bluuebunny/crossref_metadata_2025 huggingface dataset:
Application of the Absolute Nodal Coordinate Formulation to Large Rotation and Large Deformation Problems
Authors: Shabana A. A. , Hussien H. A. , Escalona J. L.
Published: February 2008

There are three basic finite element formulations which are used in multibody dynamics. These are the floating frame of reference approach, the incremental method and the large rotation vector approach. In the floating frame of reference and incremental formulations, the slopes are assumed small in order to define infinitesimal rotations that can be treated and transformed as vectors. This description, however, limits the use of some important elements such as beams and plates in a wide range of large displacement applications. As demonstrated in some recent publications, if infinitesimal rotations are used as nodal coordinates, the use of the finite element incremental formulation in the large reference displacement analysis does not lead to exact modeling of the rigid body inertia when the structures rotate as rigid bodies. In this paper, a simple non-incremental finite element procedure that employs the mathematical definition of the slope and uses it to define the element coordinates instead of the infinitesimal and finite rotations is developed for large rotation and deformation problems. By using this description and by defining the element coordinates in the global system, not only the need for performing coordinate transformation is avoided, but also a simple expression for the inertia forces is obtained. The resulting mass matrix is constant and it is the same matrix that appears in linear structural dynamics. It is demonstrated in this paper that this coordinate description leads to exact modeling of the rigid body inertia when the structures rotate as rigid bodies. Nonetheless, the stiffness matrix becomes nonlinear function even in the case of small displacements. The method presented in this paper differs from previous large rotation vector formulations in the sense that the inertia forces, the kinetic energy, and the strain energy are not expressed in terms of any orientation coordinates, and therefore, the method does not require interpolation of finite rotations. While the use of the formulation is demonstrated using a simple planar beam element, the generalization of the method to other element types and to the three dimensional case is straightforward. Using the finite element procedure presented in this paper, beams and plates can be treated as isoparametric elements.
Design for Robustness Based on Manufacturing Variation Patterns
Authors: Yu Jyh-Cheng , Ishii Kosuke
Published: February 2008

This paper addresses interacting manufacturing errors and their impact on the design robustness and constraint activity. Manufacturing errors often affect design variables with characteristic patterns. This paper defines the Manufacturing Variation Pattern (MVP) to represent this characteristic and investigates its effects. The application of the concept of MVP to design optimization leads to an improved robust optimum. The design of molded gears with minimum transmission error illustrates the proposed scheme’s effectiveness. Our model readily accommodates correlation among dimensional errors and significantly reduces performance variation.
Representation of Design Object Based on the Functional Evolution Process Model
Authors: Shimomura Y. , Yoshioka M. , Takeda H. , Umeda Y. , Tomiyama T.
Published: February 2008

One of the crucial issues for developing computer aided conceptual design system is representation of functions which represent designers’ intention. Representing functions is also crucial not only for representing design objects but also for describing conceptual design processes, in which designers operate mainly functional concepts. Namely, function is a key concept to integrate object modeling and process modeling in design. In this paper, first we extend the FBS (Function-Behavior-State) diagram, which we have already proposed, by introducing three additional concepts for representing a function; namely, function body that represents designers’ intention directly, function modifier that qualifies a function body, and objective entity on which the function body occurs. This extended FBS diagram, called FBS/m (modifier) diagram, enables us to represent designers’ intention more precisely than the original FBS diagram. Then, we propose an FEP (Functional Evolution Process) model to represent design processes. In the FEP model, the FBS model of a design object is evolved through three steps, i.e., functional actualization, functional evaluation and functional operation. Functional actualization depicts a process to obtain physical descriptions from functional description. Functional evaluation is a process to measure realizability of functions of the design object. Functional operation is a process to operate functions to improve the design. Based on the FEP model, we analyze an actual design process, and show that the FEP model is suitable for representing designers’ intention along with design processes.
Topological Synthesis of Geared Robotic Mechanisms
Authors: Chen Dar-Zen , Shiue Shuen-Chen
Published: February 2008

An efficient and systematic methodology for the topological synthesis of geared robotic mechanisms is developed. The approach is based on the idea that the kinematic structure of a geared robotic mechanism can be described by an equivalent open-loop chain (EOLC) and mechanical transmission lines (MTLs) which drive the joints of the EOLC. It is shown that an MTL can be decomposed as an input unit and several transmission units connected in series. The characteristics of the input and transmission units are laid out and a systematic methodology is developed to enumerate all admissible input and transmission units from the existing atlas of nonfractionated geared kinematic chains. The atlas of admissible MTLs are then generated accordingly. Thus, all admissible geared robotic mechanisms can be enumerated efficiently with the atlas of admissible MTLs and a preferred form of the EOLC. With this new methodology, some novel structures of geared robotic mechanisms are obtained and it is believed that new areas of application can be further explored.
Dynamic Analysis of Geared Robotic Mechanisms Using Graph Theory
Authors: Tsai Lung-Wen , Chen Dar-Zen , Lin Ta-Wei
Published: February 2008

