bluuebunny/crossref_metadata_2025 huggingface dataset:
The Curve-Mesh Concept in Reconstructing Smooth Surface From Noisy Data
Authors: Kaklis P. D.
Published: April 2021

This paper is concerned with the problem of filtering the noise encountered in the measurements taken from a smooth (GC2-continuous) surface in the three-dimensional space. For this purpose, the data points are firstly considered to belong to a three-dimensional entity which is drastically simpler than a surface, namely the noisy curvature-continuous quadrilateral curve-mesh connecting the data points. The curve-mesh concept, apparently introduced by Hosaka (1969), is then combined with the concept of fairing in a statistical framework introduced by Reinsen (1967; 1971), yielding a constrained minimization problem for the fairing curve-mesh. After establishing that this problem has a unique solution in an appropriate Hilbert space, a convergent Newton-Raphson-type algorithm for constructing it in a cubic-spline subspace is presented in detail. Finally, the numerical performance of this algorithm in the context of a Monte-Carlo experimentation with the so-called Franke’s principal test function (1979,1980,1982) is discussed.
Topological and Geometric Consistency in Boundary Representations of Solid Models
Authors: Jablokow Andrei G. , Uicker John J. , Turcic David A.
Published: April 2021

This paper describes a method of verifying the consistency between the topology and geometry of boundary representation (B-rep) of solid models. This verification is well suited for implementation as an algorithm and has been implemented as such in a polyhedral boundary representation solid modeling system (Jablokow 1989). Information regarding boundary representations is typically divided into the geometry and topology. It is important that the two are consistent for a valid solid model. In this work the genus of an object is calculated topologically and geometrically and then compared to verify the consistency of the solid model. The genus of an object gives insight as to the geometric complexity of the object. This is equivalent to verifying the Gauss-Bonnet Theorem for the model, and is discussed in the paper.
A Geometric Investigation of the Skeleton of CSG Objects
Authors: Dutta Debasish , Hoffmann Christoph M.
Published: April 2021

We sketch an algorithm for computing the skeleton (medial-axis surface) of an object defined using constructive solid geometry (CSG). The skeleton can be used in blending, motion planning, medical tomography, computer vision, and in mesh generation. We also present a geometric analysis of Voronoi surfaces from which the skeleton is composed, for a large number of surface pairs arising often in practice.
An Interactive Graphical Approach to Feature Modeling Using Halfspaces and Geometric Constraints
Authors: van Emmerik Maarten J. G. M.
Published: April 2021

Feature modeling enables the specification of a model with standardized high-level shape aspects that have a functional meaning for design or manufacturing. In this paper an interactive graphical approach to feature-based modeling is presented. The user can represent features as new CSG primitives, specified as a Boolean combination of halfspaces. Constraints between halfspaces specify the geometric characteristics of a feature and control feature validity. Once a new feature is defined and stored in a library, it can be used in other objects and positioned, oriented and dimensioned by direct manipulation with a graphics cursor. Constraints between features prevent feature interference and specify spatial relations between features.
Decomposition of Measured Contours Into Geometric Features
Authors: Etesami Faryar , Rajkumar Devaraj
Published: April 2021

In dimensional measurement applications where the object boundary data is indiscriminately collected, the need for detecting transition points from one feature to another arises. In addition, measured features must be matched with their corresponding nominal counterparts. In this paper, a solution to this problem is presented for planar contours which are composed of straight and circular edges. Two algorithms are presented, the first algorithm detects the transition points involving straight edges and the second algorithm finds the transition points between circular edges. The performance of these algorithms are demonstrated by simulated as well as actual part measurements.
Tolerances and Robustness in Engineering Design Optimization
Authors: Parkinson Alan , Sorensen Carl , Free Joseph , Canfield Bradley
Published: April 2021

This paper describes a new strategy for incorporating tolerances as part of engineering design optimization. The tolerance problem is defined in a general way that allows for tolerances on all model variables and parameters and includes worst case and statistical analysis. Two methods are described for taking tolerances into account during optimization such that an optimal design will remain feasible despite fluctuations in variables or parameters. Methods are also presented for directly controlling transmitted variation, and a framework for optimal tolerance allocation is proposed.
Dynamic 3-D Visualization of Dimensions and Tolerances on Solid Models Using ANSI Standard
Authors: Dori Dov , Miller James R.
Published: April 2021

