bluuebunny/crossref_metadata_2025 huggingface dataset:
Worst Case and Statistical Tolerance Analysis of the Daughter Card Assembly
Authors: Guilford James , Sethi M. , Turner Joshua
Published: March 2021

Designers are increasingly finding the need for an automated tolerance analysis package which interprets tolerances according to established tolerancing standards. Unfortunately, most of the commercial packages available make simplifying assumptions for the conventional plus-minus tolerances and do not support geometric tolerancing at all. Construction of a tolerance analysis models with these packages can be time consuming.

GEOS is an automated tolerance analysis package which overcomes these shortcomings. It is based on variational modeling and feasibility space approaches. This report presents the results for a worst case amd statistical tolerance analysis done on an industrial assembly using GEOS. For this analysis, no special models had to be created as GEOS can accept the 3-D CAD model directly. The models used both conventional plus-minus tolerances as well as geometric tolerances. A GEOS graphical front-end, integrated with a commercial CAD system, was used to define the assembly relations, design function, and analysis parameters.
On the Effects of Parallelism on Computer-Aided Process Planning
Authors: Levin Jordan B. , Dutta Debasish
Published: March 2021

Computer-aided process planning is a critical function in the overall scheme of computer-integrated manufacturing (CIM). Progress in CIM is key to increased productivity. Furthermore, as new CIM systems evolve, the latest advancements from the constituent areas must be incorporated. Toward that end, our ongoing research deals with the development of methodologies to enable the inclusion of a new class of machine tools characterized by their ability to carry out machining operations in parallel. In this paper, we identify and elaborate on the effects of parallelism on computer-aided process planning, which are brought about by these new machine tools.
Numerical Design Method to Obtain Minimum Pressure Losses in Duct Elbows
Authors: Paul James C. , Noles David R.
Published: March 2021

A numerical procedure has been developed for the design of duct elbows that exhibit minimum pressure loss. A two-dimensional potential flow modeling method is used to determine the ideal static pressure distribution for a given elbow geometry. A turbulent boundary layer separation criterion is then used to determine whether the ideal distribution can be obtained. Those elbow designs for which flow does not separate are shown to produce minimum pressure loss. The procedure is also shown to be effective in the design of turning vanes. The design method is confirmed by experiments with a 90 degree elbow within a square duct.
The Use of Von Karman’S Similarity Hypothesis in Turbulent Fluid Flow Computation
Authors: Foster David J.
Published: March 2021

Von Karman’s similarity hypothesis for the turbulent mixing length in boundary layer type flow is extrapolated to a plausable two dimensional expression. The corresponding incompressible turbulent flow equations are developed in terms of the transient vorticity transfer and stream function equations. Numerical solutions for the separated flow behind a step and in a rectangular cavity were obtained and the results are presented pictorally. The streamlines computed for the step flow solution compare favorably with those calculated from experimental measurements at a similar Reynolds Number.
Development of Finite Element Analysis Support System Based on the Hybrid Knowledge Model
Authors: Nagasawa S. , Sakuta H. , Goto M.
Published: March 2021

This paper deals with conceptual orientation and system development of intelligent support system for general purpose FEA (finite element analysis) programs.

An integrated support system called “InhierTalk” (Integrated interactive environment for hierarchical representation for FEA) has been developed in Smalltalk, an object oriented language, in order to confirm effectivity of hierarchical representation and to establish an optimum method of the system development.

Two object-oriented knowledge models which consist of macro visual data representation and micro regularized data representation are proposed. In the development, it is found to be clear that active and passive evaluation methods are effective for construction of support system.
A Blackboard Based Approach to Intelligent Finite Element Modeling and Analysis
Authors: Grosse Ian R. , Corkill Daniel D.
Published: March 2021

In this paper a methodology and associated system architecture is proposed for the development of an intelligent finite element modeling assistant. The technique is ideally suited for specific application domains in which the physical system to be modeled can be constructed from a limited and well defined set of features. The development of knowledges sources needed to support automatic finite element modeling and analysis is discussed. A computational framework is proposed for interfacing the various knowledge sources and controlling the execution of the knowledge sources in an opportunistic manner based on the multiple expert blackboard paradigm. An example application in the domain of finite element modeling and analysis of multichip module microelectronic devices is presented and discussed.
A Domain Decomposition Study for a Parallel Finite Element Code
Authors: Rodriguez J. , Sun J.
Published: March 2021

The primary objective of this study was the implementation and comparison of domain decomposition algorithms for a parallel Finite Element Method (FEM) used in the area of Computational Structural Mechanics (CSM). A parallelized FEM code exploits the concurrency inherent in the method to improve its computational efficiency. In order to use a larger size granularity in the parallel computation, the parallel FEM needs to partition its domain into subdomains in a proper manner. It is therefore necessary to search for domain decomposition algorithms to satisfy the special requirements of a parallel FEM.