In this paper, an efficient methodology for the dynamic analysis of geared robotic mechanisms is presented. The approach makes use of the topological structure of mechanical transmission lines to simplify the analysis. The links in a geared robotic mechanism are divided into several levels. Each level contains one primary link and several secondary links. It is shown that the inverse dynamic problem can be solved from the highest level links toward the base link, one or two levels at a time depending on the topological structure of the mechanical transmission lines. Thus, the inverse dynamic problem can be solved without the need of simultaneously solving the entire system of equations. A two degree-of-freedom manipulator is used to illustrate the procedure.
Metrics on Motion and Deformation of Solid Models
Authors: Chirikjian G. S. , Zhou Shiyu
Published: February 2008

Recently, the importance of metrics on the group of rigid body motions has been addressed in a number of works in the kinematics and robotics literature. This paper defines new metrics on motion which are particularly easy to compute. It is shown how these metrics are applicable to path generation for rigid body motions, and also as a means for generating interpolated sequences of deformed solid models. In order to address both problems in a unified framework, general metrics on Lie groups are discussed.
A Synthesis Method For Placing Workpieces In RPR Planar Robotic Workcells
Authors: Chaney K. D. , Davidson J. K.
Published: February 2008

A new method is used for determining both a satisfactory location of a workpiece and a suitable mounting-angle of the tool for planar RPR robots that can provide dexterous workspace. All three joints of the robot have excursion-limits that bound their displacement. For the purposes of this paper, the third joint, a revolute, permits exactly one full turn. Successful locations for the workpiece are those places where the rotations at each task-axis and the third joint are synchronized. For a fixed mounting angle of the tool, the radial location and orientation of the workpiece are determined by just two 2π-rotations of the tool. When the mounting-angle of the tool is also a variable, the tool can be rotated a full turn at three locations on the workpiece. The method is particularly well suited to applications in which the task requires large rotations of the end-effector. The results are presented as coordinates of points in a two-dimensional Cartesian reference frame attached to the workcell. Consequently, a technician or an engineer can determine the location for the workpiece by laying out these coordinates directly in the workcell. Example problems illustrate the method. Practical applications include welding and deposition of adhesives.
Influence of Cam Motions on the Dynamic Behavior of Return Springs
Authors: Yu Q. , Lee H. P.
Published: February 2008

Based on the analytical solution of the equation of motion for a single degree-of-freedom model of a spring, the relation between the dynamic behavior and the kinematic features of input cam motions is discussed in this paper. A simple expression for the dynamic response spectrum of the vibration excited by the input motion is presented. It provides a useful tool to estimate the effect of cam motions on the dynamic behavior of springs. A method for the selection of cam motion curves based on this response spectrum is also presented in the paper. Examples are given to illustrate the method.
An Introduction to Mechanical Advantage in Compliant Mechanisms
Authors: Salamon B. A. , Midha A.
Published: February 2008

An energy approach is utilized to determine mechanical advantage in compliant mechanisms by duly accounting for lost work due to deformation. Three mechanical advantage types are then defined which examine the isolated influences of various parameters. Finally, a case study is investigated to exemplify these definitions and demonstrate resulting trends in mechanical advantage.
Active Control of Elastodynamic Vibrations of a Four-Bar Mechanism System With a Smart Coupler Link Using Optimal Multivariable Control: Experimental Implementation
Authors: Sannah M. , Smaili A.
Published: February 2008

This paper presents an experimental investigation on active control of the elastodynamic response of a four-bar (4R) mechanism system using “smart” materials featuring piezoelectric sensor/actuator (S/A) pairs and multivariable optimal control. The experimental 4R mechanism is made such that its coupler link is flexible, its follower link is slightly less flexible and its crank is relatively rigid. Two thin plate-type piezoceramic S/A pairs are bonded to the flanks of the coupler link at the high strain locations corresponding to the first and second vibration modes. Based on the optimal multivariable control theory, a controller which consists of a linear quadratic regulator (LQR) and a Luenberger observer as a state estimator is designed and implemented. The results of the experimental investigation prove that in order to prevent high mode excitations, the controller design should be based on the modes representing vibrations of all components comprising the mechanism system rather than the modes corresponding to the link to which the S/A pairs are bonded. Response amplitude attenuation ratios up to 50 percent are achieved and high mode excitations are prevented.
Generation of Identical Noncircular Pitch Curves
Authors: Tong Shih-Hsi , Yang Daniel C. H.
Published: February 2008

