bluuebunny/crossref_metadata_2025 huggingface dataset:
A Form Tolerancing Theory Using Fractals and Wavelets
Authors: Srinivasan R. S. , Wood K. L.
Published: February 2008

Tolerancing is a crucial problem for mechanical designers, as it has quality and cost implications on product design. Research in tolerancing has addressed specific areas of the problem, but lacks a theoretical basis. A formal approach for geometric tolerancing with fractal-based parameters has been recently developed. This paper presents an enhanced error profile analysis and synthesis method, based on wavelets, that maintains and extends the use of fractals for surface error abstraction. An overview of the theory of wavelets is provided, and the link between fractals and wavelets is established. Physical test data are used to illustrate the application of wavelet theory to surface profile reconstruction and synthesis. The synthesis methods are then implemented in the functional design of ball-bearing elements, demonstrating the utility of fractal-based tolerancing. Plans for further study and implementation conclude the paper.
LADD Transmissions: Design, Manufacture, and New Compliance Models
Authors: Mennitto G. , Buehler M.
Published: February 2008

We introduce new compliance models for LADD transmissions which reduce inelastic model errors by an order of magnitude. These errors are due to fiber bending, as opposed to the traditionally assumed fiber elasticity. The new LADD models are experimentally verified and applied to the modeling of concentric LADD devices. The new models are essential for the design of LADD based systems, the online estimation of LADD forces, and accurate control. Details of the design, manufacture and break-in phenomena are given, as well as the first experimental measurement of LADD efficiency, which is better than 90%.
The Effects of Actuation Schemes on the Kinematic Performance of Manipulators
Authors: Matone R. , Roth B.
Published: February 2008

This paper is concerned with the effects of actuation schemes on three measures of kinematic performance which depend upon a manipulator’s Jacobian matrix (namely, the minimum singular value, the manipulability, and the condition number). We begin by presenting a simple framework on how to incorporate actuator location and drive mechanisms in the kinematic model. Then, we redefine the performance measures using the new model. For each measure we derive properties relating its joint space to its actuator space description. Next we demonstrate that the choice of actuation scheme influences the size, shape, and direction of the velocity ellipsoid of the end-effector. Finally, we employ the above concepts in the design of a 2R planar mechanical arm. Its transmission ratios and drive mechanisms are selected in order to obtain good kinematic characteristics. We show that the choice of actuation scheme can be used to improve kinematic performance.
Automatic Synthesis of Crank Driven Four-Bar Mechanisms for Two, Three, or Four-Position Motion Generation
Authors: Bawab S. , Sabada S. , Srinivasan U. , Kinzel G. L , Waldron K. J.
Published: February 2008

The synthesis of motion generation of crank driven four-bar mechanisms designed to go through two, three, or four precision positions based on optimization theory and rectified synthesis are discussed. The techniques for automatic synthesis presented have been implemented in the interactive synthesis package RECSYN.
Synthesis of Programmable Mechanisms Using Adjustable Dyads
Authors: Chuenchom T. , Kota S.
Published: February 2008

Conventional hard automation such as linkage mechanisms and cam-driven mechanisms provide high speed capability at a low cost, but fail to provide the flexibility required in many industrial applications. On the other hand, for most manufacturing automation applications in high production industries, expensive multi-axis robots are employed for simple repetitive operations that require only limited flexibility. In order to provide a true middle ground between conventional mechanism-based hard automation and overly flexible anthropomorphic robots, we incorporate flexibility in conventional mechanisms, thereby creating “programmable mechanisms” or Adjustable Robotic Mechanisms (ARMs). This paper introduces the concept of ARMs and presents generalized analytical methods for designing adjustable mechanisms based on synthesis of adjustable dyads. The synthesis methods presented here, which are extensions of the well-known Burmester precision point theory, enable one to design multi-purpose mechanisms for multiple sets of precision points, thereby enabling conventional mechanisms to perform multiple tasks. The analytical synthesis method has been implemented in a computer program that generates all adjustable dyad solutions for given sets of precision points. Two or more adjustable dyads are assembled together to form a programmable linkage mechanism that performs multiple tasks. Synthesis formulations and a design example illustrating the analytical and computer-aided synthesis methods are presented.
On the Geometry of Spatial Polygons and Screw Polygons
Authors: Mavroidis C. , Roth B.
Published: February 2008

In this paper we study spatial polygons which are closed figures composed of ordered sets of lines and their common normals. It is shown how to solve for up to six of the parameters which define a polygon’s geometry, after all the other parameters are specified. It is also shown that when screws are used instead of lines, the resulting figures, called screw polygons, can be analyzed in order to determine up to twelve parameters, provided all the other parameters which define the screws and the screw polygon are known. Finally, it is pointed out that these results have many potential uses in kinematics.
Two-Stage Algorithm for Determination of the Bending Sequence in Sheet Metal Products
Authors: Radin B. , Shpitalni M. , Hartman I.
Published: February 2008