The domain decomposition algorithms investigated in this study physically decompose a meshed domain into a desired number of subdomains. Addressing the requirements of the parallel FEM, these algorithms are able to handle any type of two- and three-dimensional domains, balance the workloads across the multiple processors, minimize the communication overhead among the processors, maintain the integrity of each subdomain, minimize the overall bandwidth of the resulting system matrix, and require only a small amount of CPU time for the decomposition.

Modifications to existing decomposition algorithms, such as the single wave propagating method and the bisecting method using vertical/horizontal cuts, are investigated. A new algorithm, based on the proposed multiple wave propagating method and the bisecting method using middle cuts, is formulated. These algorithms are compared with each other using performance criteria based on the overall FEM code and the algorithms themselves. An optimal combination algorithm is proposed. This algorithm combination is flexible and intelligent in some sense since several judgements are suggested to guide and organize different decompositions based on the general geometry of the meshes. The combination algorithm possesses both the desirable features of wave propagating and bisecting methods.

As an application, the present algorithm is included in an existing parallel FEM code and some improvements in this code are made. The overall efficiency of the FEM code was increased.
Error Estimation and Mesh Optimization for Finite Element Analysis of Short Fiber Reinforced Composite Materials
Authors: Kim H. G. , Grosse Ian R. , Nair S. V.
Published: March 2021

Knowledge of internal stress fields in fiber or whisker reinforced composites is crucial to the design, manufacturing and applications of composites. Finite element analysis (FEA) presents the only rigorous approach to a solution of this problem. However, the application of FEA to composites requires careful attention to the geometry of the optimum mesh used in the analysis. Standard energy analysis and mesh refinement procedures have yet to be generalized or extended to the special case of fiber or whisker reinforced non-homogeneous composites. Current automatic mesh generation codes do not provide the optimum mesh for composites.

This paper is concerned with the development of a generalized approach for optimal mesh refinement in a short fiber reinforced composite. Optimization procedures are based on the calculation of the error in energy norm for global convergence and the traction differential approach at the fiber/matrix interface for local convergence whereas the mesh refinement strategy is based on the use of elongated elements at the fiber/matrix interface. An isoparametric finite element model that has a periodic hexagonal array of elastic fibers surrounded by an elastic matrix was used in the investigation. It is shown that this approach provides the optimum mesh with a much more rapid convergence than conventional meshes. In this manner converged local solutions can be obtained with significantly lower degrees of freedom than by conventional mesh refinement methods.
Response of a Cylindrical Section to an Internal Blast
Authors: Gupta Aaron Das
Published: March 2021

Transient response analysis of a hollow cylindrical section subjected to an internal explosive blast has been conducted from a structural integrity standpoint. The reflected blast overpressure upon the internal surface of the cylinder was estimated based on a cube root scaling law and the modified Friedlander exponential decay. A closed form solution of the governing equation of motion for the internally pressurized cylinder was obtained subject to initial conditions. The solution was optimized by a trial and error approach to yield an optimum time which was employed to predict the peak response.
Matrix Solution of Digitized Planar Human Body Dynamics for Biomechanics Laboratory Instruction
Authors: Alciatore David G. , Abraham Lawrence D. , Barr Ronald E.
Published: March 2021

The dynamics of planar human body motion, solved with a non-iterative matrix formulation, is presented. The approach is based on applying Newton-Euler equations of motion to an assumed 15 body segment model resulting in a system of 48 equations. The system of equations was carefully ordered to result in a banded system (bandwidth = 10) which is solved efficiently. The method is more favorable than a traditional iterative solution because it is more easily coded, reaction forces are more easily dealt with, and multiple solutions for a given body position can be readily obtained. The results described are limited to planar body motion but the method is easily extendible to general three-dimensional motion. A computer program was developed to process digitized body point coordinate data and calculate resultant joint forces and moments for each frame of data.

This method of human body dynamics analysis was developed to support laboratory instruction for an Engineering Biomechanics course. Athletic activities are captured with a three-dimensional video digitizing system and the data is processed resulting in time histories of force and moment distributions throughout the body during the captured event. Computer software performs the analyses and provides real-time graphical illustrations of the kinematics and dynamics results. The dynamics results for the leg of a runner are presented here as an example of the application of the method.
Comparison of Web Stress Concentration Factors and Safety Margins for a Thin Webbed Spur Gear Subjected to Static and Cyclic Loading Conditions
Authors: Clerici Paolo , Girotti Ambrogio , Perazzolo Alessandro
Published: March 2021

The stress distribution in the holed web of a gear was studied in order to evaluate the effects of overstress caused by a reduction in weight in comparison with a gear without lightening holes. The analysed gear is a component of a helicopter principal transmission: geometry and dimensions (web with eight circular holes) are usually employed.