In this paper the theory and algorithm for generating pairs of identical noncircular conjugate pitch curves are presented. A set of criteria for two identical rigid bodies engaging in conjugate rolling motion is established. Based on these criteria, an algorithm is developed, which can be used to design this type of rolling pairs with almost unlimited profile varieties and any number of lobes. Geometrical conditions for having C1 (or slope) continuity at the intersections of tips and roots of lobe profiles are also established. A family of similar profiles can be designed at the same time by using a single parameter, the pitch noncircularity, via a dimensionless analysis. Results from this investigation should have applications to the design of noncircular gears and lobe pumps.
Analysis of Transmission Errors Under Load of Helical Gears With Modified Tooth Surfaces
Authors: Zhang Y. , Fang Z.
Published: February 2008

This paper presents a model for the analysis of transmission errors of helical gears under load. The model accommodates the modification of tooth surfaces, gear misalignments and the deformation of tooth surfaces caused by contact load. In this model, the gear contact load is assumed to be nonlinearly distributed along the direction of the relative principal curvature between the two contacting tooth surfaces. As compared with conventional tooth contact analysis (TCA) that assumes gear surfaces as rigid bodies, the model presented in this paper provides more realistic simulation results on the gear transmission errors and other gear meshing characteristics when the tooth surfaces are deformed under load. The proposed model is applied to a pair of helical gears in the numerical example included in the paper.
Generation and Classification of Structural Topologies With Genetic Algorithm Speciation
Authors: Duda J. W. , Jakiela M. J.
Published: February 2008

Extending previous efforts, this article describes how a speciating genetic algorithm is used to distribute subsets of the evolving population of solutions over the design space. This distribution of solutions is analogous to different species exploiting different niches in an ecosystem. In addition to reviewing genetic algorithms with an emphasis on techniques to cause such niche exploitation, we describe how we use statistical cluster analysis techniques to quantify the extent to which a population is speciated and how this measure can be used to probabilistically encourage mating of reasonably similar designs (i.e., intraspecies mating). Results demonstrate the creation of different good designs of characteristically different topology and shape.
Improved Calculation of Eigenvector Sensitivities Using Matrix Perturbation Analysis
Authors: Lin R. M. , Lim M. K. , Wang Z.
Published: February 2008

Derivatives of eigenvalues and eigenvectors have become increasingly important in the development of modern numerical methods for areas such as structural design optimization, dynamic system identification and dynamic control, and the development of effective and efficient methods for the calculation of such derivatives has remained to be an active research area for several decades. Based on the concept of matrix perturbation, this paper presents a new method for the improved calculation of eigenvector derivatives in the case where only few of the lower modes of a system under study have been computed. By using this new proposed method, considerable improvement on the accuracy of the estimation of eigenvector derivatives can be achieved at the expense of very tiny extra computational effort since only few matrix vector operations are required. Convergency criterion of the method has been established and the required accuracy can be controlled by including more higher order terms. Numerical results from practical finite element model have demonstrated the practicality of the proposed method. Further, the proposed method can be easily incorporated into commercial finite element packages to improve the accuracy of eigenderivatives needed for practical applications.
Mechanical Design for JET-X Aperture Door
Authors: Mahmoud S. M. , Goodall C. V.
Published: February 2008

The joint European X-ray Telescope, JET-X, is one of the core instruments in the scientific payload of the Russian Spectrum Roentgen-Gamma-RG which is a high energy astrophysics mission. The JET-X structure is constructed from three carbon fibre tubular sections, and contains the instruments and acts as an optical bench. The forward section of the structure has a deployable door, which remains closed until the satellite has reached orbit. The function of the door is to protect sensitive optical surfaces from contamination and moisture from ground operations, during launch and early orbits operations. The door is fabricated from a honeycomb core faced with aluminium alloy skins. The door is approximately 1 m in diameter and weighs about 6 Kg only. The door body, the cutter assembly and the hinge assembly were designed to withstand the mechanical stresses arising during the launch environment. The door assembly was integrated to the main structure and vibration tests which simulate the conditions during the launch were conducted. These tests were: Sine, Random and Shock. This paper presents the door assembly design, the finite element modelling and the dynamic responses during the tests.
A Systems Approach to Structural Topology Optimization: Designing Optimal Connections
Authors: Jiang T. , Chirehdast M.
Published: February 2008

In this paper, structural topology optimization is extended to systems design. Locations and patterns of connections in a structural system that consists of multiple components strongly affect its performance. Topology of connections is defined, and a new classification for structural optimization is introduced that includes the topology optimization problem for connections. A mathematical programming problem is formulated that addresses this design problem. A convex approximation method using analytical gradients is used to solve the optimization problem. This solution method is readily applicable to large-scale problems. The design problem presented and solved here has a wide range of applications in all areas of structural design. The examples provided here are for spot-weld and adhesive bond joints. Numerous other potential applications are suggested.
Evaluation of Failure Diagnosis in Conceptual Design of Mechanical Systems
Authors: Paasch R. K. , Ruff D. N.
Published: February 2008

