bluuebunny/crossref_metadata_2025 huggingface dataset:
The Modeling of Bevel Gears Using the Exact Spherical Involute
Authors: Al-Daccak M. J. , Angeles J. , Gonza´lez-Palacios M. A.
Published: June 2008

The solid modeling of bevel gears has been recognized as a major design challenge. Various approaches have been proposed to approximate the theoretical involute-generated contact surface of bevel gears. As a means to accurately represent contact surfaces of these gears, the exact spherical involute is introduced here. The solid models of straight and spiral bevel gears are obtained by applying simple sweeping techniques to their tooth profiles, which are described by the exact spherical involute. Futhermore, the volumetric properties of the modeled bevel gears are readily computed from their piecewise-linear approximation.
The Generation of Contact Surfaces of Indexing Cam Mechanisms—A Unified Approach
Authors: Gonza´lez-Palacios M. A. , Angeles J.
Published: June 2008

In this paper the ruled surfaces of two rigid bodies that are in contact while moving with a prescribed time-varying angular-velocity ratio are generated. These are then used as the contact surfaces of indexing cam mechanisms. In this way, planar, spherical, and spatial mechanisms are synthesized in a unified framework, the pressure angle, for all these cases, being analyzed. The approach is illustrated with various examples.
Optimal Packaging of Complex Parametric Solids According to Mass Property Criteria
Authors: Landon M. D. , Balling R. J.
Published: June 2008

A solution to the 3-D optimal packaging problem is presented. The positions and orientations of arbitrarily shaped objects in arbitrarily shaped 3-D containers are found. Mass property and spatial criteria are addressed. The robustness and speed of the optimal packaging solution is increased by supplying explicit gradients for the optimization search routines.
A New Approach for Designing Fast Expert Systems
Authors: Lu Peng , Siddall J. N.
Published: June 2008

A new method is proposed for rapidly solving expert system applications using Boolean algebra formulations. The method consists of two algorithms, applied after the conventional hierarchical type rules have been converted to Boolean expressions. The first algorithm automatically reduces the expressions to the equivalent of only two levels in a logic network, eliminating all intermediate conclusions, and also minimizes the number of inputs per rule. This algorithm has general application in the condensation of rule systems, and makes possible the use of high speed bit matching in specific solutions. The second algorithm operates on the reduced rule set so that, in a given application, a rapid solution is achieved using the fewest possible items of evidence, or user inputs. It is believed that these algorithms will be particularly useful in applications where high speed solutions are important.
An Optimization-Based Framework for Simultaneous Plant-Controller Redesign
Authors: Beyers R. , Desa S.
Published: June 2008

In this paper we develop a framework for the redesign of computer-controlled, closed-loop, mechanical systems for improved dynamic performance. A central notion which underlies the redesign framework is that, in order to achieve the best possible performance from a constrained closed-loop system, the plant and controller should be designed simultaneously. The framework is presented as the formulation and solution of a progression of optimization problems which establish the limits of performance of the dynamic system under various conditions of interest, thereby enabling the engineer to systematically establish the various redesign possibilities. Using a second order linear dynamic system and a nonlinear controller as an example, we demonstrate the application of the framework and substantiate the idea that in order to achieve the best possible performance from a constrained closed-loop system, the plant and controller should be redesigned simultaneously. We then show how the redesign framework can be used to select the best control strategy for a robotic manipulator from a dynamic performance standpoint. Finally, in order to demonstrate that the redesign framework yields solutions which the engineer can implement with confidence, we present the experimental verification of the numerical solution of a manipulator redesign optimization problem.
An Augmented Lagrange Multiplier Based Method for Mixed Integer Discrete Continuous Optimization and Its Applications to Mechanical Design
Authors: Kannan B. K. , Kramer S. N.
Published: June 2008

An algorithm for solving nonlinear optimization problems involving discrete, integer, zero-one, and continuous variables is presented. The augmented Lagrange multiplier method combined with Powell’s method and Fletcher and Reeves Conjugate Gradient method are used to solve the optimization problem where penalties are imposed on the constraints for integer/discrete violations. The use of zero-one variables as a tool for conceptual design optimization is also described with an example. Several case studies have been presented to illustrate the practical use of this algorithm. The results obtained are compared with those obtained by the Branch and Bound algorithm. Also, a comparison is made between the use of Powell’s method (zeroth order) and the Conjugate Gradient method (first order) in the solution of these mixed variable optimization problems.
Rule-based Shape Optimization of Disks Subjected to Transient Thermoelastic Loading
Authors: Ke J. , Elbella A.
Published: June 2008