A 3-D mesh of the gears was made using PATRAN and a FEM analysis was carried out using NASTRAN 65a2.

Moreover the principal stress history in one revolution of the gear was reconstructed at the critical points of the web. Thus it was possible to evaluate the actual fatigue cycle and the consequent safety margin for the different load conditions under which helicopter transmissions are generally checked.

It was found that the stress variations in one revolution of the gear are significant even in constant power conditions and that the stresses at each point on the border of the holes always have the same sign in a complete revolution.

Safety margins in the web were evaluated and compared using different formulas.
A Study on the Hourglass Worm Gearing Manufactured by a Pinion Cutter
Authors: Maki Minoru , Nagashima Sakae , Horiuchi Akiyo
Published: March 2021

A method to obtain the higher productivity of hourglass worm gearing with high performance is developed. For this purpose, a method for manufacturing the worm by a pinion cutter is developed, along with a method for analyzing how the cutting blades generate the worm tooth surface.

A method to calculate the true profiles of the worm tooth surface generated by the pinion cutter blades is discused. These calculating method are available for any kind of the gearing manufactured by any type of cutting tool.
Characteristics of a Modified Double Enveloping Worm Gear Drive
Authors: Simon Vilmos
Published: March 2021

A modified new type of double enveloping worm gearing is developed. The gear tooth surface is generated by a flying tool whose cutting edge has the modified profile of the entering edge of the worm, and the worm surface has a straight-lined axial profile and circular lead changed to the established rule. The same rule governs the motion of the flying tool in processing the gear teeth.

To compare the performance characteristics of the classical and the modified new type of double enveloping worm gearings, the load distributions are calculated and the elastohydrodynamic analysis of lubrication is carried out for both types of worm gearings. The obtained results show the advantages of the new type of double enveloping worm gear drive.
A Study on Hourglass-Worm Gearings Designed to Concentrate Surface Normals: Design for Worm Gearings With a Large Lead Angle
Authors: Gunbara Hiroshi , Shimachi Shigeyuki , Kobayashi Tohru , Kawada Hiroshi
Published: March 2021

For moderating the edge contact of gear tooth surfaces on load, a new concept has been proposed on designing worm gearing. As a first step of research, restricting a field of application of the designing concept, a few methods for generating tooth surface of hourglass worm gearing having a small lead angle have been devised.

This paper tries to apply this designing concept to wider general use — an hourglass worm gearings with a large lead angle. First, the worm axis displacement relative to the wheel axis is roughly calculated by means of elastic deformation theory. And, this idea is applied to the gear designs using two kinds of hourglass worm gearings. As a result, validity of this design concept is substantiated also in the case of large lead angle of worm gearing.
Laser Holographic Measurement of Tooth Flank Form of Cylindrical Involute Gear: Part 1 — Principle and Measurement of Spur Gear
Authors: Kubo A. , Fujio H. , Tochimoto S. , Honda T. , Saitoh S. , Suzuki M.
Published: March 2021

Form deviation of tooth flank of spur gear is measured by laser holographic interferometer. To get the reflected ray from the objective tooth flank, laser beam is irradiated with large incident angle to the objective tooth flank which has considerably rough surface finish in comparison with that of optical parts. Some tooth flanks with various kinds of form deviation were measured, and image patterns of interference fringe were obtained. The conversion of the coordinates of the image figure of the gear tooth flank on CRT to the coordinate system of the gear is worked out by fitting the contour form of simulated figure to that of observed images. The algorithm of transformation from interference fringe pattern to tooth flank form deviation is shown: The brightness of the interference fringe image on the CRT is converted to the amplitude of form deviation defined on the plane of action of the gear via phase difference of light beam which is obtained by phase stepping method. The form deviations of tooth flanks of spur gear obtained by this interference method were compared with the results of conventional measuring method using contacting stylus.
Computer-Aided Optimal Gear Design
Authors: Andrews G. C. , Argent J. D.
Published: March 2021

Gear-sets designed using standard tooth profiles are rarely optimum strength designs, where “optimum strength” is defined as the maximum tooth bending strength for minimum tooth numbers and tooth size. However, standard tooth profiles are widely used because of the difficulty of determining the amount of hob (or rack) “offset” necessary to cut optimum strength non-standard gears. Also, stresses are not easily calculated for non-standard tooth profiles since geometry factors (I and J) are not tabulated. This paper describes a computer-aided method for obtaining optimum strength designs of spur gears, through iterative strength calculations. Two common cases are considered in which a non-standard gear-set is to replace a standard gear-set with the same center distance. When the speed ratio must be rigidly maintained, the “long and short addendum method” can be used; when minor variations in speed ratio are permissible, the “non-standard center distance” method can be used and much larger increases in strength can be achieved. The methods are illustrated by a numerical example. Increases of strength in the range of 10 to 20 percent are typical when standard gears-sets are replaced by non-standard gears with the same center distance, assuming material properties remain constant. The procedure for estimating the hob offsets which yield optimum design is simple and novel, and has proved efficient in obtaining convergence in a few iterations of the optimization process.
Analysis of an Eight Speed Gear Train Using a Narrowing Iterative Step Algorithm
Authors: Osman M. O. M. , Dukkipati R. V. , Siva Prasad V.
Published: March 2021

