bluuebunny/crossref_metadata_2025 huggingface dataset:
Shape Synthesis and Optimization Using Intrinsic Geometry
Authors: Tavakkoli S. , Dhande S. G.
Published: June 2008

The present paper outlines a method of shape synthesis using intrinsic geometry to be used for two-dimensional shape optimization problems. It is observed that the shape of a curve can be defined in terms of intrinsic parameters such as the curvature as a function of the arc lenght. The method of shape synthesis, proposed here, consists of selecting a shape model, defining a set of shape design variables and then evaluating Cartesian coordinates of a curve. A shape model is conceived as a set of continuous piecewise linear segments of the curvature; each segment defined as a function of the arc length. The shape design variables are the values of curvature and/or arc lengths at some of the end-points of the linear segments. The proposed method of shape synthesis and optimization is general in nature. It has been shown how the proposed method can be used to find the optimal shape of a planar Variable Geometry Truss (VGT) manipulator for a prespecified position and orientation of the end-effector.
Prediction of Mechanical States in Wound Capacitors
Authors: Reuter R. C. , Allen J. J.
Published: June 2008

The problem of determining the mechanical states inside wound capacitor rolls is addressed through the application of two dimensional, linear elasticity. Allowances are made for heterogeneous wound construction of the capacitor, orthotropic material behavior of the capacitor constitutents, and arbitrary winding tension. A key element in the formulation is the derivation of material properties for a wound, orthotropic layer which is equivalent in behavior to a stack of dissimilar piles such as are actually wound on the capacitor simultaneously during one turn of the mandrel. The dissimilar plies are necessary by virtue of the conductor and dielectric materials which must be present in a capacitor. The derivation of predictive equations is based on winding the equivalent layer on an appropriate mandrel, followed by a recovery of the individual ply responses. The capability to explicitly calculate the winding tensions which would be necessary to produce a required wound tension dependence upon capacitor radius is also developed. Numerical results for typical capacitor design and construction are presented, and justification for the application of optimization theory in capacitor development is demonstrated.
Optimization of Mechanical States in Wound Capacitors
Authors: Allen J. J. , Reuter R. C.
Published: June 2008

The winding process is encountered frequently in manufacturing, such as winding of polymer films and paper, laminated pressure vessel construction, and the manufacture of wound capacitors. The winding of capacitors will typically involve hundreds of plies of conductor and dielectric wound over a core. Due to the large number of layers, the calculation of the mechanical states within a wound capacitor is a significant computational task. Techniques for calculation of the mechanical states within a wound capacitor are derived and discussed in reference [1]. The focus of this paper is the formulation and application of optimization techniques for the design of wound capacitors. The design criteria to be achieved is a specified uniform wound tension in a capacitor. The paper will formulate an optimization statement of the wound capacitor design problem, develop a technique for reducing the numerical calculation required to repeatedly analyze the capacitor which is required by the optimization algorithm, and apply the technique to an example. The following effects will be investigated using the example. (1) The ability of low order winding tension profiles, such as constant, linear, or bilinear profiles, to meet the optimization objective. (2) The usefulness and practicality of high order winding tension profiles, which require a significant number of design variables to meet the optimization objective. (3) Differential weighting of the aluminum and mylar layer wound tensions in the objective function will be investigated as a technique for achieving the optimization/design goal.
Reasoning on the Location of Components for Assembly Packaging
Authors: Kim J. J. , Gossard D. C.
Published: June 2008

The process of locating components in an available space while satisfying spatial relationships among the components is called packaging. The task requires extensive spatial reasoning about geometric shapes. It is a generic design task common to many domains. It is also very time-consuming, especially as machines become more compact and complex. This paper describes progress toward automation of the packaging problem. An approach is proposed to determine the optimal locations of components in an assembly from spatial relationships between the components. The approach utilizes a novel combination of optimization and solid modeling techniques.
PRIMA: A Production-Based Implicit Elimination System for Monotonicity Analysis of Optimal Design Models
Authors: Rao J. R. , Papalambros P. Y.
Published: June 2008

Monotonicity analysis is a useful method for analyzing optimal design models prior to numerical computation. Much of the information required for such analysis is represented in the monotonicity table. Rigorous procedures using the monotonicity principles and the implicit function theorem have been combined with heuristics, to extract additional constraint activity knowledge based only on the information contained in the monotonicity table. PRIMA is a production system implemented in the OPS5 programming environment. The system receives as input the monotonicity table of the initial model and derives global facts about boundedness and constraint activity by heuristic search of sequences of successively reduced models. Such reduction is obtained by implicit elimination of active constraints. Global facts generated automatically by this reasoning system can be used either for a global solution, or for a combined local-global active set strategy.
Geometry of Contact and Hertzian Stress Analysis of Frictional Coupling Elements of Multidisk Stepless Transmission With Initial Point Contact
Authors: Lukowski S. A. , Medeksza L. A. , Claar P. W.
Published: June 2008