This study introduces a rule-based geometric approach to the form optimization of axisymmetric components subjected to transient thermoelastic loading. A finite element algorithm is used for structural analysis and the computation of objective function and design constraints values. To satisfy a prescribed design objective, programmed geometric rules are used to iteratively modify the shape. The posed optimization problem is the minimization of the component’s weight while maintaining the stresses in the structure within allowable limits. A conventional optimization, the penalty function technique, coupled with the finite element algorithm is carried out for comparison. The effects of different loading conditions on component shape and performance are also investigated. A weight reduction of up to 57 percent is obtained for the casting shape of the disk. The results show the superiority of the rule-based approach to mathematical programming techniques. These results are obtained at lower computational costs and with accurate analysis.
An Orthogonal Complement Matrix Formulation for Constrained Multibody Systems
Authors: Blajer W. , Bestle D. , Schiehlen W.
Published: June 2008

A method is proposed for the automatic generation of an orthogonal complement matrix to the constraint matrix for the dynamic analysis of constrained multibody systems. The clue for this method lies in the determination of local constraint matrices and their orthogonal complements relative to the local reference frames of particular constrained points. These matrices are then transformed into the system’s configuration space in order to form the final constraint matrix and its orthogonal complement. The avoidance of singularities in the formulation is discussed. The method is especially suited for the dynamic analysis of multibody systems with many constraints and/or closed-loops.
Automated Linearization of Nonlinear Coupled Differential and Algebraic Equations
Authors: Trom J. D. , Vanderploeg M. J.
Published: June 2008

This paper presents a new approach for linearization of large multibody dynamic systems. The approach uses an analytical differentiation of terms evaluated in a numerical equation formulation. This technique is more efficient than finite difference and eliminates the need to determine finite difference pertubation values. Because the method is based on a relative coordinate formalism, linearizations can be obtained for equilibrium configurations with non-zero Cartesian accelerations. Examples illustrate the accuracy and efficiency of the algorithm, and its ability to compute linearizations for large-scale systems that were previously impossible.
Modeling of Flexible Bodies for Multibody Dynamic Systems Using Ritz Vectors
Authors: Wu H. T. , Mani N. K.
Published: June 2008

Vibration normal modes and static correction modes have been previously used to model flexible bodies for dynamic analysis of mechanical systems. The efficiency and accuracy of using these modes to model a system depends on both the flexibility of each body and the applied loads. This paper develops a generalized method for the generation of a set of Ritz vectors to be used in addition to vibration normal modes to form the modal basis to model flexible bodies for dynamic analysis of multibody mechanical systems. The Ritz vectors are generated using special distribution of the D’Alembert force and the kinematic constraint forces due to gross-body motion of a flexible body. Combined with vibration normal modes, they form more efficient vector bases for the modeling of flexible bodies comparing to using vibration normal modes alone or using the combination of static correction modes and vibration normal modes. Ritz vectors can be regenerated when the system undergoes significant changes of its configuration and the regeneration procedure is inexpensive. The effectiveness of using the combination of vibration normal modes and the proposed Ritz vectors is demonstrated using a planar slider-crank mechanism.
Recursive Linearization of Multibody Dynamics and Application to Control Design
Authors: Lin Tsung-Chieh , Yae K. Harold
Published: June 2008

The nonlinear equations of motion in multibody dynamics pose a difficult problem in linear control design. It is therefore desirable to have linearization capability in conjunction with a general-purpose multibody dynamics modeling technique. A new computational method for linearization is obtained by applying a series of first-order analytical approximations to the recursive kinematic relationships. The method has proved to be computationally more efficient. It has also turned out to be more accurate because the analytical perturbation requires matrix and vector operations by circumventing numerical differentiation and other associated numerical operations that may accumulate computational error.
Applications of Kinematic/Kinetic Performance Tools in Synthesis of Multi-DOF Mechanisms
Authors: Lee Ming-Yih , Erdman A. G. , Gutman Y.
Published: June 2008

Analytical and graphical performance synthesis tools for multi-DOF mechanisms are developed in the companion of this two-part paper [1]. Various performance indices derived from the Jacobian matrix for analyzing performance characteristics of multi-DOF mechanisms were proposed. These performance indices are the local kinematic coupling index (inner product of the Jacobian column vectors), the local directional mobility index (ratio of the Jacobian’s eigenvalues), and the local efficiency index (product of the Jacobian’s eigenvalues). In this paper, effort is placed on the applicability of the proposed analytical and graphical synthesis tools used to aid the design of multi-DOF mechanisms. Two examples representing open and closed chain mechanisms will be used to illustrate the effectiveness and efficiency of the proposed method. First, a two-link planar robotic manipulator is used to apply the proposed method. Following that, a two DOF parallel drive road simulator illustrates applicability of the suggested tools. Through these examples, geometric parameters and joint range limits of the mechanism are optimized through the evaluation of performance indices, eigen-ellipse and intersection angle between trajectory contours.
Parametric Excitation of Robotic Manipulators
Authors: Sankaranarayanan H. K. , Streit D. A. , Kim H. Y.
Published: June 2008