Analysis of double composite gear trains using the algebraic equations method involves a great deal of manual manipulations. Though the tedium of the process is reduced to some extent by the use of the General Theory, it will not lead to realization of computer algorithm generalized for all kinematic versions of a drive. The present algorithm based on the Unified Theory provides an efficient method to find values of the largest gear at a design optimization point Sop. The narrowing iterative step technique facilitates rapid convergence to the pivotal point. Six kinematic versions of open type having uniform group structure are analysed using the algorithm.
The Linear Approximated Equation of Vibration for a Pair of Spur Gears: Theory and Experiment
Authors: Cai Yurong , Hayashi Teru
Published: March 2021

The nonlinear equation for the rotational vibration of a pair of spur gears has a restriction that the analytical solution of the equation cannot be obtained. In this paper, the linear equation of vibration is derived theoretically and its physical model, i.e. the linear model of vibration is presented. The analytical solution of the linear equation, which is derived by analytical method, agrees well with the numerically calculated result by the nonlinear equation. By analyzing the analytical solution of the linear equation in detail, we clarified the relation between the waveforms of the vibration and the profile error of gear pairs, and also found that the effect of the contact ratio to the vibration is large and complex. The equivalent error, accounting for effects of the static load, the time-varying stiffness and the profile error of gear pairs, is proposed in this paper. It can be considered as promising for evaluating the profile error, because the vibration of gear pairs is excited mainly by the equivalent error. Finally, for confirming the above results, the vibration of two tested gear pairs has been measured by an experimental set-up for this purpose.
Recursive Determination of Conjugate Profiles in Planar Motion With Application to Gear Design
Authors: Innocenti Carlo
Published: March 2021

A general procedure for determining the envelope of the outline of planar rigid figures is presented which allows both local and finite undercutting to be taken into account. A suitable parametrization of the enveloped curves, together with the insertion of cusps wherever undercutting occurs, enables the procedure to be applied recursively while maintaining high accuracy in describing the resulting envelopes. The proposed procedure provides the basis for an original validation method regarding parallel-axis spur and helical gears. The method takes into account possible undercutting during hobbing or shaping, considers the desired amount of meshing clearance over the entire tooth profile, and is able to detect meshing interference. Further, it provides a criterion in choosing the proper cutter profile. A numerical example showing the application of the method is discussed at the end of the paper.
A Few Aspects on Lubricant Selection for Stepless Chain Coverters: Efficiency and Service Life
Authors: Schönnenbeck G.
Published: March 2021

Stepless vehicle drives will assume their place next to automatic switching units throughout the world if they meet their expected fuel-saving potential. This necessitates optimizing the individual components of the CVT as regards their efficiency. The main source of losses are the hydraulic supply units and the losses which result specifically from non-positive transmission. In the case of stepless chain conveners, these result mainly from friction disk deformation. These losses account for 50 to 70 % of total CVT losses. Both loss components are influenced by the lubricant to a significantly greater extent than it would appear at first sight: In the case of fully-hydraulic clamping and control systems, the viscosity and its long-term stability determines the degree of leakage losses and therefore the size of the pump or pump combinations. This applies to pressure levels between 20 and 40 bar. This in turn is directly proportional to the hydraulic losses on the CVT. The friction coefficient of the lubricant determines the level of the necessary clamping forces. These are responsible for friction-disk deformation. Also of importance as far as the selection of lubricant is concerned is its influence on the CVT service life. The critical service life limits for chain converters are chain breakage (not the subject of this report) and evidence of wear, i.e. grey staining, sheave-grooving, pitting, scoring and rocker pin wear. Standardized test methods exist at P.I.V. for both wear manifestations and for the friction coefficient, these tests allowing a targeted selection of lubricants.
Mechanics of Roller Chain-Sprocket Contact: A General Modelling Stragegy
Authors: Kim Mahn Shik , Johnson Glen E.
Published: March 2021

An extensive analysis of the contact phenomenon occuring between a roller chain and sprocket was given by Binder in 1956. Naji and Marshek complemented Binder’s work by presenting a theoretical and experimental investigation of the contact phenomenon under quasi-static conditions during the early 1980’s. The problem is very complex, and significantly complicated due to the non-trivial geometry of the sprocket tooth, manufacturing tolerances, and changes in clearances between components due to wear. Accordingly, several simplifying assumptions were necessary in the previous investigations.

