bluuebunny/crossref_metadata_2025 huggingface dataset:
Tooth Contact and 3-D Stress Analysis of Involute Helical Gears
Authors: Arikan M. A. Sahir , Tamar Mustafa
Published: March 2021

An involute helical gear tooth is modelled by using helical gear geometry and a solid modelling package, and this model is used to determine the load distribution on contact lines of mating teeth, and to make the stress analysis by using three-dimensional tetrahedron finite elements with four nodes.

Tooth contact analysis is made by using the theory of gearing. Geometry of the cutting tool is used to determine the surface equations of the pinion and the gear in their own coordinate systems, then these equations are transformed to a fixed coordinate system to make the tooth contact analysis and to find the coordinates of contact points. Found contact point coordinates are then transformed back to the original coordinate systems and contact lines on helical gear teeth are formed. Results of this analysis is used to determine the application points and directions of the forces acting on the tooth. Then the stiffnesses of meshing teeth and the load distributions on contact lines are found, which are then used for stress analysis.
Optimum Design of a Gearbox for Low Vibration
Authors: Inoue Katsumi , Townsend Dennis P. , Coy John J.
Published: March 2021

A computer program was developed for designing a low vibration gearbox. The code is based on a finite element shell analysis method, a modal analysis method, and a structural optimization method. In the finite element analysis, a triangular shell element with 18 degrees-of-freedom is used. In the optimization method, the overall vibration energy of the gearbox is used as the objective function and is minimized at the exciting frequency by varying the finite element thickness. Modal analysis is used to derive the sensitivity of the vibration energy with respect to the design variable. The sensitivity is representative 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.

The computer code is applied to a design problem derived from an experimental gearbox in use at the NASA Lewis Research Center. The top plate and two side plates of the gearbox are redesigned and the contribution of each surface to the total vibration is determined. Results show that optimization of the top plate alone is effective in reducing total gearbox vibration.
An Extended Model for the Analysis of the Dynamic Behavior of Planetary Trains
Authors: Saada A. , Velex P.
Published: March 2021

An extended model for determining dynamic tooth loads on spur and helical gear planetary trains is proposed. Torsional, flexural and axial generalized displacements of all the components are considered and a finite element procedure is used for generality.

In order to avoid modulations between meshing pulsations and the carrier angular velocity, equations are written relative to rotating frames fixed to satellite centers. Depending on their architectures, complex drives are broken down in basic 12 degree of freedom elements, namely:

- external gear element (sun-satellite element)

- internal gear element (ring-satellite element)

- pin-carrier element

- classical elements for shafts, bearings, couplings, ...

Details are given for elementary stiffness matrices. Due to contact conditions between mating teeth, these matrices are full and torsional, bending and traction effects are coupled.

State equations point to parametrically excited differential systems with gyroscopic contributions. A first application of the model is conducted on a 3 satellite epicyclic drive whose gyroscopic terms are neglected. Potentially dangerous frequencies for sun-satellite and satellite-ring contacts are determined and contributions of the environment of the planetary train are discussed. Numerical results underline the influence of satellite-carrier links on critical frequencies for tooth loading.
Composite Technology in Couplings and Shafting for Power Transmission
Authors: Fromknecht Thomas G.
Published: March 2021

Composite technology is growing in the power transmission industry. Composite structures of predominately carbon fibers and epoxy resins form a matrix structure for which one use is to transmit mechanical power. Of significant importance in this paper is the use of composite structures for shafting and coupling flexible elements.

Filament wound composite shafting consists of winding a continuous band of the carbon fiber and epoxy resin matrix around a mandrel to obtain optimized end product characteristics. These optimized characteristics include: minimized weight with superior tensile strength when compared to steel, variable modulus of elasticity for critical speed requirements, virtually no thermal expansion of the composite shaft and corrosion resistance. The ability to modify the wind angles during the manufacture of the composite shaft permits the designer to achieve desirable system characteristics through variations in the composite matrix or laminate with negligible change in component cost or delivery.

Coupling flexible elements are also manufactured from carbon fiber and epoxy resin laminates. These flexible elements take advantage of the greater tensile strength of the carbon fiber versus carbon or stainless steels to achieve a superior torque capacity within a given coupling outside diameter, or greater power density with equivalent or greater misalignment capacities. The carbon fiber and epoxy resin composite coupling flexible element embodies the desirable coupling characteristics of low deflection stiffnesses resulting in low reaction forces transmitted to the connecting equipment, with minimized possibility of fretting fatigue and significant corrosion resistance.