The predominant compliance in the dynamic response of the PUMA 560 robot manipulator arises in joints 2 and 3. Considering compliance of these two joints, the effects of user controlled variables on system stability are studied using Floquet theory. Specifically, manipulator configuration, operating speed, and trajectory amplitude are considered. For some configurations, instabilities are expected for ranges of operating frequencies which are significantly removed from the neighborhood of multiples of resonant frequencies of the stationary system. Results demonstrate overall trends in stability regions for several ranges of system configuration. Results also identify regions of rapidly changing stability of this industrial manipulator.
Optimal and Conforming Motion of a Point in a Constrained Plane
Authors: Ahrikencheikh C. , Seireg A. A. , Ravani B.
Published: June 2008

This paper deals with automatic generation of the motion of a point under both geometric and kinematic constraints. Optimal point paths are generated which are not only free of collisions with polygonal obstacles representing geometric constraints but also conform to kinematic constraints such as limits on velocity and acceleration. A specified minimum clearance from the boundaries of the obstacles is also satisfied. The new computational tools employed are an efficient representation of the free space, and a new motion generation algorithm with a computational time complexity of only O(n3 log n), where n is the total number of obstacle vertices. The algorithm finds the shortest or fastest curved path that also conforms with preset constraints on the motion of the point.
Process and Tolerance Considerations in the Automated Design of Fixtures
Authors: King D. A. , de Sam Lazaro A.
Published: June 2008

The long lead time for jig and fixture design is a serious bottleneck in modern manufacturing. Efforts to automate the design process using intelligent CAD systems have not been taken beyond the prototype stage mainly because of several impediments. These include the requirement of complex data structures to represent the workpiece and its attributes. Two deficiencies in existing systems for fixture design are addressed. These are (a) design for a sequence of operations and (b) design with tolerance considerations. Tolerance and process specifications are obtained from the user during an interactive session. A knowledge-based design system, REFIX, then designs a fixture for the workpiece. The fixture is optimized for a particular datum specification and sequence of operations. It is then analyzed and presented via the CAD system. REFIX is automated to minimize user-induced errors.
Formal Solution of N-Type Robust Parameter Design Problems with Stochastic Noise Factors
Authors: Michelena N. F. , Agogino A. M.
Published: June 2008

The Taguchi method of product design is a statistical experimental technique aimed at reducing the variance of a product performance characteristic due to uncontrollable factors. The goal of this paper is to provide a monotonicity analysis based methodology to facilitate the solution of N-type parameter design problems. The design obtained is robust in that the sensitivity to variations of uncontrollable factors (noise) has been minimized. The performance characteristic is unbiased in the sense that its expected value equals a target or specification. The proposed loss function is based on the absolute deviation of the characteristic with respect to the target, instead of the common square error approach. Conditions, like those imposed by monotonicity analysis, on the monotonic characteristics of the performance function are proven even for problems where the objective function is not monotonic and contains stochastic parameters. These conditions allow the qualitative analysis of the problem to identify the activity of some constraints. Identification of active sets of constraints allows a problem reduction strategy to be used, where the solution to the original problem is obtained by solving a set of problems with fewer degrees of freedom. Results for the case of one uncontrollable factor are independent of the probability measure on the factor. However, conclusions for the multiparametric case must take into account the characteristics of the probability space on which the random parameters are defined.
Design for Assembly Factors for Large and Heavy Parts
Authors: Wong J. H. , Sturges R. H.
Published: June 2008

Traditional Design for Assembly methods are limited to part sizes between a few millimeters to a few tens of centimeters in overall size and to part weights under a few kilograms. Parts in the range of a meter in overall size and weighing a few tens of kilograms are examined in this paper. An experimental plan separates weight, mass, and inertia and correlates these properties with assembly difficulty and time. When windage, part flexibility, and operator fatigue are absent, a set of three parameters serve to model these effects on human assembly performance. Adaptation of this result is made to extend a Design for Assembly methodology.
Fuzzing Ratings for Multiattribute Design Decision-Making
Authors: Carnahan J. V. , Thurston D. L. , Liu T.
Published: June 2008

Early in the design process, problems can arise when information is incomplete and goals are not known precisely. When preliminary design evaluation is approached as a multiattribute decision-making problem, both the levels of attributes and their relative importance can be treated as fuzzy numbers elicited from the designer. However, information regarding estimated attribute levels might be lost in limiting the designer to the standard universe of discourse. Another problem is that the attribute weights might be difficult for the designer to determine. A methodology is demonstrated for ranking alternatives based on the fuzzy distance from a fuzzy goal. The concept of a fuzzy line segment is introduced in order to make the universe of discourse continuous, thus not restricting the designer to a small set of fuzzy inputs. The fuzzy line segment makes it possible to more closely reflect the designer’s estimates of performance of design alternatives and the relative weight assigned to each attribute. It facilitates more accurate and precise linguistic input, and also provides a way to “fuzzify” numeric input. As a result, Saaty’s Analytic Hierarchy Process (AHP) can be employed to assist the designer in more accurately determining attribute weights.
A Method for Integrating End-User Preferences for Design Evaluation in Rule-Based Systems
Authors: Thurston D. L. , Crawford C. A.
Published: June 2008