The use of current solid modelers as a comprehensive MCAE system is hampered by the lack of proper annotation capabilities, primarily dimensioning and tolerancing (D&T). An initial design done on a solid modeler must be transferred to some wire-frame module for D&T annotation and analysis and for blueprint production. We propose a solid modeler which has D&T capabilities that will eventually enable a complete design cycle. Dimensions and size tolerances that follow the ANSI D&T standard are treated as objects in 3D that are attached to relevant object features. We discuss implementation issues and show how ANSI-based blueprints can be genereted directly from the solid modeler.
Computer-Assisted Pattern Development
Authors: Ganter M. A. , Tuss L. L.
Published: April 2021

Patternmaking and moldmaking are the first stages in a casting process whether the materials involved are either metals or plastics. The development of a pattern is a crucial part of the overall molding process. Results from an investigation to automate the process of patternmaking will be presented. This investigation focussed on three major areas; development of a rule-set for parting, parting search strategies, and back draft detection. While no “official” set of parting rules exists today, a collection of rules was developed using various sources of casting literature and in plant pattern surveys. Using this rule set, a parting procedure was developed which was realized through the use of computers and solid modeling technology. Results from these procedures have proven successful enough to warrant continued research in automated pattern design.
Efficient Intersection of Surface Normals With Milling Tool Swept Volumes for Discrete Three-Axis NC Verification
Authors: Oliver James H.
Published: April 2021

An efficient algorithm is presented for intersecting vectors with swept solids which represent three-axis numerically controlled (NC) milling tool motions. The intersection calculation proceeds in hierarchical steps through a series of progressively more exact definitions of the shape of the tool swept volume. At each step, results of intermediate calculations are used to determine whether intersection with an exact representation of the solid is possible and, if so, where and how the swept volume model must be refined for the next step. This structure ensures that superfluous intersection calculations are minimized. This intersection technique has been successfully implemented as part of an algorithm for automatic verification of three-axis NC milling programs, and may also be useful for applications in robotics and factory automation.
Computational Geometry on the Sphere With Application to Automated Machining
Authors: Chen Lin-Lin , Woo Tony C.
Published: April 2021

Based on observations made on the geometry of the cutting tools and the degrees of freedom in 3-, 4-, 5-axis numerical control machines, a new class of geometric algorithms is induced — on the unit Sphere. Spherical algorithms are useful for determining the type of tool, its path, workpiece fixturing, and the type of machine.

Basic to these algorithms are four that are presented here: detection of convexity on the sphere, computation for spherically convex hull, determination of the spherical convexity of a union and the intersection of hemispheres. These four algorithms are related by duality and the sharing of partial results.
Collision-Free Path Planning by Using Non-Periodic B-Spline Curves
Authors: Yang D. C. H.
Published: April 2021

This paper presents a method and a algorithm for the planning of collision-free paths through obstacles for robots end-effectors or autonomously guided vehicles. Fifth-order non-periodic curves are chosen for this purpose. The main ideas are twofold: firstly, to avoid collision by moving around obstacles from the less blocking sides; and secondly, to assign two control points to all vertices of the control polygon. This method guarantees the generation of paths which have C3 continuity everywhere and satisfy the collision-free requirement. In addition, the obstacles can be of any shape, and the computational complexity and difficulty are relatively low. A computer code is developed for the implementation of this method. Cases study is given for illustration.
Automatic Generation of Tolerance Chains From Mating Relations Represented in Assembly Models
Authors: Wang Nanxin , Ozsoy Tulga M.
Published: April 2021

This paper presents an algorithm for generating tolerance chains from the mating relations between components of assemblies. The algorithm is developed upon a feature-based assembly modeling strategy that represents each component in close relation to its mating features, dimensions and tolerances. The mating relations within an assembly are described by a mating graph. Tolerance chains together with their dimensions and tolerances are generated automatically by searching through a mating graph for matching mating features. A prototype program package based on the presented algorithm has been developed, and several examples of various complexity have been tested with success.
Designing and Mapping Trimming Curves on Surfaces Using Orthogonal Projection
Authors: Pegna Joseph , Wolter Franz-Erich
Published: April 2021

In the design and manufacturing of shell structures it is frequently necessary to construct trimming curves on surfaces. The novel method introduced in this paper was formulated to be coordinate independent and computationally efficient for a very general class of surfaces. Generality of the formulation is attained by solving a tensorial differential equation that is formulated in terms of local differential properties of the surface.

In the method proposed here, a space curve is mapped onto the surface by tracing a surface curve whose points are connected to the space curve via surface normals. This surface curve is called to be an orthogonal projection of the space curve onto the surface. Tracing of the orthogonal projection is achieved by solving the aforementionned tensorial differential equation. For an implicitely represented surface, the differential equation is solved in three-space. For a parametric surface the tensorial differential equation is solved in the parametric space associated with the surface representation. This method has been tested on a broad class of examples including polynomials, splines, transcendental parametric and implicit surface representations.