This paper will provide an overview on the composite structure, the materials used, the filament winding process, other manufacturing processes and the application and benefits of this technology in mechanical power transmission.
Gear Case Shape and Rib Distribution for Reducing Automobile Transmission Gear Noise
Authors: Maruyama N. , Morikawa K. , Hitomi N.
Published: March 2021

This paper deals with an analysis of gear case shape and rib distribution with the aim of reducing automobile transmission gear noise. Modal analysis results and FEM calculations are presented to show that the vibration characteristics of the transmission case are basically determined by its cross section shape. A case with a cocoon section shape, composed of two curved planes, is shown to have greater plane stiffness, resulting in higher natural frequencies and a smaller number of modes in the 0–5 KHz bandwidth. It is concluded that, in order to raise the natural frequency of vibration of a plate mode, a reinforcement rib should be placed orthogonally to the bending direction at the antinode. A simplified formula for estimating natural frequencies with respect to the relationship between flat and ribbed plates is proposed.
Improvement in Surface Fatigue Life of Hardened Gears by High-Intensity Shot Peening
Authors: Townsend Dennis P.
Published: March 2021

Two groups of carburized, hardened, and ground spur gears that were manufactured from the same heat of vacuum-induction-melted vacuum-are-remelted (VIM-VAR) AISI 9310 steel were endurance tested for surface fatigue. Both groups were manufactured with a standard ground 16-rms surface finish. One group was subjected to a shot-peening intensity of 7 to 9A, and the second group was subjected to a shot-peening intensity of 15 to 17A. All gears were honed after shot peening to a surface finish of 16 rms. The gear pitch diameter was 8.89 cm (3.5 in.). Test conditions were a maximum Hertz stress of 1.71 GPa (248 ksi), a gear temperature of 350 K (170 °F), and a speed of 10 000 rpm. The lubricant used for the tests was a synthetic paraffinic oil with an additive package. The following results were obtained: The 10-percent surface fatigue (pitting) life of the high-intensity (15 to 17A) shot-peened gears was 2.15 times that of the medium-intensity (7 to 9A) shot-peened gears, the same as that calculated from measured residual stress at a depth of 127 μm (5 mil). The measured residual stress for the high-intensity-shot-peened gears was 57 percent higher than that for the medium-intensity-shot-peened gears at a depth of 127 μm (5 mil) and 540 percent higher at a depth of 51 μm (2 mil).
Effect of Operating Conditions on Gearbox Noise
Authors: Oswald Fred B. , Zakrajsed James J. , Townsend Dennis P. , Atherton William , Lin Hsiang Hsi
Published: March 2021

Low-contact-ratio spur gears were tested in the NASA gear-noise rig to study the noise radiated from the top of the gearbox. The measured sound power from the gearbox top was obtained from a near-field acoustic intensity scan taken at 63 nodes just above the surface. The sound power was measured at a matrix of 45 operating speeds and torque levels. Results are presented in the form of a spectral speed map and as plots of sound power versus torque (at constant speed) and as sound power versus speed (at constant torque). Because of the presence of vibration modes, operating speed was found to have more impact on noise generation than torque level.

A NASA gear dynamics code was used to compute the gear tooth dynamic overload at the same 45 operating conditions used for the experiment. Similar trends were found between the analytical results for dynamic tooth overload and experimental results for sound power. Dynamic analysis may be used to design high-quality gears with profile relief optimized for minimum dynamic load and noise.
Experimental Investigation of the Impact Force That Occurs When a Roller Seats on the Sprocket During Normal Operation of a Roller Chain Drive
Authors: Conwell James C. , Johnson Glen E. , Peterson S. W.
Published: March 2021

As a roller “seats” onto a sprocket, an impact force occurs between these two elements due to the relative velocity between the roller and the sprocket tooth recess. This impact force is of interest because it can be related to chain noise, vibration, wear, and other phenomena of practical concern in the performance of chain drives. The magnitude of the impact force is equal to the product of the effective mass, the relative velocity, and the reciprocal of the time associated with the impact event. Unfortunately, it is difficult to estimate the effective mass, relative velocity, and appropriate impact time in order to estimate the impact force.