Expert systems for design often include provisions for comparison of preliminary design alternatives. Historically, this task has been done on an ad hoc basis (or not at all) due to two difficulties. The first difficulty is design evaluation of multiple attributes. The second is that of taking into account highly subjective end-user preferences. Design experts have developed techniques which have enabled them to deal with these two difficulties; weighted average methods for the former and heuristic “rules of thumb” which categorize end-users for the latter. Limitations of these techniques are that the accuracy and precision of weighted average methods is inadequate, and that the “rules of thumb” might be reasonable and valid for most end-users, but not for some others. This paper brings quantitative rigor to the modelling of end-user preferences which is equal to that used in other phases of engineering analysis. We present a technique by which a heuristic rule base derived from technical experts can be analyzed and modified to integrate quantitative assessment of end-users’ subjective preferences. The operations research tool of multiattribute utility analysis is integrated with artificial intelligence techniques to facilitate preliminary evaluation of design alternatives of multiple attributes specific to individual users. The steps of the methodology are: develop the heuristic rule base, analyze the rule base to separate subjective from objective rules, add a subjective multiattribute utility assessment module, add an uncertainty assessment module, make objective rules explicit, and express performance attributes in terms of design decision variables. The key step is making the distinction between subjective and objective aspects of rules, and replacing the former with utility analysis. These steps are illustrated through an expert system for materials selection for a sailboat mast. Results indicate improved expert system performance for both “typical” and “atypical” end-users.
Composite Materials Design Database and Data Retrieval System Requirements
Authors: Rasdorf W. J.
Published: June 2008

Researchers and materials engineers require a greater understanding of the problems and solutions that emerge when integrating composite materials data with computer technology so that utilitarian composite materials databases can be developed to effectively and efficiently support analysis and design software. This paper primarily serves to analyze several of the problems facing developers of composite materials databases, evolving from the complexity of the materials themselves and from the current lack of testing and data representation standards. Without a clear understanding of the scope and nature of these problems, there is no possibility of designing concise yet comprehensive composites data models, yet we feel that such an understanding is presently lacking.
Experimental Study of Load-Deflection and Creep Characteristics of Compressed Rubber Components for Vibration Control Devices
Authors: Rivin E. I. , Lee B. S.
Published: June 2008

Elastomeric (rubber-like) materials are extensively used in various machine design applications, especially for flexible elements of vibration/shock/noise control devices and of power transmission couplings. In order to have high performance characteristics, such elements should accommodate large static and dynamic loads and/or large deflections in a limited size. In many applications high damping, low creep and substantial nonlinearity of the load-deflection characteristic are required. Since these specifications are contradictory, they are frequently impossible to satisfy just by selecting special rubber blends. The paper describes some results of an experimental study of geometric shape influence on the above specifications. It is demonstrated that for unbonded rubber flexible elements of a cylindrical shape loaded in a radial direction, a desirable nonlinear load-deflection characteristic can be naturally obtained (e.g., so-called “constant natural frequency” characteristic for vibration isolators), and creep rate can be significantly reduced as compared with conventional shapes of bonded rubber elements loaded in compression. This can lead to increased permissible deformations and/or loads on a flexible element, and/or to possibility of using rubber blends having higher damping (which is usually associated with higher creep rates). During the course of the research, an accelerated creep test technique has been developed which allows to use state-of-the-art servohydraulic testing machines for creep evaluation. It was also demonstrated that two definitions of the relative creep rate being used in the literature are not equivalent. More consistent results are obtained using the initial (free) height of the specimen (vs the deformation after 1 min of loading) as a reference dimension.
Member Stiffness and Contact Pressure Distribution of Bolted Joints
Authors: Lehnhoff T. F. , Ko Kwang Il , McKay M. L.
Published: June 2008

Member stiffnesses and the stress distributions in the bolts and members of bolted joints have been calculated for various bolt sizes, as well as thicknesses and materials of the members. The finite element method has been used to calculate the displacement and the stress distributions in the components of the bolted joint. Using axisymmetric elements, the bolted joint could be analyzed as a two-dimensional problem. Member stiffness ratios were calculated from the finite element results and compared with those calculated by a commonly used theory. The values were approximately comparable (16–30 percent difference) for the assumptions under which the theory was applied. Formulas and dimensionless curves which can be used to estimate the member stiffness ratios for several kinds of bolted joints are presented.
The Linear Approximated Equation of Vibration of a Pair of Spur Gears (Theory and Experiment)
Authors: Cai Y. , Hayashi T.
Published: June 2008