Orthogonal projection of a curve onto a surface was also developed in the context of surface blending. The orthogonal projection of a curve onto two surfaces to be blended provides not only a trimming curve design tool, but it was also used to construct smooth natural maps between trimming curves on different surfaces. This provides a coordinate and representation independent tool for constructing blend surfaces.
Computer Aided Geometric Design of Line Constructs
Authors: Ravani B. , Wang J. W.
Published: April 2021

This paper develops a mathematical foundation for Computer Aided Design (CAD) of sculptured shapes based on line geometry. First, a new representation is presented for a line based on Plücker coordinates that would allow specification of a line segment (rather than an infinite line) in an elegant manner and suitable for computational purposes. Then, methods are presented for geometric design of shape patches (here referred to as line constructs) by interpolating or approximating a set of control lines (rather than control points) using ruled surfaces, line congruences and line complexes. The methods presented are general and allow utilization of different basis functions such as Bézier, Cardinal and B-spline bases. As Computer Aided Manufacturing (CAM) application of the theory, methods are developed for generation of offsets of ruled surfaces useful in Numerical Control (NC) milling and tool motion generation in the Wire Cut Electric Discharge Machining (EDM) operation.
Blending Between Quadric Surfaces Using Partial Differential Equations
Authors: Cheng S. Y. , Bloor Malcolm I. G. , Saia A. , Wilson Michael J.
Published: April 2021

The aim of this paper is to further illustrate the application of the PDE method in the field of blend generation, in particular the specification of the boundary conditions and their use in controlling the shape of the blend.
An Approach to Plant Layout Design Based on Constraint-Directed Search
Authors: Akagi Shinsuke , Fujita Kikuo , Nakatogawa Tetsundo , Inoue Motohiro
Published: April 2021

This paper presents an approach to plant layout design based on constraint-directed search. In layout design, the plant has to be arranged to satisfy spatial constraints imposed by the plant components. In our approach, the layout space is divided into finite compartments with a modular size, and the problem is treated as a search problem to assign the facilities to the set of compartments under various constraints. For the classification of the constraints we have implemented a prototype system which introduces a depth-first search algorithm and the concept of layout potential. This has been applied to the design of a nuclear power plant in order to check its validity and effectiveness.
Parametric Computer Aided Hydraulic Cylinder Design: Cylinder Product Modeling
Authors: Johannesson Hans L.
Published: April 2021

In a hydraulic cylinder each cylinder component contributes to the total function, and the components interact and are dependent on each other. The geometry of some components can be completely determined by other surrounding interacting components. In this work it is shown how computer aid can be applied in hydraulic cylinder design when considering component interaction.

A special hydraulic cylinder product model is developed. It is stored in an external CAD system independent data base. The parameters stored in the data base are used when retrieving component data from component family data bases, standard component data bases, and when running parametric component and system design programs.

The software system used in this work consists of an ordinary 2D wire frame modeling turn-key CAD system, FORTRAN application programs, a data base management system, CAD system independent data bases and CAD system dependent interface programs.
Development of a Mechanical Power Transmission Design Supervisor System
Authors: Goulding John R. , Zarefar Hormoz
Published: April 2021

Computer Aided Design and Computer Aided Manufacturing (CAD/CAM) software programs are used in mechanical engineering industries to reduce the time it takes to draft, simulate, machine, and plan a product. When knowledge-based expert rules, equations, and proprietary languages extend CAD/CAM software, previously designed mechanisms can be scaled to satisfy new design requirements in the shortest time.

Two major drawbacks exist in current technology. First, embedded design alternatives needed by design engineers during the product conception and rework stages are lacking. Second, an operator is required who has a thorough understanding of the intended design and the how-to expertise needed to create and optimize the design alternatives.

The focus of our research and development was to automate the intellectual operations; e.g., questioning, identifying, selecting, and coordinating the design process. A robust system emerged which:

1. Selects the best mechanisms necessary to design a power transmission device from proven solutions.

2. Aids the inexperienced operator in developing complex design solutions.

3. Provides design alternatives which add back-to-the-drawing-board capabilities to knowledge-based mechanical power transmission CAD programs.
A Formal Approach to Design Specifications
Authors: Kusiak Andrew , Szczerbicki Edward
Published: April 2021

In this paper a methodology for the specification stage in conceptual design is presented. It allows for problem solving in an active interaction with the designer. An important part of the proposed methodology is the requiremental and functional tree representing the overall logic and structure of the design problem.