In this paper, a more detailed model of the quasi-static contact phenomenon is developed from first principles. The new model includes the external loading conditions, the curvature difference between the roller and the seating curve, the net error in the chain pitch (defined as the error in the chain pitch minus the error in the sprocket pitch), and Coulomb friction between the tooth and roller, the roller and bushing, and the bushing and pin. No assumption regarding the pressure angle at each contact point is made — rather the pressure angle at each contact point is calculated during the solution. (This is a very significant difference between the present and previous analyses). An efficient strategy for the computation is outlined.

In a companion paper (“Mechanics of Roller Chain - Sprocket Contact: Observations About the Contact Phenomenon and Load Distribution” submitted for presentation at this conference), results generated by the new model are presented and discussed. A comparison with experimental data taken from the literature (Naji and Marshek, 1983) indicates that excellent quantitative prediction of load distribution is possible. Finally, practical observations about chain performance (including effects of manufacturing tolerance and wear, and guidelines for incorporation of idler sprockets) are presented.
Optimization in a Design System for Complex Products
Authors: Malmqvist Johan
Published: March 2021

This paper describes a system for parametric design and optimization of complex products. In the system, the use of knowledge-based and mathematical programming methods is combined. The motivation is that while knowledge-based methods are well suited for modeling products, they are insufficient when dealing with design problems that can be given an optimization formulation. This weakness was approached by including the information necessary for stating an optimization problem in the product models. A system optimization method can then be applied. The system also performs sensitivity analysis and has an interactive optimization module.

The use of the system is illustrated by an example; the design and optimization of a two-speed gearbox.
A Computational Investigation Into the Structure of Form and Size Errors Based on Machining Mechanics
Authors: Srinivasan R. S. , Wood Kristin L.
Published: March 2021

The central theme of this paper is the representation of tolerances in engineering design and manufacturing. A sub-problem of this central theme is the structure of form and size errors created by typical machining processes. This subproblem is addressed using a fractal-based procedure. In particular, workpiece profiles are generated for the shaping manufacturing process, using a simulation model and incorporating the basic shearing mechanism of machining with typical error sources. The resultant profiles are analyzed using a fractal-based, box counting algorithm. The results, which reveal the presence of variational structure, are discussed, emphasizing the relationship between total variability and function. Finally, modifications and future directions to the research are presented.
An Investigation Into Model Aggregation in Optimal Design
Authors: Hebert R. , Rao J. R. Jagannatha
Published: March 2021

In this article we examine the behavior of optimal design models when the parameters are progressively unfixed in a process referred to as model aggregation. While this is a common modeling practice, its consequences on solution properties are not always predictable. Using no special assumptions on problem data, we develop an upper bound result for the aggregation process and highlight the difficulties which arise when even a single parameter is unfixed. We also present a generalization of the commonly studied “portal frame” problem as a design case study. While aggregation has only benign effects on the solution of this model, interesting new results are obtained when model perturbations more severe than simple aggregation are imposed on this problem.
Optimal Design of an Overhead Crane Runway Girder
Authors: Rajagopalan Rajkumar , Trabia Mohamed B.
Published: March 2021

The objective of this paper is to minimize the manufacturing cost of an overhead crane runway girder. The work involves the minimization of the material cost of the girder, the welding cost, and the bolting cost. An I section was selected for the problem. The main constraint imposed on the problem is that stiffeners of any kind are not to be used. AISC design specifications are used to formulate the problem. Condition for separation of the optimization problem into two subproblems is presented.
Two-Level Nonlinear Mixed Discrete-Continuous Optimization-Based Design: An Application to Printed Circuit Board Assemblies
Authors: Praharaj S. , Azarm Shapour
Published: March 2021

In this paper, a new approach for optimization-based design of non-linearly mixed discrete-continuous problems has been developed. The approach is based on a two-level decomposition strategy in which the entire domain of variables is partitioned into two levels, one involving the continuous variables and the other involving the discrete variables. Variables in one level are optimized for fixed values of the variable from the other level. A modified penalty function is formed, based on monotonicity analysis, to solve for the discrete variables, and a conventional optimization method was used to solve for the continuous variables. To improve the computational effectiveness of the approach, a constrained derivative relationship was also adopted. The performance of the entire algorithm is then demonstrated through an example involving printed circuit board assemblies. The objective in the example is to maximize assembly reliability by: (1) adding redundant components to the boards and (2) optimally distributing allocated mass flow to the individual channels of the circuit boards. Number of variables in the example is then varied to investigate the effectiveness and potential of the approach for large-scale problems.
Second Order Design Sensitivity Analysis of Kinematically-Driven Mechanical Systems
Authors: Cao Qiushu , Krishnaswami Prakash
Published: March 2021