This paper presents an analysis of the contact stresses and the contract area of mating disks in frictional transmission. Hertz’s formulations are adopted to determine the maximum contact stresses as well as the size of the contact area resulting from elastic deformation due to clamping force. Hertz’s formulations are expressed in terms of geometrical features of the active surface of mating disks. The obtained relationships can be readily applied for quantitative estimation of the contact stresses and the contact area parameters for different range of transmission ratio. Samples of numerical results are presented in graphical form.
Straddle Design of Spiral Bevel and Hypoid Pinions and Gears
Authors: Litvin F. L. , Kuan C. , Kieffer J. , Bossler R. , Handschuh R. F.
Published: June 2008

The design of spiral bevel and hypoid gears that have a shaft extended from both sides of the cone apex (straddle design) is considered. A main difficulty of such a design is determining the length and diameter of the shaft that might be undercut by the head cutter during gear tooth generation. A method that determines the free space available for the gear shaft is proposed. The approach avoids collision between the shaft being designed and the head cutter during tooth generation. The approach is illustrated with a numerical example.
Design Curves for Maximum Stresses in Blocks Containing Pressurized Bore Intersections
Authors: Sorem J. R. , Shadley J. R. , Tipton S. M.
Published: June 2008

Intersecting bore geometries are used in a number of industrial applications such as in fluid ends of reciprocating pumps. Maximum tensile stresses at stress concentration points in the block can be many times the fluid pressure in the bores. Obtaining good estimates of the maximum stresses in the structure is necessary for making sound design decisions on the block dimensions. Finite element models of the bore intersection geometry were analyzed for ranges of bore sizes and block dimensions. Results of the finite element model were compared with predictions provided by a popular approximation method based on mechanics of materials principles. The approximation method was found to underpredict the maximum stresses in the block in almost every case analyzed. For some conditions, the maximum stresses computed from the finite element model were more than two times the predictions provided by the approximation method. Design curves, based on the ratio of the sizes of the intersecting bores, are presented for selecting block dimensions to meet desired maximum stress criteria.
Computation of Member Stiffness in Bolted Connections
Authors: Wileman J. , Choudhury M. , Green I.
Published: June 2008

The member stiffness in a bolted connection has a direct influence upon safe design with regard to both static and fatigue loading, as well as in the prevention of separation in the connection. This work provides a simple technique for computing the member stiffness in many types of bolted connections. Finite element analyses are performed for joints having a range of materials and geometries, and the results are generalized by nondimensionalization. An exponential expression for the stiffness is determined, and the results are compared with those of some of the techniques currently used.
Generic Models for Designing Dwell Mechanisms: A Novel Kinematic Design of Stirling Engines as an Example
Authors: Kota S.
Published: June 2008

The desirable motion characteristics of mechanisms are so implicit that they are difficult to express analytically. Our design methodology involves development of generic design models through abstractions of entire emotion characteristics. We have developed a finite set of generic models (for straight-line, circular-arc, and dwell mechanisms) that represents the entire design space in the sense that a given design specification falls under at least one of the generic design models. This paper presents the generic design models for four-bar straight-line, circular arc, and six-bar dwell linkage mechanisms. The models presented here provide ready-made designs for many dwell applications. We have also presented a new concept in mechanisms design in which multiple coupler points on a four-bar linkage are used to drive different output dyads resulting in multiple dwell outputs. Finally, a new mechanism for the opposed piston stirling engine is presented to illustrate the use of generic design models and the application of a single-input controlling dual output motions with dwells.
The Synthesis of Manipulators with Prescribed Workspace
Authors: Gosselin C. M. , Guillot M.
Published: June 2008

This paper presents an algorithm for the optimization of the workspace of planar manipulators. The objective is to be able to synthesize manipulators whose workspace is as close as possible of being equal to a prescribed working area. The procedure begins with a geometric description of both the desired and the actual workspaces. Methods of computing the intersection of these regions are then developed. Finally, the optimization aims at minimizing the area of the regions contained in one of the workspaces—prescribed or actual—but not in the other. Results obtained with serial and parallel planar manipulators are shown and the possibility of extending the method to spatial cases is considered.
Swept Volume Determination and Interference Detection for Moving 3-D Solids
Authors: Kieffer J. , Litvin F. L.
Published: June 2008

The volume swept out by a moving 3-dimensional (3-D) solid has been recognized as important for the simulation of interference between moving solids. Its use has been proposed for the detection of collision (Ganter and Uicker, 1986), as well as for simulation of the machining process (Wang and Wang, 1986). This paper proposes: (a) a general approach for swept volume determination and (b) a method for interference detection that is based on 2-D projections of swept volumes.
On the Synthesis of Straight Line, Constant Velocity Scanning Mechanisms
Authors: Hodges P. H. , Pisano A. P.
Published: June 2008