This paper presents an algorithm for solving the complex and critical problem of bending sequence in sheet metal manufacturing. Finding the bending sequence and required tool assignment presents a large combinatorial problem which is impossible to solve optimally for practical applications within a reasonable period of time. The paper presents a two-stage algorithm. The first stage finds a feasible solution based upon collision avoidance heuristics. The second stage rapidly seeks an alternative feasible sequence with a lower cost without exceeding time limitations. The algorithm is very practical because it reaches a low-cost solution quickly within computer memory limitations. In this paper, the problem is defined, the approach is presented formally, and finally, the power of the algorithm is demonstrated by solving bending sequences for real products.
Computation of Self-Intersections of Offsets of Be´zier Surface Patches
Authors: Maekawa Takashi , Cho Wonjoon , Patrikalakis Nicholas M.
Published: February 2008

Self-intersection of offsets of regular Be´zier surface patches due to local differential geometry and global distance function properties is investigated. The problem of computing starting points for tracing self-intersection curves of offsets is formulated in terms of a system of nonlinear polynomial equations and solved robustly by the interval projected polyhedron algorithm. Trivial solutions are excluded by evaluating the normal bounding pyramids of the surface subpatches mapped from the parameter boxes computed by the polynomial solver with a coarse tolerance. A technique to detect and trace self-intersection curve loops in the parameter domain is also discussed. The method has been successfully tested in tracing complex self-intersection curves of offsets of Be´zier surface patches. Examples illustrate the principal features and robustness characteristics of the method.
Systematic Synthesis and Applications of Novel Multi-Degree-of-Freedom Differential Systems
Authors: Kota S. , Bidare S.
Published: February 2008

A two-degree-of-freedom differential system has been known for a long time and is widely used in automotive drive systems. Although higher degree-of-freedom differential systems have been developed in the past based on the well-known standard differential, the number of degrees-of-freedom has been severely restricted to 2n. Using a standard differential mechanism and simple epicyclic gear trains as differential building blocks, we have developed novel whiffletree-like differential systems that can provide n-degrees of freedom, where n is any integer greater than two. Symbolic notation for representing these novel differentials is also presented. This paper presents a systematic method of deriving multi-degree-of-freedom differential systems, a three and a four output differential systems and their applications including all-wheel drive vehicles, universal robotic grippers and multi-spindle nut runners.
Use of Noncircular Gears to Reduce Torque and Speed Fluctuations in Rotating Shafts
Authors: Dooner D. B.
Published: February 2008

A methodology is presented where noncircular gears are used to reduce unwanted torque and speed fluctuations that may exist in rotating shafts. A noncircular gear pair is used to drive an auxiliary shaft where a flywheel is mounted, thus creating an auxiliary torque fluctuation. The form of the undesirable torque fluctuation is used to determine a motion specification for the synthesis of a noncircular gear pair. The undesired torque fluctuation and the auxiliary torque fluctuation are added to reduce the net torque fluctuation. Two illustrative examples are included. This approach of torque balancing is compared to the classical method of mounting a flywheel onto the shaft that experiences the unwanted torque fluctuation to reduce its speed variation.
Kinematic Optimization of a Modified Helical Gear Train
Authors: Chang Shinn-Liang , Tsay Chung-Biau , Tseng Ching-Huan
Published: February 2008

A mathematical model of a modified helical gear train (MHGT), manufactured with a practical hobbing machine using a curved-template guide, and which takes considerations of center-distance variation and axial misalignment into account, is developed. Tooth contact analysis (TCA) and kinematic errors of a MHGT due to mis-assembly are investigated. A multiple optimization method is applied to reduce the level of MHGT kinematic errors, and to investigate optimal gear tooth modifications. Computer simulation programs for TCA and optimization are also developed. Two numerical examples are presented to illustrate the kinematic optimization of the proposed helical gear train. The results of this study are most helpful in designing and analyzing a MHGT.
Automatic Detection of Embedded Structure in Planetary Gear Trains
Authors: Hsu Cheng-Ho , Wu Yi-Chang
Published: February 2008

The detection of embedded structure is one of important steps in the structural synthesis of planetary gear trains. The purpose of this paper is to develop a computer program for the automatic detection of embedded structure in planetary gear trains. First, the graph representation of a planetary gear train is used to clarify the kinematic structure. Next, the concept of fundamental circuit is applied to derive an algorithm for the detection of embedded structure in a planetary gear train. Using the notation of adjacency matrix, an interactive computer program has been developed such that embedded structure in a planetary gear train can be automatically analyzed by only entering the corresponding graph.
General Equations of a Helical Spring With a Cup Damper and Static Verification
Authors: Wu Ming Hsun , Ho Jing Yuan , Hsu Wensyang
Published: February 2008