This paper discuses a methodology for improving quality and reducing life cycle costs of mechanical systems. The principal concept is that a system can be designed, in the conceptual stages, to be easier to diagnose for failures. To perform this, functional decomposition and form-to-function mapping are utilized to demonstrate the relation of design to diagnosis and for diagnosis itself. Four diagnosability metrics are developed and four hypothetical conceptual designs are evaluated for diagnosability and compared. An example is presented wherein three conceptual designs for a toolhead positioning system are evaluated for diagnosability at two levels of abstraction and the results compared. The area of design for diagnosis offers promise in improving system quality and reducing life cycle cost; research is continuing to refine and integrate the procedures with other aspects of the concurrent engineering design process.
Using Manufacturing Planning to Generate Manufacturability Feedback
Authors: Gupta S. K.
Published: February 2008

This paper describes how manufacturing planning can be used for generating manufacturability feedback for machined parts to be made on a 3-axis machining center. The approach presented in this paper involves systematic exploration of high level machining plans. It is expected that such analysis capabilities will give designers an opportunity to correct manufacturing related problems during the design stage and thereby reduce the number of design iterations.
An Elastic Suspension Design Framework for Tuned Gyroscopes
Authors: Yang Yu-Neng , Chieng Wei-Hua
Published: February 2008

This paper presents a design for a new tuned gyroscope framework consisting of a heavy rotor supported by a heli-flex suspension. Inherently free of 2ω drift-error, the gyro can be precisely tuned by adjusting pre-extension between two ends of its helix. The symmetrical support structure of this isotropic helical suspension design significantly reduces error moment caused by linear acceleration, and the device eliminates G2 drift by virtue of its desirable anisoelasticity characteristic. The gyro design is simple, highly manufacturable, and when appropriate suspension parameters are used, produces a long-term drift-rate of 0.01 deg./hr.
Contact Stress Analysis in Ball Screw Mechanism Using the Tubular Medial Axis Representation of Contacting Surfaces
Authors: Huang Hual-Te T. , Ravani B.
Published: February 2008

A simple method is presented for analysis of contact stresses and deformation conditions between the bearing balls, screw, and nut of the ball screw mechanism. The method is based on representation of contact geometry and curvature analysis of contacting surfaces using a generalization of the medial axis transform (MAT) to tubular surfaces. Simplified Hertzian contact solutions are obtained using the curvature information. The results are approximate but do include the effect of complex thread profiles as a result of the helical grooves and are suitable for mechanical design purposes.
A Fuzzy Kinetostatic Analysis of Imprecisely-Defined Mechanisms
Authors: Chen L. , Rao S. S. , Ku K.
Published: February 2008

Many engineering systems are ill-defined and imprecisely known, due to fuzziness, especially in the conceptual/preliminary design phase. In this work, a fuzzy kinetostatic methodology is proposed for the dynamic analysis of mechanisms involving imprecision. The fuzzy dynamic bearing reactions as well as driving torque are computed using the proposed method. The analysis of a high-speed planar mechanism for path generation is considered to illustrate the computational aspects of the approach. The fuzzy analysis provides the variation of system performance over the entire range of design parameter space compared to the traditional sensitivity analysis approaches which give variations in system performance only at one design point.
Assembly Configurations and Branches of Planar Single-Input Dyadic Mechanisms
Authors: Foster D. E. , Cipra R. J.
Published: February 2008

This paper examines the problem of enumerating the assembly configurations (ACs), also called circuits, and branches of planar single-input dyadic (SID) mechanisms which have links with pin joints and sliding joints. An SID mechanism is a multiloop mechanism which can be defined by adding one loop at a time such that the mechanism has one degree of freedom after each loop is added. A method is given to find the ACs of such a mechanism. The emphasis is on using graphical interpretation to determine the mobility regions of the mechanism which are preserved when each new loop is added to the mechanism. This method of interpretation is readily automated. Each AC can be represented as a set of instructions for the input link to follow, along with a list of dyad configurations for each instruction. Each instruction corresponds to a branch of the mechanism. Examples are given to demonstrate the use of this method.
Experimental and Finite Element Modal Analyses of Planar Mechanisms With Three-Dimensional Geometries
Authors: Smaili A. , Bagci I.
Published: February 2008

This article presents the results of numerical and experimental modal analyses of a planar four-bar (4R) mechanism having three dimensional geometry due to the offsets between its links. An experimental mechanism is built and modern modal testing techniques are used. A five-node isoparametric finite element is developed and used to model the mass and flexibility of the links and joints, link offsets, and drive and load shafts. The results obtained from the finite element solution matched closely the experimental results, a testimony to the accuracy of the proposed element. The results indicated that link offsets have considerable influence on the dynamic characteristics of a mechanism system and should be considered in dynamic modeling of planar mechanisms.
ZK-Type Dual-Lead Worm and Worm Gear Drives: Geometry
Authors: Bair B.-W. , Tsay C.-B.
Published: February 2008