The specification stage aims at providing requirements and transforming them into functions of the designed object. It occurs at the highest level of abstraction and it must provide enough information to begin the synthesis process where functions are transformed into design components that are further synthesized into the designed object. The proposed approach was motivated by the following problems: specification of requirements, specification of functions, incorporation of logic into functional and requiremental trees, representation of requirements-functions interaction, and optimization in the functional space.

The methodology presented is illustrated with examples.
Configuration Tree Solver: A Technology for Automated Design and Configuration
Authors: Kott Alexander , Agin Gerald , Fawcett Dave
Published: April 2021

Configuration is a process of generating a definitive description of a product or an order that satisfies a set of specified requirements and known constraints. Knowledge-based technology is an enabling factor in automation of configuration tasks found in the business operation. 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.
QUINT: A Problem-Solving Strategy for Mechanical System Conceptual Design: Part II — Analysis, Evaluation, and Example
Authors: Qun Wang , Haibin Yang , Ji Zhou , Jun Yu
Published: April 2021

In part I, the characteristics of mechanical system conceptual design, the main idea of of QUINT and how to realize the first-stage, second-stage and third-stage reasoning were discussed. The part II will continue to study the last two stages of QUINT strategy, and give an example.
A Sequential Linearization Approach for Solving Mixed-Discrete Nonlinear Design Optimization Problems
Authors: Loh Han Tong , Papalambros Panos Y.
Published: April 2021

Design optimization models often contain variables that must take only discrete values, such as standard sizes. Nonlinear optimization problems with a mixture of discrete and continuous variables are very difficult, and existing algorithms are either computationally intensive or applicable to models with special structure. A new approach for solving nonlinear mixed-discrete problems with no particular structure is presented here, motivated by its efficiency for models with extensive monotonicities of the problem’s objective and constraint functions with respect to the design variables. It involves solving a sequence of mixed-discrete linear approximations of the original nonlinear model. In this article, a review of previous approaches is followed by description of the resulting algorithm, its convergence properties and limitations. Several illustrative examples are given. A sequel article presents a detailed algorithmic implementation and extensive computational results.
A Parallel Dual Projection Algorithm for Solving Positive Definite Quadratic Programming Problems
Authors: Wang Yugang , Sandgren Eric
Published: April 2021

Two parallel algorithms, a dual projection algorithm and a hybrid dual projection algorithm, are proposed for solving positive definite quadratic programming problems. In each iteration of the algorithms, the search point is always a local optimum point on the current active constraint basis for both adding and dropping constraint operations. The advantage of this strategy is that the computation is stable and all operations maintain parallel properties. Only a pseudo-inverse matrix must be updated instead of two matrices in Goldfarb’s dual algorithm in a basis change. Both computational and space complexities are reduced by about half. When the search point reaches a vertex in the dual space, a pivot operation is employed to update the basis in the hybrid dual projection algorithm in place of the addition and deletion operations in the dual projection algorithm. This reduces the computational complexity by half in future iterations. Some suggestions are presented to further enhance the computational speed of the algorithm. Numerical results are presented based on randomly generated test problems. Comparison with other methods demonstrates that the new algorithm is efficient and stable and points to the possibility of implementation on a parallel computer.
Constrained Variable Metric Method With Feasible Directions
Authors: Jianhua Wang , Ji Zhou , Jun Yu
Published: April 2021

This paper proposes a new feasible direction algorithm based on the constrained variable metric method of Powell in order to handle the design optimization problmes which demand that all iterative points are feasible. The algorithm retains many advantages of the constrained variable metric method, makes use of the properties of the solutions of quadratic programming problems and information of iterative points to define feasible directions, and uses the monotonicity analysis to establish the linesearch strategy which is especially suitable for feasible direction algorithms and a simple and efficient method for finding feasible initial points. The numerical results presented in the paper demonstrate that its rate of convergence is faster than those of Powell’s method and another feasible direction algorithm of Herskovits and its iterative procedure avoids Maratos effect.
Cluster Analysis for the Cognitive Selection of Nonlinear Programming Algorithms
Authors: Ma Jin-xian , Xie Shi-huai , Chen Yong
Published: April 2021

In recent years, cluster analysis has played an increasingly important role in statistical pattern recognition. Hoeltzel and Chieng have shown an example on cognitive selection of nonlinear programming algorithms in a mechanical design expert system. In this paper, an improved dynamic clustering of 3000 samples came from a comparative performance evaluation of six typical nonlinear programming softwares with randomly generated test problems has been made. Explanations resulting from the cluster analysis have been used to build rules to form the knowledge base of an optimization expert system.
A New Conjugate Direction Algorithm for Unconstrained Function Minimization
Authors: Li Bailin , Chen Yong
Published: April 2021

Based on the properties of conjugate vectors, a new algorithm for unconstrained function minimization is developed. The algorithm belongs to the direct search method and is a conjugate direction-type method with the property of quadratic termination. Comparing with some convensional direct search methods including the modified Powell method, the number of one dimensional search is greatly reduced. In addition, the algorithm presented in this paper is simple in calculating and easy in coding, and it has the capability of accelerating along the ridges.