In this study, we derive the general equations of motion for the helical spring with a cup damper by considering the damper’s dilation and varying pitch angle of the helical spring. These dynamic equations are simplified to correlate with previous models. The static force-displacement relation is also derived. The extra stiffness due to the damper’s dilation considered in the force-displacement relation is the first such modeling in this area. In addition, a method is presented to predict the compressing spring’s coil close length and is then verified by experimental data. Moreover, the simulation results of the static force-displacement relation are found to correspond to the experimental data. The maximum error is around 0.6 percent.
Operational Envelope of a Spatial Stewart Platform
Authors: Adkins F. A. , Haug E. J.
Published: February 2008

This technical brief presents the operational envelope for the spatial Stewart platform and dome of a six degree of freedom driving simulator, extending prior work that has been limited to planar mechanisms and manipulators. The set of all points in space that can be occupied by any point in the dome of the simulator is defined as its operational envelope. The geometry of the driving simulator’s dome and unilateral constraints on actuator lengths are incorporated and details of the defining equations for the operational envelope are given. Numerical methods are used to calculate the boundary of the operational envelope and results are presented in graphical form.
Matrix System for the Analysis of Planetary Transmissions
Authors: Tian Lei , Li-qiao Lu
Published: February 2008

This paper presents a new general analysis method for planetary gear transmission systems. Instead of studying portions of a transmission, one can analyze a whole planetary transmission system with a general program. Not only the kinematics, but also dynamics of a transmission are studied. The whole process of analysis is standardized to become very straight forward, making it especially suitable for the computer-aided analysis of the vehicle planetary transmissions.
Measures of Positional Error for a Rigid Body
Authors: Gupta K. C.
Published: February 2008

Properties of Euclidean error measures for rigid body position are investigated. For two positions represented by 4 × 4 matrices A1 and A2, it is shown that matrices [A2 − A1] and [(A1)−1 A2] lead directly to desirable measures of rotational and translational errors, while the matrix [A2(A1)−1], although physically very meaningful, does not do so. With a proper choice of the origin of the body system, it is shown that the simple difference matrix [A2 − A1] leads to positional error measures which are meaningful both analytically and physically, and can be computed efficiently.
Analytical and Graphical Solutions to the Forward Position Problem of Two Robots Manipulating a Spatial Linkage Payload
Authors: Pennock G. R. , Mattson K. G.
Published: February 2008

This paper presents a solution to the forward position problem of two PUMA-type robots manipulating a spatial four-bar linkage payload. To simplify the kinematic analysis, the Bennett linkage, which is a special geometry spatial four-bar, will be regarded as the payload. The orientation of a specified payload link is described by a sixth-order polynomial and a specified joint displacement in the wrist subassembly of one of the robots is described by a second-order polynomial. A solution technique, based on orthogonal transformation matrices with dual number elements, is used to obtain closed-form solutions for the remaining unknown joint displacements in the wrist subassembly of each robot. An important result is that, for a given set of robot input angles, twenty-four assembly configurations of the robot-payload system are possible. Repeated roots of the polynomials are shown to correspond to the stationary configurations of the system. The paper emphasizes that an understanding of the kinematic geometry of the system is essential to verify the number of possible solutions to the forward position problem. Graphical methods are also presented to provide insight into the assembly and stationary configurations. A numerical example of the two robots manipulating the Bennett linkage is included to demonstrate the importance of the polynomial and closed-form solutions.
An Off-Road Bicycle With Adjustable Suspension Kinematics
Authors: Needle S. A. , Hull M. L.
Published: February 2008

The purpose of designing and constructing the adjustable dual suspension off-road bicycle presented was to provide a research tool for quantifying and optimizing off-road bicycle performance in three categories: energy efficiency, comfort, and handling. Key variables affecting performance in each category were identified and then the bicycle was designed and constructed so that one variable may be changed at a time. For both the front and rear suspensions, independent modular springs and dampers may be used, so that the travel limit, damper quantities, and spring, quantities can all be independently tested. On the rear suspension, the swingarm pivot point height may be moved along the seat tube from the bottom bracket to 22 cm above the bottom bracket. The swingarm was integrated into a four-bar linkage such that the effective spring and damping rates at any pivot point height were constant as the suspension compressed. For the front suspension a four-bar linkage was also used. The links may be adjusted to change the trajectory of the front wheel as the suspension compresses. Additionally, the shock mounts may be moved to prevent any change in effective spring and damping rates resulting from a change in linkage geometry. To demonstrate the usefulness of the design, an experiment was performed to determine the pivot point height at which the energy dissipated from the rear shock was a minimum. At various pivot point heights, the bike was ridden on an inclined (6 percent grade) treadmill at 23.3 km/hr. Minimum energy was dissipated at a pivot height of 8.4 cm above the bottom bracket.
Impact Analysis of Plates Using Quasi-Static Approach
Authors: Shivaswamy S. , Lankarani H. M.
Published: February 2008