This paper presents a kinematic synthesis of constant-velocity, straight-line coupler-point motion of two planar mechanisms. After the derivation of synthesis equations, the numerical results of a grid search to determine the linkage dimensions for maximum constant velocity, with minimal straight line error, are presented. Plots of acceleration magnitude, transmission angles, and transverse velocity are presented as a function of the percentage of the constant velocity portion of a cycle of input motion. For a 5R2P Stephenson 6-bar linkage, normalized velocity errors as small as 2 percent can be maintained over 40 percent, or more, of the input cycle. A 7R Watt 6-bar linkage, while not achieving quite as high values as the 5R2P linkage, nevertheless can maintain normalized velocity errors as low as 2.5 percent over as much as 39 percent of the input cycle. These levels of performance must be weighed against unfavorable transmission angles, and in many cases, other undesirable effects, such as large accelerations and large transverse travel. The results show that, in order to maintain minimally acceptable transmission angle requirements, the velocity error and scan fraction requirements may be as little as 2.0 percent and as much as 35 percent, respectively.
A Complete Solution for the Inverse Kinematic Problem of the General 6R Robot Manipulator
Authors: Lee H. Y. , Woernle C. , Hiller M.
Published: June 2008

The inverse kinematic problem of the general 6R robot manipulator is completely solved by means of a 16th degree polynomial equation in the tangent of the half-angle of a revolute joint. An algorithm is developed to compute the desired joint angles of all possible configurations of the kinematic chain for a given position of the end-effector. Examples for robots with maximal 16 different configurations show that the polynomial degree 16 is the lowest possible for the general 6R robot manipulator. Further, a numerical method for the determination of the boundaries of the workspace and its subspaces with different numbers of configurations is developed. These boundaries indicate the singular positions of the end-effector.
A Recursive Quadratic Programming Based Method for Estimating Parameter Sensitivity Derivatives
Authors: Beltracchi T. J. , Gabriele G. A.
Published: June 2008

Parameter sensitivity analysis is defined as the estimation of changes in the modeling functions and design point due to small changes in the fixed parameters of the formulation. There are currently several methods for estimating parameter sensitivities which either require second order information, or do not return reliable estimates for the derivatives. This paper presents a method based on the use of the recursive quadratic programming method in conjunction with differencing formulas to estimate parameter sensitivity derivatives without the need to calculate second order information. In addition, a modified variable metric method for estimating the Hessian of the Lagrangian function is presented that is used to increase the accuracy of the sensitivity derivatives. Testing is performed on a set of problems with Hessians obtained analytically, and on a set of engineering related problems whose derivatives must be estimated numerically. The results indicate that the method provides good estimates of the parameter sensitivity derivatives on both test sets.
Definition of Pressure and Transmission Angles Applicable to Multi-Input Mechanisms
Authors: Dresner T. L. , Buffinton K. W.
Published: June 2008

Pressure angle is an important measure of the effectiveness with which a force is transmitted between a cam and follower. A pressure angle of zero degrees indicates that the force is transmitted with maximum effectiveness while a 90 deg pressure angle indicates that the force cannot make the desired contribution to the follower motion. There are a number of definitions available in the literature that can be used to determine pressure angle. These definitions are all consistent with the meaning of pressure angle described above when applied to followers driven by only a single cam. For followers driven by multiple inputs, however, we have found that none of these definitions provides a value of pressure angle that retains this same meaning. The purpose of this paper is to draw attention to this fact and to present a precise definition of pressure angle, as well as a discussion of its mathematical consequences, that property characterizes the performance of either single-input or multi-input cam-follower mechanisms. For single-input systems, this definition is shown to be equivalent to the definitions for pressure angle found in the literature. The applicability of this definition to the determination of transmission angle for linkages with multiple inputs is also discussed.
Perfect Equilibrators for Rigid Body Spatial Rotations About a Hooke’s Joint
Authors: Streit D. A. , Chung H. , Gilmore B. J.
Published: June 2008

Perfect spring equilibrator designs are identified which eliminate the effects of gravity on spatial rotations of a rigid body. The rigid body is connected to ground via a Hooke’s joint and all possible one and two zero-free-length spring equilibrator designs are identified. A general design procedure for n-spring equilibrators is also discussed.
Kinestatic Control: A Novel Theory for Simultaneously Regulating Force and Displacement
Authors: Griffis M. , Duffy J.
Published: June 2008