The method presented is compared with two direct search methods including the modified Powell method on many test problems. Numerical results show the robustness and efficiency of the new algorithm.
Monotonicity Analysis of Taguchi’s Robust Circuit Design Problem
Authors: Wilde Douglass J.
Published: April 2021

A recent article showed how to formulate Taguchi’s robust circuit design problem rigorously as an optimization problem. A necessary condition for optimality was found to be that the control range be centered about the target value. This generates a constraint on the two design variables which cannot be solved for either variable. The present article shows that by approximating this unsolvable constraint with a simpler constraint that is solvable, one variable can be eliminated and the problem reduced to an unconstrained one in a single variable. Since this reduced objective turns out to be monotonic in the remaining design variable, its optimum value must be at the limit of its range. The corresponding optimum value of the other variable is then determined exactly from the true, not approximate, constraint. Since no model construction, experimentation, statistical analysis or numerical iteration is needed, this procedure is recommended whenever the input-output relation is known to be a monotonic algebraic function.
Flexible-Body Dynamics Modelling With a Reduced-Order Model
Authors: Yae K. Harold , Inman Daniel J.
Published: April 2021

In the dynamics modeling of a flexible body, finite element analysis employs Guyan’s reduction that removes some of the “insignificant” physical coordinates, thus producing a dynamic model that has smaller mass and stiffness matrices. Despite such reduction, the resultant model is still too large for flexible-body dynamic analysis. That warrants further reduction as is frequently used in control design by approximating a large dynamical system with a fewer number of state variables. When the reduced model is being assembled with other bodies in a multi-body mechanism, a problem, however, arises because a model usually undergoes, before being reduced, some form of coordinate transformations that do not preserve the physical meanings of the states. To correct such a problem, we developed a method that expresses a reduced model in terms of a subset of the original states.

The proposed method starts with a dynamic model that is originated and reduced in finite element analysis. Then the model is converted to the state space form, and reduced again by the internal balancing method. At this stage, being in the balanced coordinate system, the states in the reduced model have no apparent resemblance to those of the original model. Through another coordinate transformation that is developed in this paper, however, this reduced model is expressed by a subset of the original states. Then finally the model can be represented by the states assigned to the degrees of freedom of the selected nodal points.
Nonholonomic Constrain Models for Recursive Dynamic Analysis
Authors: Wang J. Y. , Wu J. K.
Published: April 2021

This paper presents mathematic formulations of nonholonomic constrain models, such as differential kinematic constraints, that can be used in dynamic analysis based on recursive formulations. Rolling and rotating between a pair of bodies are considered in the formulation. These mathematic models include state vector notations, cut differential kinematic constraints, and the right-hand side of constraint acceleration equations using joint coordinates. In addition, the paper describes the factors that need to be considered in selecting cut-joints in spanning tree analysis, that is needed for the recursive formulation. The weighting factors of certain nonholonomic constraints are suggested. In addition to current dynamic formulations, this study provides a systematic method to formulate the dynamic analysis for the mechanical systems with nonholonomic constraints. The results of applying this new formulation to several well-known examples are presented.
Optimal Blank Nesting Using Simulated Annealing
Authors: Jain P. , Fenyes P. , Richter R.
Published: April 2021

Since the cost of high volume stamped parts is largely dependent on material usage, scrap minimization is a primary goal of the design process. Although many factors influence the scrap rate for a given stamping, one of the most critical is the actual nesting, or positioning, of the part blanks onto the metal strip or sheet stock. Blank nesting is often done by hand, resulting in inefficient nestings with high scrap rates. Greater material efficiency can be achieved by automating this process. We have developed an automated system based on mathematical programming techniques which optimizes blank nestings for continuous strip stamping processes. We formulate the problem by first describing the geometry of the part or parts to be nested for stamping and specifying an initial layout. We use a novel integer grid technique to efficiently and accurately compute the overlap between parts and then apply simulated annealing, a probabilistic global optimization technique, to determine a new part layout with zero overlap and minimal scrap. Using representative part configurations, we present several examples illustrating the efficient nestings produced using this method.
Development of a User Interface for a Design Sensitivity Analysis and Optimization Workstation
Authors: Godse Mohan , Koch Peter , Santos Jose L. T.
Published: April 2021