Impact analyses suffer from several practical limitations which limit their application to predict the approximate magnitude of the various phenomena involved. The transient force deformation response of a body subjected to impact can be explained accurately using the stress wave propagation theory. As this approach is complicated, a simpler approach utilizing a quasi-static equilibrium condition can be employed. Nonlinear force-deformation Hertzian relations can be used for the impact analysis. These relations though can not explain the energy dissipation and permanent deformations encountered during the impact. This necessitates independent nonlinear force deformation relations for compression and restitution phases of impact. In this paper, modeling of contact forces during impact on stiff systems (systems which do not undergo gross deformation but experience only local deformation) has been presented. Experiments were conducted on stiff systems to verify the methodology. A plate which is fixed on a rigid base and clamped completely represents a stiff system. Hence experiments were conducted on Aluminum and Steel plates to simulate impact on stiff systems for the verification of the proposed models. The theoretical results matched well with the experimental results. A nonlinear force deformation model with independent relations for compression and restitution phases was found to be a suitable approach to analyze impact problems.
A Multibody/Finite Element Analysis Approach for Modeling of Crash Dynamic Responses
Authors: Ma D. , Lankarani H. M.
Published: February 2008

Computer models of the human body are robust tools for gaining insight into the gross motion of ground vehicle or aircraft occupants and evaluating the loads and, deformations of their critical parts. The knowledge of occupant responses will help in the determination of the type and probable causes of injuries that may he sustained during a crash. An important aspect in crash analysis is how the large motion of the relatively rigid segments of an occupant, such as the limbs, and the small deformations of flexible segments, such as the spine column, are interrelated. To this end, a general methodology for kineto-static analysis of multibody systems with flexible structures undergoing large motion and structural deformations is developed. Rigid multibody dynamics is used to predict the gross motions and displacements at the boundaries between the relatively bulky (rigid) bodies and relatively flexible ones. A mixed boundary-condition finite-element analysis is formulated and solved at every numerical integration time to determine the corresponding reaction forces and moments at the boundaries and also the structural deformations. Based on this methodology, a multibody model of the occupant with a nonlinear finite element model of the lumbar spine is developed for a Hybrid II anthropomorphic crash test dummy. The analytical results obtained are compared with the experimental results from the impact sled tests. Comparison of the results has shown better correlation between the analyses and the experiments compared with earlier studies.
A Shape Annealing Approach to Optimal Truss Design With Dynamic Grouping of Members
Authors: Shea K. , Cagan J. , Fenves S. J.
Published: February 2008

A shape annealing approach to truss topology design is presented that considers the tradeoff between the mass of the structure and the grouping of members, where all members of a group are given the same size. The problem of optimal grouping involves finding a structural design with an optimal number of groups and the optimal sizes for each group. In this paper cross-sectional area is considered as the measure of group size. Designs incorporating multiple members with the same cross-sectional area are advantageous when considering the cost of purchasing and fabricating materials. The shape annealing method is used as an approach to solve this problem by incorporating a method for dynamic grouping of members based on cross-sectional area that creates a tradeoff between mass and the number of groups through a weighted objective function that includes a group penalty function. This method is demonstrated on transmission tower and general truss problems.
A New Circuit Identification Method in Four-Position Four-Bar Linkages
Authors: Bawab S. , Li H.
Published: February 2008

This paper describes an efficient procedure to rectify circuit defects in rocker-crank and double-rocker at the synthesis level based on the angular joint displacements. This method complements the crank-rocker and double-crank circuit rectification to complete the circuit rectification of four-bar linkages. The procedure utilizes the algebraic method where special points followed by a line construction procedure are employed to validate the range of the critical angle that can identify the circuit defects as a function of the design positions prior to the completion of the linkage. As a result, a direct technique is implemented at the computational level to efficiently identify the infeasible solutions.
Analysis of Spur and Straight Bevel Gear Teeth Deflection by the Finite Strip Method
Authors: Gagnon P. , Gosselin C. , Cloutier L.
Published: February 2008

A linear Finite Strip element for the analysis of rectangular and annular sector thick plates is presented to permit the deflection analysis of spur and straight bevel gear teeth, which are respectively modeled as rectangular and annular sector cantilever plates. Plate deflections are obtained by a hybrid procedure based on the minimum total potential energy theorem, which retains advantages of both the orthotropic-plate method and the Finite Element concept and is called the Finite Strip Method. The formulation accounting for transverse shear deformation is based on Mindlin’s plate theory. Since the presented Finite Strip element supports any combination of continuous thickness variations, the true shape of the tooth is used in the solution. The formulation can be easily applied to any boundary conditions and supports any type and combination of transverse loads and moments. Application of the Finite Strip Method to predict the deflection of spur and straight bevel gear teeth is demonstrated and results are compared to those obtained by the Finite Element Method.
Implicit Function Modeling of Solidification in Metal Castings
Authors: Rvachev V. L. , Sheiko T. I. , Shapiro V. , Uicker J. J.
Published: February 2008