A new theory for the simultaneous control of force and displacement for a partially constrained end-effector is established based upon the general spatial stiffness of the manipulator. In general, the spatial stiffness of a compliant coupling that connects a pair of rigid bodies is used to map a small twist between the bodies into the corresponding interactive wrench. This mapping is based upon a firm geometrical foundation and establishes a positive-definite inner product (elliptic metric) that decomposes a general twist into a twist of freedom and a twist of compliance. A study of the invariant properties of this mapping leads to the discovery of what are defined as the eigen-screws of stiffness. Further, the spatial stiffness of a compliant coupling is modeled by theoretically replacing the coupling with a passive Stewart Platform-type parallel mechanism. It is important to recognize that this model does not depend upon the existence of a center-of-compliance. In fact, it describes a general state of spatial stiffness between any two rigid bodies. The culmination of these finding yields a practical and meaningful theory of Kinestatic Control, viz., the simultaneous regulation of force and displacement solely via the control of displacement.
Robert’s Theorem—A Proof
Authors: Johnston R. C. R.
Published: June 2008

This proof was written as a class handout, to flesh out the bare Theorem. Hunt, [1] mentions it in his discussion. It has similarities to that given by Hall [2], yet the differences give hope that an even more direct proof may be devised.
Kinematic Geometry of Spherical Evolutes
Authors: Schaaf J. A. , Yang An Tzu
Published: June 2008

In this paper, we define spherical evolutes corresponding to the trajectory of a point in spherical kinematics. We derive general expressions for the curvature properties of the nth spherical evolute in terms of the geodesic curvature and the derivative of the geodesic curvature for the (n-1)the spherical evolute. The results are illustrated by numerical examples for the motion of a circular cone rolling on a fixed circular cone, of a spherical turning-block linkage, and of a spherical four-bar linkage.
Conceptual Design of a Modular Robot
Authors: Cohen R. , Lipton M. G. , Dai M. Q. , Benhabib B.
Published: June 2008

In flexible automation approach to batch or job-shop production the main emphasis has always been on the re-programmability of the elements of a manufacturing system. The assumption that lies behind this philosophy is that “system flexibility” can be achieved through (mainly) software flexibility and limited hardware flexibility. Modular robots introduce a new dimension to flexible automation in terms of hardware flexibility, when compared to conventional industrial robots, in terms of yielding individual global optimal arm geometries for each of the tasks at hand. The objective of our ongoing research in the area of “mechanical design of modular robots” is to develop an inventory of basic modular units, which will allow a user to configure the most suitable robot geometry for a task (or a set of tasks) at hand. Standardization of these units and minimization of the size of the inventory constitute the two main goals of this research. In this paper some of our research results on the conceptual design of a modular robot are presented. The individual modular robot units that are presented include: one degree-of-freedom (dof) main joints (rotary and prismatic types), one dof end effector joints (Yaw, Pitch and Roll types), links and connectors.
Dynamic Stability Considerations in Elastic Closed Loop Linkage Systems
Authors: Nagarajan S. , Turcic D. A.
Published: June 2008

In this work a theoretical method is developed to identify critical speeds for elastic linkage systems. Critical speeds are input operating speeds where the response of the system is larger when compared to neighboring noncritical speeds. A survey of the literature reveals that theoretical methods of determining the critical operating speeds with experimental verification have not been applied by researchers for linkage systems with large number of elastic degrees of freedom and with all links considered as elastic members. Research works that address this problem are usually limited to mechanisms with only one link treated as an elastic member. The method of determining critical speeds in this work is an efficient implementation of Floquet theory, and is applicable for mechanism systems with large numbers of elastic degrees of freedom and with all links considered as elastic members. Experimental verification for the results obtained using this approach is provided in Nagarajan and Turcic (1991).
Effects of Geometric Parameters on Manipulator Dynamic Performance
Authors: Wiens G. J. , Zarrugh M. Y. , Scott R. A.
Published: June 2008

The sensitivity of the eigenvalues of a manipulator’s generalized inertia matrix with respect to the geometric parameters are used to form a set of indices as a measure of manipulator performance. The effects due to the geometric parameters and those due to purely mass characteristics of the manipulator’s links are separated by using the Denavit-Hartenberg representation and expressing each link’s local ineratia tensor in terms of principal moments about its center of mass. A global measure of the indices is defined and correlated with quantities such as workspace volume and reach.
Substitute-Wrists to Aid in the Placing of Tools on Robots With 3-R Spherical Wrists
Authors: Trabia M. , Davidson J. K.
Published: June 2008