In this paper we present the results from a recent experimental investigation of this impact force. The experimental procedure is described, and data are presented for a wide range of initial tensions, transmitted loads, and chain speeds. As might be expected, impact force increases rapidly with increases in chain speed. An empirical relation for impact force as a function of chain speed and chain tension is presented and general observations about the data are presented and discussed.
Development of Plastic Magnetic Gears Utilized Magnetic Characteristic
Authors: Shoji Akira , Kawashima Giichi
Published: March 2021

This paper discribes the manufacture of injection mold plastic magnetic gears. The pole of the right tooth face is difficult to that of the left tooth face in one teeth. Those gears mesh with the non-backlash. This paper is primarily to study the principles of plastic magnetic gears regarding the method of injection, mold method of magnetization and measurement of flux density and the results of a dynamic test (the noise test, wear test and measurement of temperature of plastic gears teeth) Regarding preventive gear noise, plastic magnetic gears are superior according to the results of the experiment. Those gears are used with no need for lubrication, but there is some degree of wear when a grease and oil lubrication is used. The shrink fit plastic magnetic gears were made as a non-lubricating type. Those types showed a slight degree of wear. The manufacture of plastic magnetic gears and polyamid coating plastic non-lubricating type. Those types showed a slight degree of wear. The manufacture of plastic magnetic gears (less than module:2) with the establishment of a new method for magnetic york. It was possible to provide a strong magnetic field by improving the magnetic york and this providing practical non-backlash gears.
Computer-Aided Structure Modification of Electromechancal Systems Using Singular Value Decomposition
Authors: Rai Subhendu , Asada Haruhiko
Published: March 2021

A computer-aided design method for modifying the mechanical structure of electro-mechanical systems, eg. robots and positioning systems, is presented in this paper. The pole-zero locations and other system characteristics are represented in relation to the structural geometry by using a finite element method. The inverse problem of determining a geometry which will yield better dynamic characteristics is formulated and solved. Based on sensitivity analysis and the singular value decomposition of the sensitivity matrix, useful information is provided to the designer for making effective design changes and understanding trade-offs among multiple system characteristics to be improved. This decomposition also provides us with a new type of geometric design mode-shapes that characterizes all possible design changes affecting system characteristics. The design methodology is implemented to develop a computer-aided structure modification system. A design example of a flexible robot arm demonstrates the usefulness of the system.
An Extension of Design for Assembly Methods for Large and Heavy Parts
Authors: Wong John W. , Sturges Robert H.
Published: March 2021

Traditional Design for Assembly methods are limited to part sizes between a few millimeters to a few tens of centimeters in overall size and to part weights under a few kilograms. Parts in the range of a meter in overall size and weighing a few tens of kilograms are examined in this paper. An experimental plan separates weight, mass and inertia and correlates these properties with assembly difficulty and time. When windage, part flexibility and operator fatigue are absent, a set of three parameters serve to model these effects on human assembly performance. Adaptation of this result is made to extend a Design for Assembly methodology.
The Application of Intelligence Engineering to an Optimization Software: IIO
Authors: Cha Jianzhong , Dai Zuo , Lu Peng
Published: March 2021

This paper describes an Integrated Intelligent Optimization (IIO) Software System, which has been developed based on the theory and technique of Intelligence Engineering[1]. IIO has provided an environment for a series of automatic processing on optimization models given by users, such as preprocess of mathematical models, algorithm selection, parameter adjustment, numerical process monitoring and debugging, error analysis of optimal results, sensitivity analysis, as well as contour drawing and so on. In the paper we also discuss the structure of object-oriented knowledge-base, the acguisition and representation of knowledge about algorithms, parameters and postprocessing of optimal results. The IIO has been built in C and C++ within Windows 3.0 environment, and implemented on PC/386 platform. A complete example of applying the IIO system to a real world optimization problem has been described, which has shown a great promising of the new system.
Comparison of Four Non-Derivative Optimization Methods on Two Problems Containing Heuristic and Analytic Knowledge
Authors: Borup Liana , Parkinson Alan
Published: March 2021

Hybrid engineering models — models that combine both analytic and heuristic knowledge — can address a wide range of design issues. However, models that combine these two types of information are often non-smooth and thus cannot be optimized by traditional derivative-based optimization algorithms. This paper is a study of four non-derivative optimization methods: Simulated Annealing, Genetic Algorithms, Flexible Polyhedron Search, and Function Approximation. Each algorithm was tested on two engineering problems that combine heuristic and analytic information. The algorithms were then evaluated with respect to ease of implementation, robustness, and efficiency.

