensional solids.
An Integrated Kinematic-Kinetostatic Approach to Optimal Design of Planar Mechanisms Using Fuzzy Theories
Authors: Dhingra A. K. , Rao S. S.
Published: June 2008

A new integrated approach to the design of high speed planar mechanisms is presented. The resulting nonlinear programming formulation combines both the kinematic and kinetostatic synthesis aspects of mechanism design. The multiobjective optimization techniques presented in this work facilitate the design of a linkage to meet several kinematic and dynamic design criteria. The method can be used for motion, path, and function generation problems. The nonlinear programming formulation also permits an imposition of constraints to eliminate solutions which possess undesirable kinematic and motion characteristics. To model the vague and imprecise information in the problem formulation, the tools of fuzzy set theory have been used. A novel method of solving the resulting fuzzy multiobjective problem using mathematical programming techniques is presented. The outlined procedure is expected to be useful in situations where doubt arises about the exactness of permissible values, degree of credibility, and correctness of statements and judgements.
The Symmetric Rank One Formula and its Application in Discrete Nonlinear Optimization
Authors: Cha J. Z. , Mayne R. W.
Published: June 2008

The Symmetric Rank One (SR1) update formula is studied for its use in numerically accumulating second order derivative information for optimization. The unique advantage of the SR1 formula is that it does not require specific search directions for development of the Hessian matrix. This is an attractive feature for optimization applications where arbitrary search directions may be necessary. This paper explores the use of the SR1 formula within a procedure based on recursive quadratic programming (RQP) for solving a class of mixed discrete constrained nonlinear programming (MDCNP) problems. Theoretical considerations are presented along with numerical examples which illustrate the procedure and the utility of SR1.
A Procedure Using Manufacturing Variance to Design Gears With Minimum Transmission Error
Authors: Sundaresan S. , Ishii K. , Houser D. R.
Published: June 2008

This paper deals with the design of spur gears that have minimum transmission error and are insensitive to manufacturing variance. We address two stages of design: (1) generation of candidate designs (selection of number of teeth, pressure angle, etc.), and (2) tooth profile modification. The first stage involves a search of discrete combinations of design variables, while the second stage utilizes numerical optimization techniques. The key research issue is finding a candidate design and its profile modification that not only has low transmission error, but is insensitive to variations in the design values caused by the manufacturing process. To achieve this goal, the procedure applies Taguchi’s concept of parameter design. In this paper, we consider a design problem with a set specification: fixed center distance, speed ratio, and transmission torque. We seek to find a limited number of candidate designs by applying conventional design generation techniques and some design heuristics. For each candidate design, the procedure determines the optimum profile modification (linear tip relief) by linking the Load Distribution Program (LDP) for gears with an optimization program package (OPTPAK). From the resulting peak optimum, we further seek the statistical optimum using an algorithm developed in this paper. The statistical optimum shows a nominal increase in the transmission error, but is quite insensitive to typical process error associated with gear manufacturing. The developed algorithm readily applies to other gear designs as well as other types of machine elements. In particular, we foresee our procedure to be particularly effective for helical gears. We hope to further our method by developing a means to add statistical heuristics to the discrete design generation stage.
Computational Implementation and Tests of a Sequential Linearization Algorithm for Mixed-Discrete Nonlinear Design Optimization
Authors: Loh Han Tong , Papalambros P. Y.
Published: June 2008

A previous article gave the theoretical background and motivation for a new sequential linearization approach to the solution of mixed-discrete nonlinear optimal design problems. The present sequel article gives the implementation details of program MINSLIP based on this approach. Illustrative examples, modeling issues, and program parameter selection are discussed. A report on extensive computational results with test problems, as well as comparisons with other methods, shows advantages in both robustness and efficiency. Sample design applications are included.
Fatigue Reliability Functions in Semilogarithmic Coordinates
Authors: Avakov V. A.
Published: June 2008

In the previous publication [2], the transformation between fatigue life and strength distribution was established using double-logarithmic coordinate system (InN-InS). Here, a similar transformation is established using a semilogarithmic (InN-S) coordinate system. It is assumed that the set of S = Sj (N/Qj) (j = 1,2,...,p) relations, plotted in the InN-S coordinates, becomes a family of parallel straight lines. With the aid of the developed orthogonal relations, lognormal, Weibull and three-parameter logweibull life distributions have been transformed into normal, asymptotic type 1 of smallest value, and three-parameter Weibull strength distributions, respectively. This procedure may be applied to other types of fatigue life distribution.
Manufacturability Analysis for a Flexible Manufacturing Cell
Authors: Anjanappa M. , Courtright M. J. , Anand D. K. , Kirk J. A.
Published: June 2008

The conventional product development cycle time in producing a part can be reduced by eliminating design errors and difficult to machine features before manufacturing process begins. This paper discusses the identification, development, and operation of an approach which uses a global data base of flexible manufacturing cell capabilities in order to analyze a design for manufacturability. Designs which the cell is unable to produce are rejected, and ways in which a design may be made more producible are suggested to the user. This paper addresses issues, such as availability of material, fixture, and tool and the achievability of tolerance. The approach is implemented on a cell containing a machining center and material handling equipment operating under a rapid prototyping protocol. An important contribution of this work is the wide variety of manufacturability constraints covered and the convenience of including it in the overall process of product development.