The nonlinear equation for the rotational vibration of a pair of spur gears has a restriction that the analytical solution of the equation cannot be obtained. In this paper, the linear equation of vibration is derived theoretically and its physical model, i.e., the linear model of vibration is presented. The analytical solution of the linear equation, which is derived by analytical method, agrees well with the numerically calculated result by the nonlinear equation. By analyzing the analytical solution of the linear equation in detail, we clarified the relation between the waveforms of the vibration and the profile error of gear pairs, and also found that the effect of the contact ratio to the vibration is large and complex. The equivalent error, accounting for effects of the static load, the time-varying stiffness, and the profile error of gear pairs, is proposed in this paper. It can be considered as promising for evaluating the profile error, because the vibration of gear pairs is excited mainly by the equivalent error. Finally, for confirming the above results, the vibration of two tested gear pairs has been measured by an experimental set-up for this purpose.
Conceptual Design of Gear Differentials for Automotive Vehicles
Authors: Yan Hong-Sen , Hsieh Long-Chang
Published: June 2008

An automotive gear differential is a joint-fractionated planetary gear train with two degrees-of-freedom. We summarize the characteristics of planetary gear trains and the design constraints of noncoupled automotive gear differentials to synthesize their corresponding kinematic graphs. Based on these graphs and the proposed respecializing process, we generate the atlas of design concepts for automotive gear differentials with any types of gear pairs. As a result, there are 4, 25, and 156 design concepts for five-, six-, and seven-bar automotive gear differentials, respectively.
Simulation of Mechanical Systems With Multiple Frictional Contacts
Authors: Wang Yin-Tien , Kumar V.
Published: June 2008

There are several engineering applications in which nominally rigid objects are subject to multiple frictional contacts with other objects. In most previous work, rigid body models have been used to analyze such systems. There are two fundamental problems with such an approach. First, the use of frictional laws, such as Coulomb’s law, introduces inconsistencies and ambiguities when used in conjunction with the principles of rigid body dynamics. Second, hypotheses traditionally used to model frictional impacts can lead to solutions which violate principles of energy conservation. In this paper these problems are explained with the help of examples. A new approach to the simulation of mechanical systems with multiple, frictional constraints is proposed that is free of inconsistencies.
Automatic Generation of Piecewise Constant Speed Motion with Smooth Transition for Multi-Axis Machines
Authors: Yang D. C. H. , Chou Jui-Jen
Published: June 2008

This paper presents a general theory on generating a smooth motion profile for the coordinated motion of five-axes CNC/CMM machines. Motion with constat speed is important and required in many manufacturing processes, such as milling, welding, finishing, and painting. In this paper, a piecewise constant speed profile is constructed by a sequence of Hermite curves to form a composite Hermite curve in parametric domain. Given the continuity of acceleration in our proposed speed profile, it generates relatively better product quality than traditional techniques. We also provide a method for the feasibility study of manufacturing capability in terms of the given machine, the desired path, and the assigned speed. We consider machine dynamics, actuator limitation, path geometry, jerk constraints, and motion kinematics.
On the Direct Kinematics of Spherical Three-Degree-of-Freedom Parallel Manipulators with a Coplanar Platform
Authors: Gosselin C. M. , Sefrioui J. , Richard M. J.
Published: June 2008

This paper presents a polynomial solution to the direct kinematic problem of a class of spherical three-degree-of-freedom parallel manipulators. This class is defined as the set of manipulators for which the axes of the three revolute joints attached to the gripper link are coplanar and symmetrically arranged. It is shown that, for these manipulators, the direct kinematic problem admits a maximum of 8 real solutions. A polynomial of degree 8 is obtained here to support this result and cases for which all the roots of the polynomial lead to real configurations are presented. Finally, the spherical parallel manipulator with collinear actuators, which received some attention in the literature, is also treated and is shown to lead to a minimal polynomial of the same degree. Examples of the application of the method to manipulators of each category are given and solved.
On the Direct Kinematics of Spherical Three-Degree-of-Freedom Parallel Manipulators of General Architecture
Authors: Gosselin C. M. , Sefrioui J. , Richard M. J.
Published: June 2008

In this paper, the direct kinematics of general spherical parallel three-degree-of-freedom manipulators is investigated. A polynomial of degree 8 is obtained to describe this problem and it is shown that this polynomial is minimal since 8 real solutions corresponding to actual configurations have been found for a given set of actuator coordinates and a given architecture. This result completes the study on the direct kinematics of spherical three-degree-of-freedom parallel manipulators undertaken by the authors in a previous paper. An example of an architecture and a set of actuator coordinates which lead to 8 real solutions is presented to illustrate the results.
Synthesis and Analysis of Spherical-Cylindrical (SC) Link in the McPherson Strut Suspension Mechanism
Authors: Kang H. Y. , Suh C. H.
Published: June 2008