A dual-lead worm gear set is frequently used for machines to operate without backlash, which can be adjusted along the worm’s axial direction. The ZK-type dual-lead worm is generated by a cone-type straight-edged grinding wheel while an oversize worm-type hob cutter cuts the worm gear. The dual-lead worm gear set has two different axial modules and helix angles for the right- and left-side tooth surfaces. The mathematical model involving ZK-type dual-lead worm and worm gear surface geometries is developed based on the theory of gearing and gear cutting mechanism. According to the proposed mathematical model, computer graphs of the ZK-type dual-lead worm gear drives have been presented. Coordinates of the meshed grid-point on gear drive surfaces can thus be determined by applying the numerical method. Undercutting of the worm gear surface has been investigated based on the theory of gearing and the developed gear set mathematical model. The gear set mathematical model developed herein can facilitate gear set tooth contact analysis, contact teeth, contact ratio and other advanced investigations.
ZK-Type Dual-Lead Worm and Worm Gear Drives: Contact Teeth, Contact Ratios and Kinematic Errors
Authors: Bair B.-W. , Tsay C.-B.
Published: February 2008

Contact ratio is an important gear design parameter for gear bending and contact stresses. A higher contact ratio may reduce the stresses and kinematic errors of the gear set. In this study, we calculate the kinematic error of the ZK-type dual-lead worm gear set by applying the tooth contact analysis (TCA) method. Two kinds of contact ratios, the instantaneous contact teeth (ICT) and the average contact ratio (ACR), are investigated and calculated by applying TCA method. ICT is an important design parameter for a dual-lead worm gear set when the gear set is used in a machine subjected to large impact forces. ACR is also a useful design factor for assessing gear tooth strength and dynamic load. If gear surface elastic deformation 3μm is allowed for the worm gear set, the ICT may have 2, 3 or 4 teeth and the ACR reveals that the ZK-type dual-lead worm gear drive is a high-contact-ratio gear set. It is found that this type of worm gear set with a shorter center distance assembly can increase the value of ACR during the gear meshing. Illustrative examples presented herein demonstrate the effects of gear parameters on contact teeth, contact ratios, average contact ratios and kinematic errors under various conditions.
Duplex Spread Blade Method for Cutting Hypoid Gears with Modified Tooth Surface
Authors: Kawasaki K. , Tamura H.
Published: February 2008

In this paper, a duplex spread blade method for cutting hypoid gears with modified tooth surface is proposed. The duplex spread blade method provides a rapid and economical manufacturing method because both the ring gear and pinion are cut by a spread blade method. In the proposed method, the nongenerated ring gear is manufactured with cutting edge that is altered from the usual straight line to a circular arc with a large radius of curvature and the circular arc cutting edge produces a modified tooth surface. The pinion is generated by a cutter with straight cutting edges as usual. The main procedure of this method is the determination of the cutter specifications and machine settings. The proposed method was validated by gear manufacture.
A Unified Approach to the Assembly Condition of Epicyclic Gears
Authors: Simionescu P. A.
Published: February 2008

The paper gives a general method for determining the assembly condition of epicyclic gears, irrespective of the structure or gear type. According to the method, an associated mechanism is considered, having a single arm carrier and a split planet. The assembly condition of the gear train is satisfied when obtaining identical superposition of the teeth of the two half-planets after rotating the arm to the next position. By writing simple kinematic relations between some partial transmitting ratios, general formulae are obtained which can be applied to specific epicyclic gear sets as functions of teeth numbers. The same approach allows the determination of the necessary angles between the arms of the carrier, or the offset angles between the wheels of the compound planets, as alternative solutions for the case in which equidistant assembly of identical planets is not possible.
Design and Tessellation of B-Spline Developable Surfaces
Authors: Maekawa T. , Chalfant J.
Published: February 2008

Developable surfaces are widely used in various engineering applications. However, little attention has been paid to implementing developable surfaces from the onset of a design. The first half of the paper describes a user friendly method of designing developable surfaces in terms of a B-Spline representation whose two directrices lie on parallel planes. The second half of the paper investigates a new method for development and tessellation of such B-Spline developable surfaces, which is necessary for plate cutting and finite element analysis.
Knowledge Representation and Conversion for Hybrid Expert Systems
Authors: Chambers T. L. , Parkinson A. R.
Published: February 2008

Many different knowledge representations, such as rules and frames, have been proposed for use with engineering expert systems. Every knowledge representation has certain inherent strengths and weaknesses. A knowledge engineer can exploit the advantages, and avoid the pitfalls, of different common knowledge representations if the knowledge can be mapped from one representation to another as needed. This paper derives the mappings between rules, logic diagrams, decision tables and decision trees using the calculus of truth-functional logic. The mappings for frames have also been derived by Chambers and Parkinson (1995). The logical mappings between these representations are illustrated through a simple example, the limitations of the technique are discussed, and the utility of the technique for the rapid-prototyping and validation of engineering expert systems is introduced. The technique is then applied to three engineering applications, showing great improvements in the resulting knowledge base.
Achieving an Arbitrary Spatial Stiffness with Springs Connected in Parallel
Authors: Huang S. , Schimmels J. M.
Published: February 2008