This paper treats the three-jointed spherical wrist on which the tool is placed at an angle δ ≠ 0. A two-parameter set of axes is identified for the wrist such that the angular velocities and accelerations at the three joints are within acceptable limits during a 2π-rotation of the end-effector at constant speed about each such axis. This set of axes is compared both to the total set of available axes of full rotation and to the set for which the determinant of the wrist Jacobian is greater than a specified minimum value. For each set of axes, hypothetical substitute-wrists permit the generalization of design conditions for robots with spherical wrists on which δ = 0 to robots with spherical wrists on which δ ≠ 0, and they provide geometrical limits on tool-placement which bound the velocities and accelerations at the wrist joints. Lastly, comments are made about balancing the velocity and acceleration characteristics of the actuators in a spherical wrist.
Complete Solution of the Nine-Point Path Synthesis Problem for Four-Bar Linkages
Authors: Wampler C. W. , Morgan A. P. , Sommese A. J.
Published: June 2008

The problem of finding all four-bar linkages whose coupler curve passes through nine prescribed points has been a longstanding unsolved problem in kinematics. Using a combination of classical elimination, multihomogeneous variables, and numerical polynomial continuation, we show that there are generically 1442 nondegenerate solution along with their Roberts cognates, for a total of 4326 distinct solutions. Moreover, a computer algorithm that computes all solutions for any given nine points has been developed.
Optimal Blank Nesting Using Simulated Annealing
Authors: Jain P. , Fenyes P. , Richter R.
Published: June 2008

By reducing scrap, high volume stamped parts can be produced more economically. Scrap rate is heavily influenced by the nesting, or positioning, of the blanks onto the stock. Blank nesting is often done manually, resulting in inefficient nestings with high scrap rates. We have developed an automated nesting system which minimizes the scrap for continuous strip stamping processes. Using an integer grid technique, we compute the overlap between blanks and then apply simulated annealing, a probabilistic global optimization technique, to determine a new nesting with zero overlap and minimal scrap. We present several examples to illustrate the method.
Sizing Design Sensitivity Analysis of Dynamic Frequency Response of Vibrating Structures
Authors: Choi Kyung K. , Lee Jae Hwan
Published: June 2008

A continuum design sensitivity analysis method of dynamic frequency response of structural systems is developed using the adjoint variable and direct differentiation methods. A variational approach with a non-selfadjoint operator for complex variable is used to retain the continuum elasticity formulation throughout derivation of design sensitivity results. Sizing design variables such as thickness and cross-sectional area of structural components are considered for the design sensitivity analysis. A numerical implementation method of continuum design sensitivity analysis results is developed using postprocessing analysis data of COSMIC/NASTRAN finite element code to get the design sensitivity information of displacement and stress performance measures of the structures. The numerical method is tested using basic structural component such as a plate supported by shock absorbers and a vehicle chassis frame structure for sizing design variables. Accurate design sensitivity results are obtained even in the vicinity of resonance.
Automating Linear Tolerance Analysis Across Assemblies
Authors: Juster N. P. , Dew P. M. , de Pennington A.
Published: June 2008

One of the tests carried out by designers in an attempt to check whether an assembly of components will function correctly is tolerance analysis. Tolerance analysis, although relatively straightforward, is liable to be time consuming and error prone. It cannot be automated unless a suitable mathematical framework is developed to model the variations introduced by the manufacturing process. The designer allows for the variations by means of tolerances attached to the dimensions. This paper describes a suitable mathematical model and shows how it may be used to automate linear worst case tolerance analysis across assemblies. Experimental software has been written, based on the theory.
A Design Scheme for Multidisk Beier Traction Variators
Authors: Younes Y. K.
Published: June 2008

The unique design feature of the Beier traction variator is that it can provide a higher power capacity per unit volume by using multiple thin disk pairs in a planetary system. Operating with a single effective traction contact and with the absence of idlers and dummy elements, promises for high efficiencies are also encouraging. In this paper, a design scheme for such mechanical drives is developed. Kinematics and kinetics of the rolling sliding disks are presented yielding actual performance ratings. Geometrical slippage in the Hertzian contact areas is considered for evaluating power losses at different load levels and transmission ratios. A torque sensitive pressure device which automatically creates contact forces is incorporated in the analysis. Constant traction coefficient pertinent to the boundary lubrication mode nearing thin fluid film friction is adopted for actual performance estimates. Among the different geometrical parameters, the bead radius of the input disk flange was found to play a major role in limiting contact stresses and torque capacities. Efficiencies of transmission, excluding shaft support bearing losses, are above ninety percent for a power of one kilowatt per contact.
Configuration Tree Solver: A Technology for Automated Design and Configuration
Authors: Kott A. , Agin G. , Fawcett D.
Published: June 2008

Configuration is a process of generating a definitive description of a product that satisfies a set of specified requirements and known constraints. Knowledge-based technology is an important factor in automation of configuration tasks found in mechanical design. In this paper, we describe a configuration technique that is well suited for configuring “decomposable” artifacts with reasonably well defined structure and constraints. This technique may be classified as a member of a general class of decompositional approaches to configuration. The domain knowledge is structured as a general model of the artifact, an and-or hierarchy of the artifact’s elements, features, and characteristics. The model includes constraints and local specialists which are attached to the elements of the and-or tree. Given the specific configuration requirements, the problem solving engine searches for a solution, a subtree, that satisfies the requirements and the applicable constraints. We describe an application of this approach that performs configuration and design of an automotive component.
A New Graph Representation for the Automatic Kinematic Analysis of Planetary Spur-Gear Trains
Authors: Hsu Cheng-Ho , Lam Kin-Tak
Published: June 2008