Although each algorithm has advantages/disadvantages that may make it preferable for specific problems, in this study the Flexible Polyhedron Search was the best algorithm both in terms of ease of implementation and efficiency. This method found good designs in a relatively few number of design analyses. It was not, however, as robust as Simulated Annealing.
A Reduction Method for Nonhierarchichal Optimization-Based Design
Authors: Wu Bi-Chu , Azarm Shapour
Published: March 2021

Nonhierarchical decomposition-based optimization, especially when compared to the hierarchical one, has the advantage that no restriction is imposed on how the decomposed subsystems should interact with one another. However, the difficulty inherent in nonhierarchically decomposed subsystems is how to coordinate their activities so that an overall optimum design can be achieved. In this paper, a new and simple method for optimization-based design of nonhierarchically decomposed systems is presented. The driving force behind the method is to formulate and iteratively solve a reduced-size problem so that the decomposed subsystems can be coordinated. Since the size reduction measures developed in the method does not include any problem-dependent assumptions, the procedure is applicable to a wide variety of optimization problems. To illustrate the application of the method, a simple numerical and a flywheel design example are presented.
Constraint Activity Revisited: Application to Global and Discrete Design Optimization
Authors: Pomrehn Leonard P. , Papalambros Panos Y.
Published: March 2021

The concept of constraint activity, widely used throughout the optimization literature, is extended and clarified to deal with global optimization problems containing either continuous or discrete variables. The article begins by presenting definitions applicable to individual constraints, followed by definitions of groups of constraints. Concepts are reinforced through the use of examples. The definitions are used to investigate the ideas of degrees of freedom, optimization “cases,” and monotonicity analysis, as applied to global and discrete problems. Applicability to local optimization is also noted.
Design-Optimization of Machine Elements
Authors: Funk Wolfram
Published: March 2021

The incorporation of computer-aided methods in design and development requires the preparation of assessment and optimization algorithms for design purposes. With regard to generality and ease of handling, a random search procedure will be the only optimization method suitable for broad application. The multi-dimensional utility analysis, which has long been known as an assessment method for multi-dimensional systems of objectives, was employed within the framework of optimization calculations. These methods will be explained with the aid of some examples.
Runner System Balancing for Injection Molds Using Approximation Concepts and Numerical Optimization
Authors: Irani Rohinton K. , Kodiyalam Srinivas , Kazmer David O.
Published: March 2021

The goal during runner balancing is to vary the diameters of the runner segments such that all the cavities, in a multi-cavity injection mold, fill at the same time. If the runner system is unbalanced, some cavities will fill before others, begin to overpack, and result in material wastage and inconsistent part quality. Numerical optimization methods and finite element mold-filling simulation are used to solve this nonlinear discrete variable problem. Approximation concepts are used to reduce the computational effort required for solving this iterative problem. This automated system has been successfully tested on a number of family molds.
Helical Gear Design Optimization: A Random Search Methodology
Authors: Zarefar H. , Muthukrishnan S. N.
Published: March 2021

A modified random search methodology for the design of helical gears has been developed. The technique allows for the incorporation of non-linear design functions and constraints without the need for linearization. In addition, the random serarch based method is invariant to the feasibility of the initial design. Application of the proposed optimization method to the helical gear design problem have shown promisisng results. Futhermore, the methodology can be utilized in developing a robust algorithm to initiate a feasible design to be employed by other gradient-based optimization routines.
Catalog Design: Design Using Available Assets
Authors: Vadde S. , Allen J. K. , Mistree F.
Published: March 2021