Second order design sensitivity information is required for several design applications, including second order optimization, minimum sensitivity design and reliability design. The problem of computing this information in a generalized manner becomes difficult when the dependence of system response on design is not explicitly known, as in the case of kinematic systems. This paper presents a general method for second order design sensitivity analysis of constrained mechanical systems. This method uses the constrained multi-element technique for kinematic analysis combined with a direct differentiation approach for obtaining first and second order design sensitivities of the system response. The method was implemented in a computer program on which several examples were solved. Three of the examples are presented in this papers. For each example, the second order sensitivities are checked against values obtained by finite differencing. In all cases, the agreement is seen to be very close, indicating that the proposed method is accurate and reliable.
Computation of Spatial Displacements From Redundant Geometric Features
Authors: Ge Q. J. , Ravani B.
Published: March 2021

This paper follows a previous one on the computation of spatial displacements (Ravani and Ge, 1992). The first paper dealt with the problem of computing spatial displacements from a minimum number of simple features of points, lines, planes, and their combinations. The present paper deals with the same problem using a redundant set of the simple geometric features. The problem for redundant information is formulated as a least squares problem which includes all simple features. A Clifford algebra is used to unify the handling of various feature information. An algorithm for determining the best orientation is developed which involves finding the eigenvector associated with the least eigenvalue of a 4 × 4 symmetric matrix. The best translation is found to be a rational cubic function of the best orientation. Special cases are discussed which yield the best orientation in closed form. In addition, simple algorithms are provided for automatic generation of body-fixed coordinate frames from various feature information. The results have applications in robot and world model calibration for off-line programming and computer vision.
A Solid Boundary Based Tolerance Representation Model
Authors: Liu S. , Dong Z.
Published: March 2021

An ambiguous representation of design geometry and its allowed variation is essential to design and manufacturing analysis tools using geometric modeling. In this paper, a new approach for modeling and representing mechanical tolerances, using information embedded in the solid model, is introduced. The work focuses on mathematical mapping between the nominal and variant configurations of design geometry, using boundary face-based model variables. The method identifies the relation between the errors of part geometry, represented by a solid model and measured using a coordinate measuring machine, and the tolerances, specified by dimensioning and tolerancing standards. The work is of benefit in understanding of the fundamental nature of geometric errors and tolerances; it guides the specification of dimensional and geometric tolerances; and, contributes to automated mechanical tolerancing in a solid modeling based system.
A 3-D Vision System Model for Automatic Object Surface Sensing
Authors: Theodoracatos Vassilios E. , Calkins Dale E.
Published: March 2021

The development of a “light striping” (structured light) based three-dimensional vision system for automatic surface sensing is presented. The three-dimensional world-point reconstruction process and system modeling methodology involves homogeneous coordinate transformations applied in two independent stages; the video imaging stage using three-dimensional perspective transformations, and the mechanical scanning stage, using three-dimensional affine transformations. Concatenation of the two independent matrix models leads to a robust four-by-four matrix system model. The independent treatment of the two-dimensional imaging process from the three-dimensional modeling process, has reduced the number of unknown internal and external geometrical parameters. The reconstructed sectional contours (light stripes) are automatically and in real-time registered with respect to a common world coordinate system in a format compatible with B-spline surface approximation. The reconstruction process is demonstrated by measuring the surface of a 19.5-ft long by 2 feet beam rowing shell. A detailed statistical accuracy and precision analysis shows an average error, 0.2 percent (0.002), of an object’s largest dimension within the the camera’s field-of-view. System sensitivity analysis reveals a nonlinear increase for angles between the normals of the image and laser planes higher than 45 degrees.
Boundary Surface Recovery From Skeleton Elements: Part II — Skeleton Surfaces
Authors: Gelston Sean M. , Dutta Debasish
Published: March 2021

Skeleton curves and surfaces have many applications in computer aided design and analysis and the construction of skeletons has been an active area of research. We consider the inverse problem that of recovering boundary surfaces from given skeleton elements. The skeleton of any 3D object will, in general, consist of curves and surfaces. Therefore, any boundary reconstruction algorithm must systematically process the surfaces generated by the skeletal curves and the skeletal surfaces. In a companion paper (Part I) we considered the reconstruction of boundaries corresponding to skeletal curves. In this paper (Part II) we consider the reconstruction of boundaries corresponding to skeletal elements that are surfaces. Implemented examples are also included.
Three Dimensional Robot Path Planning With Workspace Considerations
Authors: Liu C. Y. , Mayne R. W.
Published: March 2021