An object-oriented user interface for a Structural Design Sensitivity Analysis and Optimization Workstation (SDSOW) is presented. The menu-driven interactive system features an object-oriented engineering spreadsheet as a mechanism to visualize, manipulate, modify, and search for the data generated during the interactive design process. A UNIX based windowing system and object-oriented programming techniques have been used to implement the user interface. Specialized engineering spreadsheets have been derived from a general spreadsheet to support specific design activities. The system can be easily extended to include new design activities by specializing the general spreadsheet to the new design tasks. Since the user interface runs under X-window system, it can be ported to several hardware platforms with minimum efforts.
Design Optimization of Machine Structures Based on Multiphase Structural Modeling of Ideal, Intermediate, and Detailed Models
Authors: Yoshimura Masataka
Published: April 2021

This paper proposes a design optimization method consisting of the multiphase structural modeling of ideal, intermediate, and detailed models for machine structures. In this method, the ideal characteristics are first obtained for a specific ideal model. Then, the detailed designs are determined so that the characteristics in the detailed model are as close to the ideal characteristics as possible. For easily and surely obtaining the final detailed designs, an intermediate model is introduced between the ideal model and the detailed model. This method not only effectively generates optimum detailed designs of machine structures but also brings about an easy realization of the optimum characteristics in practical manufactured machine products. The proposed method is applied to a machine-tool structural model for demonstrating the effectiveness of the method.
A Hamiltonian Equation of Motion for Realtime Vehicle Simulation
Authors: Bae D. S. , Won Y. S.
Published: April 2021

A relative coordinate formulation of the Hamiltonian equation of motion is derived for realtime vehicle simulation. The Baumgarte stabilization method [1] is adopted to solve the Differential-Algebraic Equations (DAE) of motion. The stability theory of multi-step integration methods is used to determine the stabilization constant. The equations of motion are first derived in Cartesian space and are reduced to relative coordinate space using the velocity transformation method [2]. Partial derivative of the kinetic energy with respect to the relative coordinate is obtained from equivalence of the Lagrangian and the Newton-Euler formulations. Parallel processing of the formulation is also discussed. Realtime simulation of a passenger vehicle is carried out to demonstrate the efficiency of the new formulation.
Real-Time Dynamic Simulation of a Robot With Rotor Dynamics
Authors: Chuang Li-Ping , Kim Sung-Soo
Published: April 2021

Rotor dynamics are important for robots that are driven by motors and high gear ratio transmission systems. New generic recursive dynamic formulations of robotic systems with motor rotor effects are presented, where motors can be mounted on inboard or outboard bodies of the actuated joints. An organized form of the system dynamics equations is obtained through adoption of a state vector representation in equation derivation. The influence of rotors on the overall system dynamics are identified. Parallelism of the derived dynamics formulations is then exploited and a real-time parallel computational algorithm is proposed. A seven degree-of-freedom telerobot is used to illustrate rotor dynamics effects in the computational model. A computational speed that is faster than real-time simulation is demonstrated.
Dynamic Analysis of Mechanical Systems With Time-Varying Topologies: Part 1 — Dynamic Model and Stability Analysis
Authors: Wang Yu
Published: April 2021

A model is developed for analyzing mechanical systems with a pair of bodies with topological changes in their kinematic constraints. It is built upon the concept of Poincaré map rather than following the traditional methods of differential equations. The model provides a set of well-defined and naturally-discrete equations of motion and is capable of giving physical insights of dynamic characteristics of deadbeat convergence of multiple collisions and periodic or chaotic responses. The development of dynamic model and a local stability analysis are presented in Part 1, and the global analysis and numerical simulation are discussed in Part 2.
Design Sensitivity Analysis and Optimization of Nonlinear Structural Systems With Critical Loads
Authors: Park Jong Sang , Choi Kyung K.
Published: April 2021

A continuum formulation for design sensitivity analysis of critical loads is developed for nonlinear structural systems that are subjected to conservative loading. Both geometric and material nonlinear effects are considered. Sizing design variables such as cross-sectional areas of beam or truss design components and thicknesses of plate or membrane design components, together with their shape design variables, are treated. A continuum approach is used to obtain design sensitivity expressions in integral form. For shape design sensitivity analysis, the material derivative concept and domain method are used to find variations of the critical load due to variations in shape of the physical domain. The total Lagrangian formulation for incremental equilibrium equation and one-point linearized eigenvalue problems are utilized. A numerical method is presented to evaluate continuum design sensitivity expressions using analysis results of established finite element codes. It is found that no adjoint system is necessary for design sensitivity analysis of the critical load. Numerical results show the proposed method for design sensitivity of critical loads is accurate for both sizing and shape design variables. A numerical procedure for optimal design of nonlinear structural systems is presented, using the proposed continuum design sensitivity analysis method. An optimal design problem with a stability constraint is solved.
Two-Level Structural Optimization Method for Multi-Processor Environment
Authors: Hsiung Ching-Kuo , El-Sayed Mohamed E. M.
Published: April 2021