The purpose of this paper is to propose a new graph representation to represent the kinematic structure of a planetary spur-gear train efficiently. Based on the graph representation, the kinematic analysis of planetary spur-gear trains is largely simplified. An interactive computer program is developed for the kinematic analysis of planetary spur-gear trains with any number of degrees of freedom. By only inputting the graph representation of a planetary spur-gear train and the data for the mating gear pairs, all possible fundamental circuits are determined and the rotational displacement equations are derived and solved automatically.
The Evolution of Commitments in the Design of a Component
Authors: McGinnis B. D. , Ullman D. G.
Published: June 2008

This paper traces the evolution of a component of a mechanical design from its initial inception to completion. This research focuses on the interplay of design objects, features, constraints, and design decisions. Based on empirical data extracted from verbal design protocols, a design terminology is developed. Constraints were identified in the protocol and classified according to their source, level of abstraction, and form or function orientation. A structure for constraints was also developed which decomposes the constraints and classifies them into ten basic feature relationships.
Vitruvius’s Auger and Galileo’s Bones: Paradigms of Limits to Size in Design
Authors: Petroski H.
Published: June 2008

Although scale effects have been known since ancient times to limit the size of structures, there has been a persistence of design errors evidently attributable to an ignorance or disregard of this limitation. Two classic case studies, one from Vitruvius and one from Galileo, of scale effects leading to failures are presented as paradigms for this genre of human error, and the repetition of it in a variety of major present-day designs is discussed. The value of the paradigms is seen to be in making the scale effect more prominent in the consciousness of students and young practitioners engaged in the process of design, thereby reducing the potential for ignoring or forgetting that successful designs cannot be scaled up indefinitely.
Some Property Data and Corresponding Weibull Parameters for Stochastic Mechanical Design
Authors: Mischke C. R.
Published: June 2008

This is the first paper in a series of three relating to stochastic methods in mechanical design. The others are entitled, “Fitting Weibull Strength Data and Applying it to Stochastic Mechanical Design,” and “Some Stochastic Mechanical Design Applications.” The purpose of this paper is to present some Weibull parameters of strength distributions that were deduced from published histographic data. Stochastic materials data are in short supply; yet a closer look shows a surprising amount available. However, the published data may need to be interpreted and personal tests reduced. This paper shows histographic data that was converted to three-parameter Weibull distributional fits with relevant goodness-of-fit information displayed.
Fitting Weibull Strength Data and Applying It to Stochastic Mechanical Design
Authors: Mischke C. R.
Published: June 2008

This is the second paper in a series relating to stochastic methods in mechanical design. The first is entitled, “Some Property Data and Corresponding Weibull Parameters for Stochastic Mechanical Design,” and the third, “Some Stochastic Mechanical Design Applications.” When data are sparse, many investigators prefer employing coordinate transformations to rectify the data string, and a least-square regression to seek the best fit. Such an approach introduces some bias, which the method presented here is intended to reduce. With mass-produced products, extensive testing can be carried out and prototypes built and evaluated. When production is small, material testing may be limited to simple tension tests or perhaps none at all. How should a designer proceed in order to achieve a reliability goal or to assess a design to see if the goal has been realized? The purpose of this paper is to show how sparse strength data can be reduced to distributional parameters with less bias and how such information can be used when designing to a reliability goal.
Some Stochastic Mechanical Design Applications
Authors: Mischke C. R.
Published: June 2008

This is the third paper in a series relating to stochastic methods in mechanical design. The two previous ones were entitled, “Some Property Data and Corresponding Weibull Parameters for Stochastic Mechanical Design,” and “Fitting Weibull Strength Data and Applying it to Stochastic Mechanical Design.” They presented the groundwork for addressing stochastic problems in machinery design to a reliability goal when strength data are sparse. The purpose of this paper is to utilize procedures for estimating reliability of machine elements when yielding, fracture, or distortion are the limiting or active constraints.
Finite Position Synthesis Using the Image Curve of a Spherical Four-Bar Motion
Authors: Bodduluri R. M. C. , McCarthy J. M.
Published: June 2008