Catalog design is a procedure in which a system is assembled by selecting standard components from catalogs of available components. Selection in design involves making a choice among a number of alternatives taking into account several attributes. The information available to a designer to do so during the early stages of project initiation may be uncertain. The uncertainty in information may be imprecise or stochastic. Under these circumstances, a designer has to balance limited resources against the quality of solution obtained or decisions made by accounting for uncertainty in information available. This complex task becomes formidable when dealing with coupled selection problems, that is problems that should be solved simultaneously. Coupled selection problems share a number of coupling attributes among them. In an earlier paper we have shown how selection problems, both coupled and uncoupled can be reformulated as a single compromise Decision Support Problem (DSP) using a deterministic model. In this paper, we show how the traditional compromise DSP can be extended to represent a nondeterministic case. We use fuzzy set theory to model imprecision and Bayesian statistics to model stochastic information. Formulations that can be solved with the same solution scheme are presented to handle both fuzzy and stochastic information in the standard framework of a compromise DSP. The approaches are illustrated by an example involving the coupled selection of a heat exchanger concept and a cooling fluid for a specific application. The emphasis in this paper is placed on explaining the methods.
Application of Expert System for a Compound Gear Train Design
Authors: Yang Saiwei , Yu Kenny
Published: March 2021

A program, written in Turbo-Prolog, was developed to provide a quick and accurate design tool for a compound gear train. The program was based on the expert system methods of backward chaining/ depth first for solution search, fuzzy logic for uncertainty and solution priority, blackboard for opportunistic control of the pc memory space.

After initial input of needed information, the system will advise the user some of default design parameters such as the gear module, tooth number, safety factor., et al., by a friendly interactive explanatory facility. The program will then select a suitable material based on the design criteria-bending stress, wearing stress, and material fatigue strength. An optimal solution is then suggested based on the desired design constraints. This package can be used in either an English or a Chinese operating environment.

Three examples: lathe gearbox, helical gear set, five speed transmission were illustrated and validated. The program performed the same or compatible solutions to the recommended data in the examples.
Kinematic Synthesis of Ordinary and Epicyclic Gear Trains for a Prescribed Velocity Ratio
Authors: Pennestrì Ettore
Published: March 2021

This paper presents a new computer algorithm for the systematic kinematic design of ordinary and four-gear epicyclic gear trains. The main features of the algorithm are simplicity and compactness. The paper discusses various analytical techniques for approximating a rational number by a fraction. Several numerical examples have been developed with the purpose of comparison with other techniques.
manuFeature: A Framework for Recognizing CAD Interactions in Design-for-Manufacturing Analysis
Authors: Gadh Rajit , Prinz Fritz B.
Published: March 2021

The current paper discusses a fundamentally new approach to defining and finding interactions in computer-aided design (CAD) forms or features. The paper provides a classification of the various interactions found among CAD forms. The paper also illustrates a robust approach to defining and recognizing stand-alone as well as interacting forms. The problem of generic form definition is resolved using a set of high-level abstract entities called loops and links. The computational difficulty in finding the forms is resolved using a mathematically defined geometric filter called the Differential Depth Filter.
Incorporating Geometrical Tolerances and Processing Inaccuracy Into Dimensioning and Tolerancing
Authors: Porchet Michel , Zhang Genbao
Published: March 2021

The geometrical tolerances and the processing inaccuracy have a great influence on dimensioning and tolerancing. However, it is quite difficult to integrate them into dimensioning and tolerancing. This paper presents a way in which geometrical tolerances and process inaccuracy can be taken into consideration. The distance between two surfaces is defined clearly. The relationship between distance tolerances, form errors and position errors is established. Different sources influencing a distance precision have been investigated. A model where geometrical tolerances and processing inaccuracy can be dealt with is proposed. This model closely approaches practice.
Using Error Diffusion With Ordered Dither Matrix Method in Displaying Shaded Graphics
Authors: Her I.
Published: March 2021

The error diffusion method and the ordered dither matrix method are the most frequently used techniques for displaying shaded graphics on bi-level devices. The error diffusion method generates images with a smooth intensity variation appearance while the ordered dither matrix method generates images composed of constant intensity areas. This paper is concerned with the use of the two methods together. It is found that the resulting images have a greater contrast than that of the input image.
Robust Fatigue Design for Combined Bending and Steady Torsion
Authors: Eggert Rudolph J.
Published: March 2021

The fatigue design of elements experiencing combined cyclic bending and steady torsion is presented. Von-Mises stresses are compared to strengths predicted by the ASME Elliptic and Langer failure relations. Propagation of variations due to materials, manufacturing, and usage is discussed. Stochastic fatigue design using random variable algebra and simulation is presented along with an illustrative transmission shaft example.
Chaotic Behavior of a Two Mass Bouncing System
Authors: Lee Chi-Wook , Seireg Ali , Duffy Joseph
Published: March 2021