This paper introduces the equations for the synthesis and analysis of the spherical-cylindrical (SC) link and its use for the McPherson suspension in automobiles. In this particular SC link, the cylindrical joint axis passes through the spherical joint and this type of SC link has yet to be investigated. The equations developed are applied to the design of a spatial mechanism—a McPherson suspension. This is modeled as a multiloop spatial rigid body guidance mechanism—an RSCS-SS, with a single degree of freedom for the guidance of the wheel assembly. Then the design equations for RS, SS, and newly developed SC links are applied to synthesize an RSCS-SS for up to three prescribed positions for the rigid body guidance. The mechanism is also analyzed for the two major motions of rigid body guidance problems: the wheel jounce/rebound and the steering, using the displacement matrix method. The displacement matrix method consists of two main components: matrices such as displacement, velocity, and acceleration matrices, and the constraint equations. Thus a McPherson suspension which is kinematically synthesized is also analyzed for the displacement, velocity, and acceleration during the entire range of guidance motion.
A Sensitivity Analysis Based Method for Robot Calibration
Authors: Kaizerman S. , Zak G. , Benhabib B. , Fenton R. G.
Published: June 2008

A new robot kinematic calibration procedure is presented. The parameters of the kinematic model are estimated through a relationship established between the deviations in the joint variables and the deviations in the model parameters. Thus, the new method can be classified as an inverse calibration procedure. Using suitable sensitivity analysis methods, the matrix of the partial derivatives of joint variables with respect to robot parameters is calculated without having explicit expressions of joint variables as a function of task space coordinates (closed inverse kinematic solution). This matrix provides the relationship between the changes in the joint variables and the changes in the parameter values required for the calibration. Two deterministic sensitivity analysis methods are applied, namely the Direct Sensitivity Approach and the Adjoint Sensitivity Method. The new calibration procedure was successfully tested by the simulated calibrations of a two-degree-of-freedom revolute-joint planar manipulator.
Direct Differential Kinematics of Hybrid-Chain Manipulators Including Singularity and Stability Analyses
Authors: Xu Yong-Xian , Kohli D. , Weng Tzu-Chen
Published: June 2008

A general formulation for the differential kinematics of hybrid-chain manipulators is developed based on transformation matrices. This formulation leads to velocity and acceleration analyses, as well as to the formation of Jacobians for singularity and unstable configuration analyses. A manipulator consisting of n nonsymmetrical subchains with an arbitrary arrangement of actuators in the subchain is called a hybrid-chain manipulator in this paper. The Jacobian of the manipulator (called here the system Jacobian) is a product of two matrices, namely the Jacobian of a leg and a matrix M containing the inverse of a matrix Dk, called the Jacobian of direct kinematics. The system Jacobian is singular when a leg Jacobian is singular; the resulting singularity is called the inverse kinematic singularity and it occurs at the boundary of inverse kinematic solutions. When the Dk matrix is singular, the M matrix and the system Jacobian do not exist. The singularity due to the singularity of the Dk matrix is the direct kinematic singularity and it provides positions where the manipulator as a whole loses at least one degree of freedom. Here the inputs to the manipulator become dependent on each other and are locked. While at these positions, the platform gains at least one degree of freedom, and becomes statically unstable. The system Jacobian may be used in the static force analysis. A stability index, defined in terms of the condition number of the Dk matrix, is proposed for evaluating the proximity of the configuration to the unstable configuration. Several illustrative numerical examples are presented.
Analytical-Form Position Analysis of the 7-Link Assur Kinematic Chain with Four Serially-Connected Ternary Links
Authors: Innocenti C.
Published: June 2008

The paper addresses the position analysis of the 7-link Assur kinematic chain that features three binary links and four serially-connected ternary links. The analysis, aimed at finding all possible assembly configurations of the Assur kinematic chain, is carried out by first devising a set of three constraint equations in a corresponding number of unknowns. Then, by an original elimination procedure, two out of the three unknowns are simultaneously dropped out. As a result, a final algebraic equation of degree sixteen with only one unknown and free from extraneous roots is obtained. The sixteen solutions of this equation provide as many assembly configurations for the Assur kinematic chain in the complex field. Finally, a case study is reported.
Mobility Analysis and Type Identification of Four-Link Mechanisms
Authors: Mallik A. K.
Published: June 2008

An alternative derivation of the simple criteria, in terms of linkage parameters, demarking the zones of nonexistence of double-crank and crank-rocker RSSR mechanisms is presented. The existence of a crank is verified by polynomial discriminants of the limit position. Closed from solutions are obtained for type identification for 4R spherical, RCCC, RSSP, and planar 4R mechanisms by treating these as the limiting cases of an RSSR mechanism.
Synthesis of Wrapping Cams
Authors: Tidwell P. H. , Bandukwala N. , Dhande S. G. , Reinholtz C. F. , Webb G.
Published: June 2008