In this paper, the synthesis of an arbitrary spatial stiffness matrix is addressed. We have previously shown that an arbitrary stiffness matrix cannot be achieved with conventional translational springs and rotational springs (simple springs) connected in parallel regardless of the number of springs used or the geometry of their connection. To achieve an arbitrary spatial stiffness matrix with springs connected in parallel, elastic devices that couple translational and rotational components are required. Devices having these characteristics are defined here as screw springs. The designs of two such devices are illustrated. We show that there exist some stiffness matrices that require 3 screw springs for their realization and that no more than 3 screw springs are required for the realization of full-rank spatial stiffness matrices. In addition, we present two procedures for the synthesis of an arbitrary spatial stiffness matrix. With one procedure, any rank-m positive semidefinite matrix is realized with m springs of which all may be screw springs. With the other procedure, any positive definite matrix is realized with 6 springs of which no more than 3 are screw springs.
Mechanism Design with MP-Neural Networks
Authors: Li J. , Gupta K. C.
Published: February 2008

The prevalent Mathematical Programming Neural Network (MPNN) models are surveyed, and MPNN models have been developed and applied to the unconstrained optimization of mechanisms. Algorithms which require Hessian inversion and those which build up a variable approach matrix, are investigated. Based upon a comprehensive investigation of the Augmented Lagrange Multiplier (ALM) method, new algorithms have been developed from the combination of ideas from MPNN and ALM methods and applied to the constrained optimization of mechanisms. A relationship between the weighted least square minimization of design equation error residuals and the mini-max norm of the structure error for function generating mechanisms is developed and employed in the optimization process; as a result, the computational difficulties arising from the direct usage of the complex structural error function have been avoided. The paper presents relevant theory as well as some numerical experience for four MPNN algorithms.
Mechanism Schemes in Teaching: A Historical Overview
Authors: Ceccarelli M.
Published: February 2008

This paper considers the teaching aspect in the evolution of mechanisms and machines drawing with the aim to recognize developments and changes in the teaching approaches of what we now call Theory of Mechanisms. The evolution of mechanism schemes has been reviewed through significant examples drawn from a few authors, who have been selected to point out basic historical developments. It is worth noting that over time mechanism design teaching has been strongly restricted to fundamentals and past methodologies so that generally current schemes for designing have not been and were not included in regular teaching curricula.
Kinematic Analysis and Singularity Loci of Spatial Four-Degree-of-Freedom Parallel Manipulators Using a Vector Formulation
Authors: Wang J. , Gosselin C. M.
Published: February 2008

The kinematic analysis and the determination of the singularity loci of spatial four-degree-of-freedom parallel manipulators with prismatic or revolute actuators are discussed in this article. A new method for the derivation of the velocity equations and the corresponding Jacobian matrices is presented. The numerical determination of the workspace boundaries is then briefly discussed. Finally, the determination of the singularity loci is performed using the velocity equations and examples are given to illustrate the results obtained. Spatial four-degree-of-freedom parallel manipulators can be used in several robotic applications as well as in flight simulators. The determination of their singularity loci is a very important design issue.
Accurate Determination of Object Position from Imprecise Data
Authors: Gupta K. C. , Chutakanonta P.
Published: February 2008

The problem of accurate determination of object position from imprecise and excess measurement data arises in kinematics, biomechanics, robotics, CAD/CAM and flight/vehicle simulator design. Several methods described in the literature are reviewed. Two new methods which take advantage of the modern matrix oriented software (e.g., MATLAB, IMSL, EISPACK) are presented and compared with a “basic” method. It is found that both of the proposed decomposition methods (I: SVD/QR and II: SVD/QS) give better absolute results than a “basic” method available from the text books. On a relative basis, the second method (SVD/QS Decomposition) gives slightly better results than the first method (SVD/QR Decomposition). Examples are presented for the cases when the points chosen are nearly dependent and when the independent points have small random errors in their coordinates.
Computation of Pressure Loads in Three Screw Pump Rotors
Authors: Mimmi G. C. , Pennacchi P. E.
Published: February 2008

In the present paper the loads, usually modeled as a force and a moment, on the rotors of a three screw pump have been analyzed. These loads, due to the pressure of the working fluid, are periodical, so their actions on the rotors vary. The calculations of the loads are possible thanks to the exact mathematical model of the sectors of surface of the rotors where the pressure works. The computation of the loads is determined as a function of the rotation angle and it is useful for the comprehension of some phenomena, such as the vibration induced and the noise generation, and for the design of a possible balancing system of the rotor loads. On the basis of the results of the calculations described, we can obtain the different types of actions on the rotors. The central screw presents loads different from those of the two satellite screws. In particular we show how the loads depend on the design parameters, especially on the pitch. The criteria for the optimum design of this parameter are indicated in detail.
A General Approach for Determining Dynamic Forces in Spur Gears
Authors: Vedmar L. , Henriksson B.
Published: February 2008