This paper presents an approach to the finite position synthesis of spherical four-bar linkages that unites traditional precision theory with recent results in approximate position synthesis. This approach maps the desired positions to points in an image space, and the motion of the coupler of a spherical four-bar to a curve. The synthesis problem then becomes one of finding the image curve that passes through the given positions (precision position synthesis) or as close as possible (approximate position synthesis), the solution of which is obtained by minimizing the normal distance error. Nonbranching constraints are incorporated into the minimization problem to give the designer control over the type of the linkage synthesized. Numerical examples are presented for five, six, and ten positions.
Approximated Grashof-Type Movability Conditions for RSSR Mechanisms With Force Transmission Limitations
Authors: Rastegar J. , Tu Q.
Published: June 2008

Closed-form Grashof-type movability conditions are derived for closed-loop RSSR mechanisms using a geometrical approximation technique. The conditions that ensure the presence of crank-rocker and drag-link type mechanisms are derived with and without force transmission limitations. The force transmission limitations may be specified as a function of the output link angle. The accuracy of the approximated conditions is analyzed. As an example, the conditions are used to synthesize a function generating mechanism with fully rotatable crank and with various force transmission requirements. The developed technique is general, and can be applied to other similar spatial mechanisms. The application of this approach to geometrical synthesis of open-loop chain manipulators is discussed.
Inverse Dynamic Models of Closed-Chain Mechanisms With Contact Compliance
Authors: Manko D. J. , Whittaker W. L.
Published: June 2008

A general inverse dynamic model which is applicable to closed-chain mechanisms with contact compliance is presented. This class of mechanism has relatively rigid members and joints, but experiences compliant interactions with objects and the environment; examples include walking machines operating on natural terrain, devices for grasping a compliant object, and wheeled mobile robots. Previous approaches for formulating inverse dynamic models of compliant mechanisms have been approximations or limited to simple configurations and open-chain mechanisms. Inverse dynamic equations for closed-chain mechanisms with contact compliance are shown to be solvable sets of differential/algebraic equtaions (DAEs) which assures that stable and accurate solutions can be calculated; relevant characteristics and solutions of DAE systems are discussed.
Kinematic Analysis of a Planar Eight-Bar Linkage: Application to a Platform-Type Robot
Authors: Pennock G. R. , Kassner D. J.
Published: June 2008

The paper presents solutions to the forward position and velocity problems of a planar eight-bar, three degree-of-freedom, closed-loop linkage. The linkage is proposed as a programmable platform-type robot which can both position and orient the platform. A sixth-order polynomial equation in the angular displacement of the platform is derived which indicates that six configurations, for a given set of input angular displacements, are possible. The polynomial equation is important in the study of the limit positions of the linkage. The forward velocity problem is solved using first-order partial derivatives of the four output angular displacements with respect to the three independent input displacements. The partial derivatives provide geometric insight into the kinematic analysis of the linkage. A graphical method, which utilizes the instantaneous centers of zero velocity, is introduced as a check of the velocity analysis. The method is solely a function of the configuration of the linkage and is, therefore, a practical alternative to other methods which rely on velocity information. For illustrative purposes, the paper includes a numerical example of the linkage used as a planar platform-type robot.
A Mathematical Model of Parametric Tooth Profiles for Spur Gears
Authors: Chang H. L. , Tsai Y. C.
Published: June 2008

A general mathematical model for describing the geometries and geometric properties of conjugate tooth profiles is presented. Three kinematic parameters and a first order differential equation are introduced to characterize this model. The condition for determining the cusp of tooth profiles is also presented. Using this model, two types of tooth fillets with their minimum radii of curvatures generated by the rack cutter and pinion cutter are described. The peculiar application of this model is that the investigated tooth profiles can be parameterized by specifying one of the three kinematic parameters as a parametric function. It is believed that the parameterization may provide a logical method for gear design.
Nonlinear Deformation of a Shear-Deformable Laminated Composite-Material Flexible Robot Arm
Authors: Gordaninejad F. , Chalhoub N. G. , Ghazavi A. , Lin Q.
Published: June 2008

In this work a general procedure to derive a nonlinear dynamic model for a three-link revolute flexible robot arm constructed from laminated fiber-reinforced composite materials is presented. The effects of geometric nonlinearity as well as rotary inertia and shear deformation are included to study the dynamic response of robotic manipulators made of moderately thick beams under large deformations. Hamilton’s principle is used to derive the equations of motion. A displacement finite element model based on the Timoshenko beam theory is implemented to approximate the solution. The digital simulation studies examine the combined effects of geometric nonlinearity, rotary inertia, and shear deformation on the arm’s end effector displacements. Furthermore, the effects of angle of fiber orientation and material orthotropy on the end-of-the-arm displacements and maximum normal bending stresses, are assessed.
Robustness of Design Through Minimum Sensitivity
Authors: Belegundu A. D. , Zhang Shenghua
Published: June 2008