This paper describes a technique for synthesizing a force-generating mechanism composed of a cam wrapped by a belt or chain. Such mechanisms will hereafter be referred to as “wrapping cams.” Synthesis methods for two configurations of this mechanism are presented. In the simplest case, the cam is wrapped by a belt or chain under constant tensile force, producing a nonlinear torque at the cam. In the second case, the cam is under constant torque, producing a nonlinear belt or chain force. While wrapping cams are far less common than cams that generate specified follower displacement functions, applications for wrapping cams exist in counter-balancing mechanisms, exercise equipment, and process machines.
Two Station Geneva Mechanisms
Authors: Zhang Y. , Fenton R. G. , Xu J.
Published: June 2008

A conventional Geneva mechanism must have at least three radial slots (stations). This paper shows that it is possible to design a Geneva mechanism with only two slots, provided that the shape of the slot is not a straight radial line but a curved line. The design procedure of the two slot Geneva wheel is outlined in this paper. In addition, two different methods are provided to reduce the size of the slot and change its shape in order to make the mechanism feasible for practical applications. The reduction of the slot size is achieved either by choosing appropriate values for α0, which is the half indexing angle of the crank, or by using the method of offsetting. The offsetting technique presents an excellent capability of suitably altering the slot shape without affecting the kinematic properties of the mechanism. The paper also shows the superior kinematic characteristics of Geneva wheels having two slots. The design and manufacture of these mechanisms are simple, and they have a good potential for wide ranging practical applications.
Six and Seven Position Triad Synthesis Using Continuation Methods
Authors: Subbian T. , Flugrad D. R.
Published: June 2008

A continuation method is used for the synthesis of triads for motion generation with prescribed timing applications. The procedure is applied to solve both six and seven position synthesis problems. Triad Burmester curves are generated for the six position synthesis problem and an eight-bar mechanism is designed to illustrate the procedure. For the seven position synthesis problem, a finite number of solutions are obtained. A geared five-bar, seven position path generation example is considered.
Verification of Boundary Representations of Solid Models
Authors: Jablokow A. G. , Uicker J. J. , Turcic D. A.
Published: June 2008

Verification of polyhedral boundary representations (B-reps) of solid models through the use of an algorithm is addressed here. The validity conditions for B-rep models are presented in a format which leads directly to a set of verification algorithms. The validity verification algorithms are intended for design automation through execution after each solid modeling operation, after localized geometry modification, on imported object model databases, prior to storage of object models, or prior to execution of an application program on the solid model.
Application of Face-Gear Drives in Helicopter Transmissions
Authors: Litvin F. L. , Wang J.-C. , Bossler R. B. , Chen Y.-J. D. , Heath G. , Lewicki D. G.
Published: June 2008

The use of face-gears in helicopter transmissions was explored. A light-weight, split torque transmission design utilizing face-gears was described. Face-gear design is discussed. Topics included basic design geometry, tooth generation, limiting inner and outer radii, and recommendation for the gear ratio. Face-gear experimental studies were also included and the feasibility of face-gears in high-speed, high-load applications such as helicopter transmissions was demonstrated. Torque-split tests were performed and demonstrated an accurate split of torque using the face-gear concept.
Computerized Analysis of Meshing and Contact of Gear Real Tooth Surfaces
Authors: Zhang Y. , Litvin F. L. , Maruyama N. , Takeda R. , Sugimoto M.
Published: June 2008

The authors propose a technique for computerized simulation and tangency of gears provided with real tooth surfaces. The deviations of real tooth surfaces from the theoretical ones are caused by the distortion of surfaces during the heat treatment and lapping. The main ideas of the proposed technique are as follows: (i) The gear real tooth surface is represented by a sum of two vector functions that determine the theoretical tooth surface and the deviations of the real surface from the theoretical one, respectively. (ii) Both vector functions mentioned above are represented in terms of the same Gaussian surface coordinates (the Gaussian coordinates of the theoretical surface). (iii) The deviations of the real surface are initially determined numerically using the data of surface coordinate measurements. The analytical representation of the vector function of deviations is based on the interpolation of a numerically given vector function by a bi-cubic spline. The interpolation provides a relatively high precision because it is accomplished for the surface of small deviations but not for the whole real surface. (iv) The computerized simulation of meshing and tangency of gears with real tooth surfaces is based on the algorithm that describes the conditions of continuous tangency of real tooth surfaces. The proposed approach is illustrated with application to the hypoid gear drive with real tooth surfaces. The data of surface deviations have been determined experimentally at the Nissan Motor Co.
Computerized Simulation of Generation of Internal Involute Gears and Their Assembly
Authors: Litvin F. L. , Hsiao C.-L. , Wang J.-C. , Zhou X.
Published: June 2008