A model is presented taking into account off line-of-action, non-linear wheel stiffness by using the finite element method, and elasticity coupling between the gear teeth. The contact points are determined by searching the common normal using the undeformed, but otherwise true theoretical, tooth shapes where the teeth have a tip rounding to prevent contact singularity in off line-of-action points. A comparative study is included, which shows the important influence of the elastic coupling and off line-of-action.
Accurate Tooth Stiffness of Spiral Bevel Gear Teeth by the Finite Strip Method
Authors: Gosselin C. , Gagnon P. , Cloutier L.
Published: February 2008

A Finite Strip element is presented for the analysis of variable height and thickness gear teeth, curved along a spiral wound on a cone. The formulation, based on Mindlin’s plate theory, accounts for transverse shear deformation and uses localized functions series in the tooth facewidth direction combined with numerical integration in all directions. The formulation is applied to the clamped-free boundary condition, usual in gearing, and supports any type of transverse loads and moments. The precision of the calculated tooth deflection is ascertained through equivalent numerical tests using Finite Element Analysis. Results agree within 5% of bending displacement at the point of load application.
Effect of CBN Grinding on the Bending Strength of Carburized Gears
Authors: Inoue K. , Sonoda H. , Deng G. , Yamanaka M. , Kato M.
Published: February 2008

The surface condition of a carburized gear is improved by CBN grinding, in addition to the generation of a compressive residual stress at the ground surface. To clarify the effect of these merits on the strength enhancement, a bending fatigue test is performed for the carburized and the CBN-ground gears. The fillet as well as involute tooth surface is ground by an electroplated threaded CBN wheel. The low axial feed rate and the spark-out treatment are effective in improving the surface finish and increasing the compressive residual stress, and the strengths of CBN-ground gears are increased from 100 MPa to 160 MPa in comparison with the carburized gears. Moreover, the test results are discussed on the basis of the fracture mechanics-based strength evaluation which has been proposed by the authors. This analysis demonstrates that the influence of CBN grinding on strength is smaller than the effects of surface-treatments such as shot peening and chemical polishing.
An Approach to Modeling & Representation of Heterogeneous Objects
Authors: Kumar V. , Dutta D.
Published: February 2008

Heterogeneous objects, composed of different materials, are increasingly being used in engineering applications. Also, a new fabrication method called Layered Manufacturing (LM) has shown potential to manufacture these objects. In order to manufacture heterogeneous objects by LM, a CAD model is required that contains both geometry and material information. However, current solid modeling techniques focus on capturing the geometric information only. In this paper, we present an approach to model and represent heterogeneous objects by integrating the material information along with the geometry/topology in the solid model. We define new modeling operations for creating and manipulating heterogeneous models and to complement traditional modeling operations. We also address the issue of computer representation of these new models. Finally, the issue of fabrication of these heterogeneous objects by LM is discussed.
Automating the Flexible Lofting Spline for Reusable Forming Devices
Authors: Hardman K. R. , Cox J. J.
Published: February 2008

A flexible lofting spline is presented as an actuated component in mechanical systems requiring the forming of continuous shapes. The spline is modeled with a piece-wise, cubic polynomial, based on minimum elastic strain energy, and nonlinear, large deflections. A flexible spline test device is explained and used to evaluate accuracy, limitations, and general issues. Conclusions and recommendations are provided.
Facilitating Concept Exploration for Configuring Turbine Propulsion Systems
Authors: Koch P. N. , Allen J. K. , Mistree F. , Barlow A.
Published: February 2008

In this Technical Brief we illustrate the efficacy of the Robust Concept Exploration Method as applied to the preliminary design of a turbine lift engine for Advanced Short Take-Off and Vertical Landing (ASTOVL) fighter aircraft. This example is defined in collaboration with the Rolls-Royce Atlanta Engineering Group.
Probabilistic Failure Prediction of SCS-6/Ti-15-3 MMC Ring
Authors: Holland F. A. , Zaretsky E. V. , Melis M. E.
Published: February 2008

Two parameter Weibull analysis was used to predict the fracture strength and fatigue life of an SCS-6/Ti-15-3 metal matrix composite (MMC) ring from coupon samples. Two methods were used. One method was to calculate an effective volume for an idealized ring on the basis of a theoretical approximation of the stress distribution. Fracture strength and fatigue life of the coupon samples were then scaled to the effective volume of the ring. The other method used finite-element analysis (FEA) to determine a stress distribution in the actual, geometrically imperfect ring. The total ring reliability was then determined by multiplying the element reliabilities. Experimental fracture strengths were obtained for two MMC rings, each having an O.D. of 176.5 mm (6.95 in.) and I.D. of 146.0 mm (5.75 in.) and a 15.2 mm (0.60 in.) width. The median value of the experimental ring fracture strength data was 173.1 MPa (25.1 ksi). Fracture strength predictions by the effective-volume and finite-element methods were 5 and 17 percent lower than the experimental value, respectively. The effective-volume and finite-element methods predicted ring fatigue lives of 2700 and 4800 cycles, respectively, at a 50 percent probability of failure and 154.4 MPa (22.4 ksi) maximum ring internal pressure. No ring fatigue data were available for comparison.
A Quick Computation of Factor of Safety for Biaxial Stress States
Authors: Deb K.
Published: February 2008