In this paper a two-level structural optimization approach is presented. At the first level, the objective of the optimization problem is to minimize the total weight of the whole structure subject to the global constraints. At the second level, the optimization problem is divided into several subproblems, each subproblem represents a substructure. The objective of each subproblem is to minimize the weight of the assigned substructure subject to its local constraints. To assure that the final solution will not violate the global constraints, the optimum values of the design variables from the first level are used to update the lower bounds on these variables at the second level. Two numerical examples are included to demonstrate the approach and its application in a multi-processor environment.
Differentiation of Mass and Stiffness Matrices for High Order Sensitivity Calculations in Finite Element-Based Equilibrium Problems
Authors: Bernard J. E. , Kwon S. K. , Wilson J. A.
Published: April 2021

Extension of sensitivity methods to include higher order terms depends on the ability to compute higher order derivatives of the mass and stiffness matrices. This paper presents a method based on the use of cubic polynomials to fit mass and stiffness matrices across a range of interest of the design variable.

The method is illustrated through an example which uses Padé approximants to expand the solution to a statics problem. The design variable is the thickness of one part of a plate with fixed boundaries. The solution gives a very good approximation over five fold change in the value of the design variable.
A New Method for 3-D Contact Problems of Four-Row Tapered Roller Bearing Using Finite Element Analysis
Authors: Zhang Qigui , Yu Jun , Li Yuanke , Zhao Caiyan
Published: April 2021

The most glaring problems in reality in the field of finite element analysis of tapered roller bearings are long calculation time and great error due to neglect of axial force. The static condensation method and solving technique are introduced in this paper to reduce the calculation time and raise the calculation precision. Due to the effects of axial force, the contact boundary becomes more complicated. Up to now, the paper dealing with axial force is rarely seen. This paper mainly studies four-row tapered steel mill bearing under reality loaded condition with finite element analysis and computation method. The contact load-distribution given by finite element calculation is in agreement with photo-elastic experiment. This paper also supplies a fast and effective numerical method for finite element analysis of many other types of bearings.
Eigenvalues for Moderately Damped Linear Systems Determined by Eigensensitivity Analysis
Authors: Reiss Robert , Qian Bo , Aung Win
Published: April 2021

A new method is presented to determine approximate closed-form solutions for the complex-valued frequencies of moderately damped linearly elastic structures. The approach is equally applicable to finite degree of freedom systems and distributed parameter systems. The damping operator is split into two components, the first of which uncouples the quadratic eigenvalue equation, and the eigenvalues are expressed as a power series in the second component of the damping operator. Specific numerical examples include both finite degree of freedom and distributed parameter systems. It is shown that for moderate damping, that is, when the second component of the damping operator is small, but not negligible, the series solution truncated after quadratic terms provides an excellent approximation to the true eigenvalues.
Design Sensitivity Analysis and Optimization of Vibrating Beams With Variable Support Locations
Authors: Hou J. W. , Chuang C. H.
Published: April 2021

The method of material derivatives is employed in this paper to derive analytical equations to calculate eigenvalue sensitivity coefficients of a continuous beam with respect to support variables. A finite element scheme is then implemented to numerically validate these sensitivity equations. Finally, design optimization of a vibrating beam subjected to frequency constraints is investigated. Results suggest that a small amount of adjustment in support locations and stiffnesses can greatly improve the quality of the design.
Minimum Sensitivity Design of Planar Kinematic Systems
Authors: Patil Umesh R. , Krishnaswami Prakash
Published: April 2021

In designing a kinematic system, it is desirable to ensure that the performance of the system is relatively insensitive to small changes in the nominal design, since this will result in a more robust system that can be manufactured economically with looser tolerances. A general method for minimizing the sensitivity of such systems is developed in this paper. The approach is based on the idea of converting the minimum sensitivity design problem into a nonlinear programming problem which is then solved using an exterior penalty function method. The constrained multi-element formulation is used for kinematic analysis and sensitivity analysis is performed using a direct differentation technique. The resulting algorithm is general enough to handle any planar kinematic system. The proposed method has been implemented in a computer program which has been tested on some sample problems. The results provide convincing proof of the power and feasibility of this method.
Subset Selection Methods for Design Sensitivity Analysis of Constrained Dynamic Systems
Authors: Twu Jun-Tien , Krishnaswami Prakash , Rampalli Rajiv
Published: April 2021