The contents of the paper cover the determination of conditions: (i) of nonundercutting by axial and axial-radial generation of internal gears by shapers, and (ii) avoidance of interference by axial and axial-radial assembly. The authors have developed computer programs for simulation of undercutting and interference, design charts and a table that allow to determine the limiting number of teeth of the cutter and pinion considering the tooth number of internal gear as known. The details of developed algorithms are given in the Appendices. The paper is illustrated with computer graphics and numerical examples.
Optimal Design of Compact Spur Gear Reductions
Authors: Savage M. , Lattime S. B. , Kimmel J. A. , Coe H. H.
Published: June 2008

The optimal design of compact spur gear reductions includes the selection of bearing and shaft proportions in addition to the gear mesh parameters. Designs for single mesh spur gear reductions are based on optimization of system life, system volume, and system weight including gears, support shafts, and the four bearings. The overall optimization allows component properties to interact, yielding the best composite design. A modified feasible directions search algorithm directs the optimization through a continuous design space. Interpolated polynomials expand the discrete bearing properties and proportions into continuous variables for optimization. After finding the continuous optimum, the designer can analyze near optimal designs for comparison and selection. Design examples show the influence of the bearings on the optimal configurations.
The Stress Intensity Factor and Stiffness for a Cracked Spur Gear Tooth
Authors: Daniewicz S. R. , Collins J. A. , Houser D. R.
Published: June 2008

The stiffness of a spur gear tooth mesh controls load sharing in an operating gearset as well as vibratory properties which further dictate fatigue resistance and gear noise. A spur gear mesh consisting of a pinion with a single cracked tooth and an uncracked gear is considered. Expressions are presented which allow the determination of stress intensity factors for small through face width fatigue cracks in spur gear teeth. Predictions of tooth pair stiffness for a cracked pinion tooth and uncracked gear tooth pair are made using an analytical model. The model is based on elastic energy methods and fracture mechanics principles. The model employs a conformal mapping technique from elasticity theory, often denoted in spur gear applications as the complex potential method, in which a gear tooth is mapped onto on elastic half-plane.
Effect of Cutter Performance on Finished Tooth Form in Gear Shaving
Authors: Moriwaki I. , Fujita M.
Published: June 2008

A computer program has been developed to simulate a gear shaving process. The present paper describes a new cutting model of a shaving process so as to incorporate the effect of a cutting performance of a shaving cutter into the simulation program. This cutting model is constructed on the assumption that an excess depth of cut over a certain criterion yields a material removal from a tooth flank of work gear. In addition, the criterion has no definite value, but its value shows the normal distribution. The mean value of the distribution can define a characteristic of cutting performance of the shaving cutter. A small mean value means that even small depth of cut can cause a stock removal. In other words, the cutter has a good cutting performance. After reliability being confirmed, computer simulations reveal an effect of the cutter performance on shaved tooth form. As a result, a pressure angle error on the shaved tooth profile becomes remarkable as the cutter performance becomes worse. Therefore, the developed computer simulation program is useful for the design of the shaving cutter and judgment of tool life expiring.
Dynamic Analysis of a Multi-Mesh Helical Gear Train
Authors: Kahraman A.
Published: June 2008

In this paper, the dynamic behavior of a multi-mesh helical gear train has been studied. The gear train consists of three helical gears, with one of the gears in mesh with the other two. A three dimensional dynamic model which includes transverse, torsional, axial and rotational (rocking) motions of the flexibility mounted gears has been developed. Two different loading conditions have been identified. In case-I, the system is driven by the gear in the middle, and in case-II, the system is driven by one of the gears at either end of the gear train. The phase difference between the two gear meshes has been determined under each loading condition. The natural modes have been predicted, and their sensitivity to the helix angle and different loading conditions has been quantified. The forced response, which includes dynamic mesh and bearing forces, due to the static transmission error excitation has been obtained. Effects of loading conditions and asymmetric positioning on the response have also been explored.
Planetary Gear Train Dynamics
Authors: Kahraman A.
Published: June 2008

A model to simulate the dynamic behavior of a single-stage planetary gear train with helical gears is developed. The three-dimensional dynamic model includes all six rigid body motions of the gears and the carrier. The generic nature of the formulation allows the analysis of a planetary gear set with any number of planets. Planets can be arbitrarily spaced (equally or unequally) around the sun gear. The model is also capable of handling different planet meshing conditions which are functions of number of gear teeth and planet positions. The linear time-invariant equations of motion are solved to obtain the natural modes and the forced vibration response due to static transmission errors. The proposed model is employed to describe the effects of the planet mesh phasing conditions on the dynamic behavior of a four-planet system.