Solidification of metal castings can be modeled by an implicit real-valued function whose behavior is determined by physical parameters prescribed on the boundary of a casting. We show how to construct such functions using theory of R-functions for two-dimensional castings represented by their boundaries. The parameterized form of the constructed functions is convenient for studying, controlling, and optimizing their behavior in terms of the physical parameters specified on the boundary of the casting. The proposed approach can also be used for modeling multiple cavities in a same sand mold, generalizes to three-dimensional castings, and is applicable to other physical phenomena that may be suitable for analysis based on empirical knowledge.
Simplifying Iterations in Cross-Functional Design Decision Making
Authors: Krishnan V. , Eppinger S. D. , Whitney D. E.
Published: February 2008

In this paper, we consider the cross-functional design decision making process and discuss how sequential decision making leads to a degradation in design quality even when downstream design tasks are not rendered infeasible by preceding upstream decisions. We focus on the problem of simplifying the design iterations required to address this quality loss. Two properties, called sequence invariance and task invariance, are introduced to help reduce the complexity of subsequent design iterations. We also discuss how these properties may be used by designers in situations where mathematical descriptions of the design performance characteristics are unavailable. We illustrate the utility of these properties by showing their applicability to the design of catalytic converter diagnostic systems at a major U.S. automotive firm.
A Combinatorial Optimization Approach to Composite Materials Tailoring
Authors: Sadagopan D. , Pitchumani R.
Published: February 2008

Composite materials offer designers the advantage of tailoring structures and materials to meet a variety of property and performance requirements in changing and demanding environments. However, the wide variety of material combinations, reinforcement geometries and architectures to choose from poses a bewildering problem of selection. Thus an appropriate, and furthermore optimal, tailoring of composite materials for applications is a challenging design problem and forms the focus of the article. Specifically, the present work addresses the problem of selecting optimal combinations of matrix and reinforcement materials, and reinforcement morphology, architecture, and volume fraction so as to meet the specified property and performance requirements. The optimal tailoring problem is solved using the combinatorial optimization technique of simulated annealing which works in conjunction with a property model base consisting of analytical relationships between the composite properties and the microstructure. The matrix materials considered in the study span the material classes of polymers, metals and ceramics while reinforcement geometries of unidirectional fibers, particulates and two-dimensional woven fabrics are considered. The overall approach and key results of the study are presented and discussed.
Optimal Synthesis of Mechanisms for Path Generation Using Fourier Descriptors and Global Search Methods
Authors: Ullah Irfan , Kota Sridhar
Published: February 2008

Generally, success in synthesis of mechanisms for path generation is limited to finding a reasonable local optima at best in spite of a very good initial guess. The most widely used Structural Error objective function is not effective in leading to practical solutions as it misrepresents the nature of the design problem by requiring the shape, size, orientation and position of the coupler curve to be optimized all at once. In this paper, we present an effective objective function based on Fourier descriptors that evaluates only the shape differences between two curves. This function is first minimized using a stochastic global search method derived from simulated annealing followed by Powell’s method. The size, orientation and position of the desired curve are addressed in a later stage by determining analogous points on the desired and candidate curves. In spite of highly non-linear mechanisms design space, our method discovers near-global and practical solutions consistently without requiring any initial guess.
Design of Displacement-Amplified Induced-Strain Actuators for Maximum Energy Output
Authors: Giurgiutiu V. , Rogers C. A. , Chaudhry Z.
Published: February 2008

General stiffness concepts for effective use of induced strain principles as they apply to quasi-static actuation of structures and devices are presented. The conventional induced-strain actuator is first reviewed. The effect of structural elasticity is then discussed. Basic principles of displacement amplification are presented. The influences of structural and amplification elasticity are then discussed. An example of effective induced-strain actuator design with displacement amplification is provided.
The Cylindroid Associated With Finite Motions of the Bennett Mechanism
Authors: Huang C.
Published: February 2008

The finite kinematic geometry of the Bennett mechanism is explored in this paper. The screw axes of all possible coupler displacements of the mechanism from any given configuration are shown to form a cylindroid. The screw system of the coupler displacement is obtained by using the intersection of finite screw systems associated with two corresponding revolute-revolute dyads. Inverse finite kinematic analysis is also performed to verify this new linear property of the Bennett mechanism.
Characteristics of a New Type of Cylindrical Worm-Gear Drive
Authors: Simon V. V.
Published: February 2008