The problem of designing mechanical systems or components under uncertainty is considered. The basic idea is to ensure quality control at the design stage by minimizing sensitivity of the response to uncertain variables by proper selection of design variables. The formulation does not involve probability distributions. It is proved, however, that when the response is linear in the uncertain variable, reduction in sensitivity implies lesser probability of failure. The proof is generalized to the non-linear case under certain restrictions. In one example, the design of a three-bar truss is considered. The length of one of the bars is considered to be the uncertain variable while cross-sectional areas are the design variables. The sensitivity of the x-displacement is minimized. The constrained optimization problem is solved using a nonlinear programming code. A criterion which can help identify some of the problems where robustness in design is critical is discussed.
Results Obtained With a Method to Improve Engineering Problem Formulation
Authors: Ennis C. W. , Gyeszly S. W.
Published: June 2008

The objective of this research project was to improve problem formulation in engineering systems design. A problem formulation method was developed which uses five characteristic aspects (time, dimensions, value, physical matter, and people) to assist in identifying boundary and performance criteria, and technical performance requirements as a means of expressing them. When tested in controlled task, guided response experiments, the method was shown to improve the quality of problem statements.
Design of Shape Memory Alloy Actuators
Authors: Liang C. , Rogers C. A.
Published: June 2008

This paper describes the design of shape memory alloy force and displacement actuators based upon the thermomechanical constitutive relations previously developed by the authors. Numerical simulations and design case studies are presented which show the utility and advantages of this method over design methods currently being used. The types of actuators described and analyzed include bias spring actuators, differential force actuators, and their hybrid systems. The design approach includes coupling between the one-dimensional thermomechanical constitutive relations and a lumped capacitance transient thermal analysis. The design approach described herein will provide a practical and convenient method for use in the design of shape memory alloy actuators.
A New Unified Strength of Materials Solution for Stresses in Curved Beams and Rings
Authors: Bagci C.
Published: June 2008

Presently existing strength of materials solutions for stresses in curved beams use an incorrect normal force equilibrium condition to define neutral axis location, and to reach a simplified solution, which neglects the curvature effect on stresses due to normal force. This article presents a new but a most general form of the strength of materials solution for determining tangential normal stresses in curved beams, including reductions to special cases. The neutral axis phenomenon is clarified and experimentally verified. Several numerical examples are included, some of which offer photoelastic experimental results, where results predicted by the exact elasticity solution, method of the article, Winkler’s theory, and the conventional simplified method are compared. The hook, diametrically loaded cut, and full ring applications are included. It is shown that simplified theory leads to very large errors. Results by the method offered are very reliable with small errors which are comparable with those of exact elasticity solutions. Stress and deflection analyses of curved beams with varying thicknesses of cross-sections by exact elasticity solutions are given in a separate article [6].
Material Nonlinearity Effects in the Stress Analysis of Conical Disk Springs
Authors: Curti G. , Raffa F. A.
Published: June 2008

The influence of material nonlinearity on the behavior of conical disk springs (Belleville springs) is investigated by means of finite element models. Both the load-deflection curve and the stress field of this kind of spring are shown to be significantly affected by the elastic-plastic behavior of the material. In particular, as far as the actual stress field is concerned, consideration of the material nonlinearity explains some apparent contradictions of well-known analytical formulations, such as the Almen-La´szlo´ theory, based on the usual assumption of linear elastic behavior of the material.
Branching Determination in Nondyadic Planar Multiloop Mechanisms
Authors: Krishnamurty S. , Turcic David A.
Published: June 2008

The paper presents the development of a sub-Jacobian based method for the identification and elimination of branch defects during synthesis in nondyadic planar multiloop mechanisms. Branching occurrences in a given mechanism can be recognized by the resulting changes in the configurations of one or more of the sets of three constraints that form the mechanism. Further, any such change in a constraint set configuration will be characterized by a corresponding change in the determinant sign of its sub-Jacobian matrix. Applying this method, branching can be eliminated during synthesis by identifying all such constraint sets for the mechanism and using the determinant signs of their sub-Jacobian matrices to maintain the mechanism’s original configuration.
On the Integrability of Screw Spaces
Authors: Peterson S. W.
Published: June 2008

In the development of a method for generating the dynamic equations of a chain of rigid bodies in elliptic line space, it has been discovered that the joint freedom spaces from the tangent space of the system’s joint space, called the configuration manifold by dynamicists. The freedom space of a joint can be calculated from the joint contact geometry using reciprocal screw theory. The present paper describes the relationship of the joint freedom spaces to the tangent space of the configuration manifold, and determines the integrability conditions which must be satisfied if the freedom space represents a valid configuration manifold. The paper also shows that the integrability of the tangent space of a chain of rigid bodies is established once the integrability of each joint freedom space has been demonstrated. These conditions are used to define valid generalized coordinates for describing the chain’s configuration. Cylindrical and spherical joints are treated as examples.