Determination of overall factor of safety of a design involves repeated calculation of factor of safety at critical points in the design. For a given stress state at a point, the factor of safety is calculated by first finding the principal stresses and then comparing them with the maximum safe stress that can be applied without causing failure of the material according to an appropriate failure theory. In this paper, we suggest quick and ready-to-use expressions and graphs for calculating factor of safety for biaxial stress states for a number of commonly-used failure theories. These graphs can be directly used as design charts for computing factor of safety in engineering design activities.
Determination of Principal Curvatures and Contact Ellipse for Profile Crowned Helical Gears
Authors: Feng P.-H. , Litvin F. L , Townsend D. P. , Handschuh R. F.
Published: February 2008

Helical gears with localized bearing contact of tooth surfaces achieved by profile crowning of tooth surfaces are considered. Profile crowning is provided by application of two imaginary rack-cutters with mismatched surfaces. The goal is to determine the dimensions and orientation of the instantaneous contact ellipse that requires the determination of principle curvatures of pinion-gear tooth surfaces. A simplified solution to this problem is proposed based on the approach developed in [1, 2] for correlation of principal curvatures and directions of generating and generated tooth surfaces. The obtained equations are applied for profile crowning where the normal profiles of the rack-cutters are either a circular arc or a straight line.
Frictional Impact Analysis in Open-Loop Multibody Mechanical Systems
Authors: Ahmed S. , Lankarani H. M. , Pereira M. F. O. S.
Published: February 2008

Analysis of impact problems in the presence of any tangential component of impact velocity requires a friction model capable of correct detection of the impact modes. This paper presents a formulation for the analysis of impact problems with friction in open-loop multibody mechanical systems. The formulation recognizes the correct mode of impact; i.e., sliding, sticking, and reverse sliding. Poisson’s hypothesis is used for the definition of the coefficient of restitution, and thus the energy gains inherent with the use of the Newton’s hypothesis are avoided. The formulation is developed by using a canonical form of the system equations of motion using joint coordinates and joint momenta. The canonical momentum-balance equations are solved for the change in joint momenta using Routh’s graphical method. The velocity jumps are calculated balancing the accumulated momenta of the system during the impact process. The impact cases are classified based on the pre-impact positions and velocities, and inertia properties of the impacting systems, and expressions for the normal and tangential impulse are derived for each impact case. The classical problem of impact of a falling rod with the ground (a single object impact) is solved with the developed formulation and verified. Another classical problem of a double pendulum striking the ground (a multibody system impact) is also presented. The results obtained for the double pendulum problem confirms that the energy gain in impact analysis can be avoided by considering the correct mode of impact and using the Poisson’s instead of the Newton’s hypothesis.
A Procedure for Upgrading an Electronic Control Diesel Fuel Injection System by Considering Several Engine Operating Regimes Simultaneously
Authors: Kegl B.
Published: February 2008

This paper describes an optimal design procedure for improving the injection rate histories of an electronic control diesel fuel injection system (ECD-FIS) with sleeve-timing-controlled pump. The research objective was to develop an approach for upgrading an existing ECD-FIS by performing only some low-cost modifications on its design. Therefore, the design variables are related to a relative small number of geometrical and control parameters of the injection system. The geometrical parameters influence only the shape of a rational Be´zier curve, representing the cam profile of the pump. The control parameters influence the injection timing and injection quantity. These control parameters are introduced into the set of design variables in order to enable good results over the whole engine operating regime. The design problem is formulated in a form of a non-linear problem of mathematical programming. Several operating regimes are simultaneously taken into account by an appropriate objective function while some geometrical properties of the cam profile as well as some injection parameters are kept within acceptable limits by the imposed constraints. The theory is illustrated with a numerical example.
Mass Center of Planar Mechanisms Using Auxiliary Parallelograms
Authors: Gokce A. , Agrawal S. K.
Published: February 2008

Center of mass is an important property of a mechanism. In biomechanics, in many studies, one monitors the motion of this point. The center of mass has importance in development of gravity compensated exercise machines and test beds on earth that mimic the behavior of systems in space. In this paper, a method is described where auxiliary parallelograms are added to a planar mechanism to identify the location of the center of mass of the original mechanism. In this procedure, the original and the augmented mechanisms have the same number of degrees-of-freedom. During motion, the center of mass is a physical point which can be monitored or used for purposes motivated from the application.