A new type of cylindrical worm-gear drive is presented. The worm is ground by a grinding wheel whose profile consists of two circular arcs, and the obtained worm profile is concave. The teeth of the gear are processed by a hob whose generator surface is identical to the worm surface. The aim of this paper is to introduce this new type of worm gearing and to compare the operating characteristics of the new type and of the commonly used worm-gear drives on the basis of tooth contact analysis, load distribution calculation, and thermal elastohydrodynamic lubrication analyses. The results obtained show the advantages of the new type of worm gear. The results of the load distribution calculation and EHD lubrication analysis are also used for the optimization of the design parameters of the new type of worm-gear drive.
Inverse Kinematic Solution of Robot Manipulators Using Interval Analysis
Authors: Rao R. S. , Asaithambi A. , Agrawal S. K.
Published: February 2008

Interval analysis is a growing branch of computational mathematics where operations are carried out on intervals instead of real numbers. This paper presents the first application of this method to robotic mechanisms for the solution of inverse kinematics. As shown in this paper, it is possible to potentially compute all solutions of the inverse kinematics problem using this method. This paper describes the preliminaries of interval analysis, the numerical algorithm, the computational complexity, and illustrations with examples.
Combining Interactive Exploration and Optimization for Assembly Design
Authors: Kim G. J. , Szykman S.
Published: February 2008

This paper presents an integrated framework for conceptual assembly design. Because the complexity of assembly design leads to extremely large design spaces, adequate support of design space exploration is a key issue that must be addressed. CAMF allows the designer to manage the overall design process and explore the design space through explicit representation of design stages and their relationships (history), assembly design constraints, and rationale. The designer is free to use both bottom-up or top-down approaches to explore different assembly configurations. Exploration of the design space is further enabled by incorporating a simulated annealing-based refinement tool that allows the designer to rapidly complete partial designs, refine complete designs, and generate multiple design alternatives.
A Fast Algorithm for Planning Collision-Free Paths With Rotations
Authors: Chen S.-F. , Oliver J. H. , Fernandez-Baca D.
Published: February 2008

Motion planning is a major problem in robotics. The objective is to plan a collision-free path for a robot moving through a workspace populated with obstacles. In this paper, we present a fast and practical algorithm for moving a convex polygonal robot among a set of polygonal obstacles with translations and rotations. The running time is O(c((n + k)N + n log n)), where c is a parameter controlling the precision of the results, n is the total number of obstacle vertices, k is the number of intersections of configuration space obstacles, and N is the number of obstacles, decomposed into convex objects. This work builds upon the slabbing method proposed by Ahrikencheikh et al. [2], which finds an optimal motion for a point among a set of nonoverlapping obstacles. Here, we extend the slabbing method to the motion planning of a convex polygonal robot with translations and rotations, which also allows overlapping configuration space obstacles. This algorithm has been fully implemented and the experimental results show that it is more robust and faster than other approaches.
Trust Region Augmented Lagrangian Methods for Sequential Response Surface Approximation and Optimization
Authors: Rodri´guez J. F. , Renaud J. E. , Watson L. T.
Published: February 2008

A common engineering practice is the use of approximation models in place of expensive computer simulations to drive a multidisciplinary design process based on nonlinear programming techniques. The use of approximation strategies is designed to reduce the number of detailed, costly computer simulations required during optimization while maintaining the pertinent features of the design problem. To date the primary focus of most approximate optimization strategies is that application of the method should lead to improved designs. This is a laudable attribute and certainly relevant for practicing designers. However to date few researchers have focused on the development of approximate optimization strategies that are assured of converging to a solution of the original problem. Recent works based on trust region model management strategies have shown promise in managing convergence in unconstrained approximate minimization. In this research we extend these well established notions from the literature on trust-region methods to manage the convergence of the more general approximate optimization problem where equality, inequality and variable bound constraints are present. The primary concern addressed in this study is how to manage the interaction between the optimization and the fidelity of the approximation models to ensure that the process converges to a solution of the original constrained design problem. Using a trust-region model management strategy, coupled with an augmented Lagrangian approach for constrained approximate optimization, one can show that the optimization process converges to a solution of the original problem. In this research an approximate optimization strategy is developed in which a cumulative response surface approximation of the augmented Lagrangian is sequentially optimized subject to a trust region constraint. Results for several test problems are presented in which convergence to a Karush-Kuhn-Tucker (KKT) point is observed.
A Novel Design for High Performance Drive Screw Systems
Authors: Springer S. L. , Dhingra A. K.
Published: February 2008