In the Lagrangian formulation of the constrained motion of mechanical systems, a system of Differential-Algebraic Equations is generally encountered. The popular Backward Differentiation Formula for the numerical solution of such problems leads to an over-determined system of equations. The correct choice of a proper exactly determined subset can greatly enhance the performance of a solution algorithm. In this paper, we discuss four solution methods with different choices of subsets. Three numerical examples are solved to compare the accuracy and efficiency of these methods.
Sensitivity Analysis for the Steady-State Response of Damped Linear Elastodynamic Systems Subject to Periodic Loads
Authors: Tortorelli Daniel A.
Published: April 2021

Adjoint and direct differentiation methods are used to formulate design sensitivities for the steady-state response of damped linear elastodynamic systems that are subject to periodic loads. Variations of a general response functional are expressed in explicit form with respect to design field perturbations. Modal analysis techniques which uncouple the equations of motion are used to perform the analyses. In this way, it is possible to obtain closed form relations for the sensitivity expressions. This eliminates the need to evaluate the adjoint response and psuedo response (these responses are associated with the adjoint and direct differentiation sensitivity problems) over the time domain. The sensitivities need not be numerically integrated over time, thus they are quickly computed. The methodology is valid for problems with proportional as well as non-proportional damping. In an example problem, sensitivities of steady-state vibration amplitude of a crankshaft subject to engine firing loads are evaluated with respect to the stiffness, inertial, and damping parameters which define the shaft. Both the adjoint and direct differentiation methods are used to compute the sensitivities. Finite difference sensitivity approximations are also calculated to validate the explicit sensitivity results.
Multi-Body Impact Motion With Friction: Analysis, Simulation, and Experimental Validation
Authors: Han Inhwan , Gilmore B. J.
Published: April 2021

When a multi-body system collides with a single body or with another multi-body system, impact dynamics with friction should be considered. This paper presents a general computer oriented analysis of impact dynamics incorporating friction. The presence of friction between sliding contacts during the impact makes the problem difficult since the events such as reverse sliding or sticking, which may occur at different times throughout the impact, must be determined. The boundary representations of the bodies are used to solve for the velocities at the points of contact. Using this information and a classification of the modes of impact, the frictional impact with sliding contact problem is solved. Using a high speed video camera, the resulting computer strategy is experimentally verified. Simulation and experimental results agree.
Recursive Linearization of Multibody Dynamics and Application to Control Design
Authors: Lin Tsung-Chieh , Yae K. Harold
Published: April 2021

The non-linear equations of motion in multi-body dynamics pose a difficult problem in linear control design. It is therefore desirable to have linearization capability in conjunction with a general-purpose multibody dynamics modeling technique. A new computational method for linearization is obtained by applying a series of first-order analytical approximations to the recursive kinematic relationships. The method has proved to be computationally more efficient. It has also turned out to be more accurate because the analytical perturbation requires matrix and vector operations by circumventing numerical differentiation and other associated numerical operations that may accumulate computational error.
Kinematic Study of the Face Gear
Authors: Chen Yih-Jen Dennis
Published: April 2021

This paper presents the kinematic study of the face gear drive system. The study includes three different configurations which are: (1) the on-center orthogonal face gear drive, (2) the on-center non-orthogonal face gear drive, and (3) the offset orthogonal face gear drive. The mathematical description for the gear meshing and the resulting face gear tooth surface is developed. This paper also presents the criteria for detecting the limitation of the effective face width due to tooth pointing and undercutting. The technique presented is applied to develop a computer program. This design automation tool allows visualizing the gear meshing and tooth geometry of the face gear drive.
Analysis and Synthesis of Mechanical Error in Universal Joints
Authors: Cagney J. L. , Rao S. S.
Published: April 2021

The modeling of manufacturing errors in mechanisms is a significant task to validate practical designs. The use of probability distributions for errors can simulate manufacturing variations and real world operations. This paper presents the mechanical error analysis of universal joint drivelines. Each error is simulated using a probability distribution, i.e., a design of the mechanism is created by assigning random values to the errors. Each design is then evaluated by comparing the output error with a limiting value and the reliability of the universal joint is estimated. For this, the design is considered a failure whenever the output error exceeds the specified limit. In addition, the problem of synthesis, which involves the allocation of tolerances (errors) for minimum manufacturing cost without violating a specified accuracy requirement of the output, is also considered. Three probability distributions — normal, Weibull and beta distributions — were used to simulate the random values of the errors. The similarity of the results given by the three distributions suggests that the use of normal distribution would be acceptable for modeling the tolerances in most cases.