This paper considers the problem of robot path planning by optimization methods. It focuses on the use of recursive quadratic programming (RQP) for the optimization process and presents a formulation of the three dimensional path planning problem developed for compatibility with the RQP selling. An approach 10 distance-to-contact and interference calculations appropriate for RQP is described as well as a strategy for gradient computations which are critical to applying any efficient nonlinear programming method. Symbolic computation has been used for general six degree-of-freedom transformations of the robot links and to provide analytical derivative expressions. Example problems in path planning are presented for a simple 3-D robot. One example includes adjustments in geometry and introduces the concept of integrating 3-D path planning with geometric design.
A Computational Environment for Dextrous Workspace Analysis
Authors: Wang J. Y. , Wu J. K.
Published: March 2021

This paper presents an interactive engineering environment for dextrous workspace analysis of manipulators. The environment contains a mechanical system modeling tool, an automatic differentiation package, and numerical solvers that map one-dimensional and two-dimensional solution sets of nonlinear parametrized kinematic constraint equations. Row-rank deficiency of constraint sub-Jacobian matrices is used as a necessary condition for characterizing the boundaries of the workspaces and dextrous workspaces of manipulators. A cursor driven animation capability, developed in an interactive graphics environment allows the user to retrieve system configurations by dragging the cursor along solution branches. An animation of the assembled configuration along that solution branch is then displayed. Thus, a better understanding of the kinematic behavior of mechanical systems that limits their dexterity can be obtained. A construction backhoe mechanical system is used to demonstrate the capability of the method developed.
Minimization of the Vibration Energy of Thin-Plate Structures
Authors: Inoue Katsumi , Townsend Dennis P. , Coy John J.
Published: March 2021

An optimization method is proposed to reduce the vibration of thin-plate structures. The method is based on a finite-element shell analysis, a modal analysis, and a structural optimization method. In the finite-element analysis, a triangular shell element with 18 degrees of freedom is used. In the optimization, the overall vibration energy of the structure is adopted as the objective function, and it is minimized at the given exciting frequency by varying the thickness of the elements. The technique of modal analysis is used to derive the sensitivity of the vibration energy with respect to the design variables. The sensitivity is represented by the sensitivities of both eigenvalues and eigenvectors. The optimum value is computed by the gradient projection method and a unidimensional search procedure under the constraint condition of constant weight.

A computer code, based on the proposed method, is developed and is applied to design problems using a beam and a plate as test cases. It is confirmed that the vibration energy is reduced at the given exciting frequency. For the beam excited by a frequency slightly less than the fundamental natural frequency, the optimized shape is close to the beam of uniform strength. For the plate, the optimum shape is obtained such that the changes in thickness have the effect of adding a stiffener or a mass.
Position Kinematics of a Mixed Mechanism
Authors: Husain Muqtada , Waldron Kenneth J.
Published: March 2021

Although robotics has traditionally focused on the serial chain structures typical of industrial robots, fully parallel structures such as the Stewart Platform have also found considerable industrial use. Actively coordinated mechanisms which have combinations of serial and parallel characteristics have been practically employed, and can be expected to become more important in the future. There has been very little study of the kinematic and static characteristics of these mechanisms which have combinations of the characteristics of fully serial and fully parallel structures. This work addresses the direct and inverse position kinematics of such a hybrid mechanism with combination of serial and parallel structure which has multiple, actively controlled actuators. While not the most general possible configuration, this particular case does include many important features of the general mechanism, and the solution obtained gives useful insight for developing a general theory of forward and inverse kinematics which will be equally applicable to serial, parallel and combination structures. Such a theory is necessary for rational design of hardware and software for such systems.
Forward Position Analysis of Nearly General Stewart Platforms
Authors: Zhang Change-de , Song Shin-Min
Published: March 2021

This paper presents the closed-form solution of forward position analysis of the nearly general stewart platform, which consists of a base and a moving planar platforms connected by six extensible limbs through spherical joints in the two planar platforms. It becomes a general stewart platform if the centers are not constrained to those two planes. In this study, transformation matrix is used to represent the position of the moving platform. Based on the six dependency equations of the rotation matrix and the six constraint equations related to the six link lengths, a set of six 4-th degree equations in three unknowns are derived. Further derivations produce twenty-one dependent constraint equations. By simultaneous elimination of two unknowns a 20-th order polynomial equation in one unknown is obtained. Due to dual solutions of other unknowns, this indicates a maximum of forty possible solutions. The roots of this polynomial are solved numerically and the realistic solutions are constructed using computer graphics.
Forward Displacement Analysis of a Class of the 6-6 Stewart Platforms
Authors: Guozhen Wang
Published: March 2021

In this paper, a special form of the Stewart platform, namely, that in which the top platform and base platform are similar and corresponding vertices are connected by six prismatic joints, is presented. We have developed the closed-form solution for the forward displacement analysis of this mechanism. When the six vertices of top platform are in a quadratic curve, this mechanism becomes singular. This new theoretical result has been confirmed by numerical example.
Geometrical Properties of Modelled Robot Elasticity: Part I — Decomposition
Authors: Lipkin Harvey , Patterson Timothy
Published: March 2021