Drive screw systems are used as linear actuators in a wide variety of machines. For traditional design of drive screw systems, critical speed vibrations limit the maximum output stroke (overall length of travel) attainable for a given screw pitch, diameter and required output speed. This paper discusses a new design and presents performance results of a working apparatus to overcome the critical speed limitations in drive screw systems. The solution approach utilizes a series of sets of nested mobile supports to minimize the critical speed vibrations. The mobile supports are rigidly connected in pairs, and are automatically positioned in proper locations to minimize the effective unsupported length of the drive screw. This in turn, reduces the drive screw vibration amplitudes. The solution method presented will theoretically permit operation of a drive screw system under any combination of diameter, length, and rotational velocity, without restriction due to critical speed vibrations. The proposed solution has been tested and has proven effective in an industrial setting.
Operational Envelopes for Working Bodies of Mechanisms and Manipulators
Authors: Haug E. J. , Adkins F. A. , Luh Chi-Mei
Published: February 2008

The set of all points in space that are occupied by points in the working body of a mechanism or manipulator, for some kinematically admissible configuration, is defined as its operational envelope. Criteria for points on the boundary of the operational envelope of working bodies with smooth boundaries are developed, for both parametric and equation representations of domains and boundaries of working bodies, in two-and three-dimensional space. The criteria derived involve kinematic constraint equations for the underlying mechanism and equations that characterize the shape of the working body. A row rank deficiency condition is derived as a criterion for the boundary of the operational envelope, and numerical methods based on this condition for mapping the boundary are presented. Examples involving a planar Stewart platform with a dome attached and the wheel assembly of a vehicle suspension system in three dimensions are analyzed numerically.
Computerized Tooth Profile Generation and Undercut Analysis of Noncircular Gears Manufactured With Shaper Cutters
Authors: Chang Shinn-Liang , Tsay Chung-Biau
Published: February 2008

Pitch curves of a conjugate noncircular gear pair are derived based on kinematic considerations. A method for considering the inverse mechanism relationship and the equation of meshing, is proposed here to derive a complete mathematical model of noncircular gears manufactured with involute-shaped shaper-cutters. The proposed method is similar to the contact line method and the envelope method, but is easier to apply to the determination of tooth profiles. A computer program is developed for generation the tooth profile with backlashes. Undercutting analysis is also investigated by considering the relative velocity and equation of meshing. Finally, modified elliptical gears are presented to illustrate the tooth profile generation when the proposed mathematical model is applied, and to investigate the phenomenon of tooth undercutting.
A Design Methodology for Self-Maintenance Machines
Authors: Umeda Yasushi , Tomiyama Tetsuo , Yoshikawa Hiroyuki
Published: February 2008

This paper proposes a design methodology for self-maintenance machines. The self-maintenance machine is a machine that can maintain its functions for a while, even though faults happen. In order to achieve capabilities for diagnosing and repair planning, a model based approach that employs qualitative physics is proposed. Regarding repair execution, two types of repair strategies are proposed; viz., control type and functional redundancy type which is a strategy to add redundancy to a machine from a viewpoint of function. A prototype of the self-maintenance machine is developed. Because this machine uses the control type of repair strategy, it succeeded to maintain its functions as far as its structure does not change. A promising candidate for dealing with faults that involve structural changes is the functional redundancy type of repair.
Cyclides in Geometric Modeling: Computational Tools for an Algorithmic Infrastructure
Authors: Srinivas Y. L. , Dutta Debashish
Published: February 2008

The Dupin cyclide is a quartic surface with useful properties such as circular lines of curvature, rational parametric representations and closure under offsetting. All natural quadrics (cone, cylinder, sphere) and the torus are special cases of the cyclide. Applications of cyclides include variable radius blending, piping design and design of tubular geometry, such as mold gates and wire harnesses. While the mathematical treatment of cyclides is well developed, the tools required to incorporate this surface into conventional modeling applications have not received sufficient attention. In this paper, we detail various methods for manipulating and computing with the cyclide. Issues such as auxiliary representations, inverse parameter mapping, point classification, normal projection of a point onto the surface, distance computation, bounding volumes and surface intersection detection are discussed in detail. We also provide implemented examples of design applications that utilize these computational tools.
Extending C and FORTRAN for Design Automation
Authors: Cheng H. H.
Published: February 2008

The CH programming language is designed to be a superset of C. CH bridges the gap between C and FORTRAN; it encompasses all the programming capabilities of FORTRAN 77 and consists of features of many other programming languages and software packages. Unlike other general-purpose programming languages, CH is designed to be especially suitable for applications in mechanical systems engineering. Because of our research interests, many programming features in CH have been implemented for design automation, although they are useful in other applications as well. In this paper we will describe these new programming features for design automation, as they are currently implemented in CH in comparison with C and FORTRAN 77.
Discrete Optimal Design Formulations With Application to Gear Train Design
Authors: Pomrehn L. P. , Papalambros P. Y.
Published: February 2008