A new geometric decomposition is introduced that diagonalizes the 6 × 6 stiffness and compliance matrices which model robot elasticity. Using screw theory, a congruence transformation is developed from the three orthogonal wrench-compliant axes and the three orthogonal twist-compliant axes. The diagonal elements are the stationary values of linear and rotational compliance and stiffness. This generalizes and is analogous to principal axes and principal values for stress, strain, and rotational inertia. It is proved that the decomposition always exists for both the nonsingular and singular cases.
The Characteristic Point and the Characteristic Length of Robotic Manipulators
Authors: Tandirci Murat , Angeles Jorge , Ranjbaran Farzam
Published: March 2021

The characteristic point of a serial manipulator is defined here as a point on the end-effector, at which the condition number of the Jacobian matrix is minimized. However, when evaluating the condition number of the Jacobian matrix, dimensional inhomogeneities arise, that render the condition number physically meaningless. As a means to cope with this problem, the entries of the Jacobian that have units of length are divided by a characteristic length L that is chosen so as to minimize the condition number of the dimensionless Jacobian matrix thus resulting. Finally, the values of the joint variables minimizing the condition number of the dimensionless Jacobian lead to a naturally defined home configuration of the manipulator. The concepts introduced here are illustrated with a few examples involving industrial manipulators.
Inverse Kinematics Analysis Using the Algebra of Rotations for Flexible Link Manipulators
Authors: Xi F. , Fenton R. G.
Published: March 2021

In this paper, a numerical method is developed for the inverse kinematics analysis of flexible link manipulators. The problem of the inverse kinematics is formulated as solving the displacement equation derived using the algebra of rotation.
Geometry-Based Optimal Rate Coordination for Robot Manipulators With Redundancy
Authors: Varma K. R. Hareendra , Huang Ming Z.
Published: March 2021

The redundancy resolution problem for kinematically redundant serial chain manipulators is addressed. In this paper, we present a generalization of the geometry based rate allocation algorithm, developed initially in [12] for only minimum norm solution, to obtain the optimal joint rate solution for any specified objective function, with or without weightage. This generalization is made possible through a geometrical interpretation of the common pseudoinverse-based gradient solution scheme, and by developing a modified formulation for the objective function as a minimum criterion not with respect to the origin of the joint rate space, but with respect to another point in the joint rate space represented by the gradient of the specified objective. Application examples of the algorithm including procedures of solution are demonstrated using 7R manipulators with two generic types of geometry. A closed form optimal solution for the 7R anthropomorphic arm considered is also presented.
Die Producibility Evaluation Method
Authors: Shivaram Arun , Naganathan Nagi G.
Published: March 2021

Given the design of a sheet metal component that is to be produced by pressworking, there can be more than one design for the die to produce that component. It will be desirable if a mechanism exists to identify the better of the design alternatives. A method referred to as Die Producibility Evaluation Method (DPEM) is presented in this paper to evaluate the design of a given pressworking die. The method involves identification and classification of the parameters involved in the design and operation of the pressworking die. These parameters are categorized as design cost factors and process cost factors. For a given die design, the design and process cost factors are identified and the results are tabulated in the DPEM table. In order to illustrate the method, a particular sheet metal component is chosen. A set of dies required to produce this component is then designed by a novice designer. This design is referred to as the initial design. The Die Producibility Evaluation Method is applied to the initial design, the DPEM table is updated, and an improved design is identified based on the evaluations recorded in the DPEM table. In order to provide a measure of quality, a second design is carried out under the guidance of an expert designer and is referred to as the reference design. It is shown that the improved design closely matches the reference design, thus illustrating the level of performance and applicability of the Die Producibility Evaluation Method.
Optimal Design of a Six-Bar Linkage for an Anthropomorphic Three-Jointed Finger Mechanism
Authors: Zhang Jichuan , Guo Gongliang , Gruver William A.
Published: March 2021

We treat the design of a three-jointed, anthropomorphic, finger mechanism for prostheses and robotic end-effectors. Based on the study of configurations for the human finger, we propose a six-bar linkage with one degree of freedom for the finger mechanism. A model of the fingertip displacement of the mechanism is derived by a vector analysis approach. We study the effects of joint friction on the transmission efficiency. By measuring the joint positions of a human finger, we develop a mathematical model of the pinching and holding configurations for the human finger. Optimal parameters for the finger mechanism are obtained by nonlinear programming based on motion posture, locus, transmission efficiency, and weight subject to geometric and bionic constraints. Simulations indicate that the mechanism is useful in a variety of prosthetic and robotic devices.