The use of discrete variables in optimal design models offers the opportunity to deal rigorously with an expanded variety of design situations, as opposed to using only continuous variables. However, complexity and solution difficulty increase dramatically and model formulation becomes very important. A particular problem arising from the design of a gear train employing four spur gear pairs is introduced and formulated in several different ways. An interesting aspect of the problem is its exhibition of three different types of discreteness. The problem could serve as a test for a variety of optimization or artificial intelligence techniques. The best known solution is included in this article, while its derivation is given in a sequel article.
A Network Reliability Approach to Optimal Decomposition of Design Problems
Authors: Michelena N. F. , Papalambros P. Y.
Published: February 2008

Methods for solving partitioned mathematical programming problems require that an appropriate structure suitable for decomposition be identified. This first step consists of identifying linking variables that effect independent subproblems coordinated by a master problem. This article presents a network reliability-based solution of the optimal decomposition problem that avoids subjective criteria to identify linking variables and partitions. The relationships among design variables are modeled as the processing units of a network. The design variables themselves are modeled as the communication links between these units. The optimal decomposition is attained by minimizing the network reliability while maximizing the number of operating links.
A Symbolic Formulation for Linearization of Multibody Equations of Motion
Authors: Lynch A. G. , Vanderploeg M. J.
Published: February 2008

This paper presents a method for obtaining linearized state space representations of open or closed loop multibody dynamic systems. The paper develops a symbolic formulation for multibody dynamic systems which result in an explicit set of symbolic equations of motion. The symbolic equations are then used to perform symbolic linearizations. The resulting symbolic, linear equations are in terms of the system parameters and the equilibrium point, and are valid for any equilibrium point. Finally, a method is developed for reducing a linearized, constrained multibody system consisting of a mixed set of algebraic-differential equations to a reduced set of differential equations in terms of an independent coordinate set. An example is used to demonstrate the technique.
Simulation on the Rotational Vibration of Helical Gears in Consideration of the Tooth Separation Phenomenon (A New Stiffness Function of Helical Involute Tooth Pair)
Authors: Cai Y.
Published: February 2008

In this paper, an exact vibration model for helical gear pairs, is developed assuming no spacing error and no shaft run-out, in consideration of nonlinear tooth separation phenomenon. Inside the model, a simple modified stiffness function, including the effect of tooth numbers and addendum modification coefficients, is proposed for a helical involute tooth pair. This new stiffness function is verified by comparing its results with theoretical calculation and experiment. The rotational vibration of helical gear pairs with comparative narrow face width is simulated clearly on a 16-bit personal computer using the finite difference method in Fortran. The total contact ratio, including transverse and overlap contact ratios, is changed in the range of 1 ≤ ε ≤ 3. As a result, the simulated vibration time waveforms and their frequency characteristics agreed precisely with Umezawa’s calculation and experiment. This simulator is also used to investigate the effect of shaft deviation and pressure angle errors on the vibration of helical gears.
Metric Relations and Displacement Groups in Mechanism and Robot Kinematics
Authors: Fanghella P. , Galletti C.
Published: February 2008

This paper presents a systematic theory for metric relations between the invariant properties of displacement groups, and shows this theory application to mechanism kinematics. Displacement groups, their invariant properties and operations are briefly described. Kinematic constraints are then introduced as tools for relating abstract group properties to actual mechanism constraints. Criteria and operating rules to employ metric relations for the generation of a meaningful set of closure equations for kinematic chains are detailed.
Optimal Model-Based Decomposition of Powertrain System Design
Authors: Michelena N. F. , Papalambros P. Y.
Published: February 2008

Optimal design of large engineering systems modeled as nonlinear programming problems remains a challenge because increased size reduces reliability and speed of numerical optimization algorithms. Decomposition of the original model into smaller coordinated submodels is desirable or even necessary. The article presents a methodology for optimal model-based decomposition of design problems, whether or not initially cast as optimization models. The overall model is represented by a hypergraph that is optimally partitioned into weakly-connected subgraphs satisfying partitioning constraints. The formulation is robust enough to account for computational demands and resources, and the strength of interdependencies between the design relations contained in the model. This decomposition methodology is applied to a vehicle powertrain system design model consisting of engine, torque converter, transmission, and wheel-tire assemblies, with 87 design relations and 119 design and state/behavior variables.
Multipulley Belt Drive Mechanics: Creep Theory vs Shear Theory
Authors: Alciatore D. G. , Traver A. E.
Published: February 2008

This paper investigates two belt mechanics theories and discusses the situations and materials for which they apply. Traditional creep theory is presented along with shear theory which was recently introduced to describe the behavior of steel-reinforced belts. Emphasis is placed on determination of tensions in the spans of a running belt and on applying results to multipulley configurations.