This study investigates the behavior of simple two mass bouncing systems which are released from a certain height. A nonlinearity exists in the discontinuity of the flight and the ground modes, although the behavior of the systems is linear in each mode. Such oscillators provide models for mechanical systems such as legged systems for hopping robots. The phase plane technique and the power spectrum analysis are used to investigate the stability of bouncing systems and the chaos that may occur. The effects of the spring constants and the damping coefficient at the ground contact on the bouncing behavior is also investigated.
Tilt-Wing Rotorcraft Dynamic Analysis Using Multibody Formulation
Authors: O’Heron Patrick J. , Nikravesh Parviz E. , Arabyan Ara , Kunz Donald L.
Published: March 2021

A model is presented that can be used to simulate the highly nonlinear transient dynamics associated with advanced rotorcraft conversion processes. Multibody equations of motion of the fuselage, the tilting wing, and the rotor assembly are derived using a minimal set of coordinates. An enhanced aerodynamics model is employed to account for unsteadiness and nonlinearity in the near-wake aerodynamics, with a dynamic uniform inflow to compute the far-wake aerodynamics, and a flight control system is employed to compute the blade pitch settings that are necessary to achieve a desired flight path. The model is subjected to a demanding flight path simulation to illustrate that it can perform vertical take-off, hover, tilt-wing conversion, and high-speed forward flight maneuvers effectively.
The Kinematic Control Equations of a Singularity Free Six Degree of Freedom Manipulator
Authors: Di Caprio F. , Stanišić M. M.
Published: March 2021

In this paper, one symmetrically actuated double pointing system is used in the shoulder subassembly, and another is used in the wrist subassembly of a six degree-of-freedom manipulator. In a previous paper, this manipulator was shown to be free of singularities. In this paper, the position control equations are derived.
A Class of Hybrid-Chain Manipulators Based on Kinematically Simple Branches
Authors: Podhorodeski Ron P. , Pittens Kenneth H.
Published: March 2021

Hybrid-chain manipulators consisting of serial branches acting in parallel on a common end effector are examined. All non-redundant, six DOF hybrid manipulator structures are enumerated and a specific hybrid-chain structure is chosen as most promising based upon performance considerations. A class of kinematically simple (KS) serial-chain branches suitable for the chosen hybrid structure is defined. Arguments based upon kinematic equivalency of the branches and mobility of the assembled hybrid chain are used to show that there exist only five unique branch structures belonging to the KS class. It is demonstrated that the solution to the inverse displacement problem for hybrid structures based on the KS branches can be expressed in a closed form. Furthermore, the KS based hybrid-chains are shown to belong to a family of manipulator structures whose forward displacement solutions can be resolved through roots of a 16th order polynomial.
Solution of the Direct Position Kinematics Problem of the General Stewart Platform Using Advanced Polynomial Continuation
Authors: Sreenivasan S. V. , Nanua Prabjot
Published: March 2021

In this paper the direct position kinematics problem of the most general geometry of the Stewart platform has been solved numerically. It is found that this problem has exactly 40 distinct, finite solutions. No closed form solutions are available for this problem. This problem was addressed for the first time by Raghavan recently, and the results obtained here are in agreement with the ones obtained by Raghavan. The formulation and the variable set used in this work lead to a simpler polynomial system of lower overall degree. Further, the geometric parameters of the general Stewart platform have been used to generate a ‘near-general’ Stewart platform. Even though the near-general Stewart platform also has exactly 40 finite, distinct, configurations, it is represented by much simpler polynomial equations. The polynomial system obtained from this near-general Stewart platform is used as the start system in an advanced polynomial continuation scheme to solve the general Stewart problem. This process eliminates a large number of solutions at infinity that have no geometric significance. This leads to an efficient numerical algorithm that is about twenty times faster than traditional continuation schemes.
A Divide-and-Conquer Method for Planning Collision Free Paths for Cooperating Robots
Authors: Weaver Jonathan M. , Derby Stephen J.
Published: March 2021

This paper presents a method for autonomously planning collision free paths for two cooperating robots in a static environment. Cooperating robots simultaneously grasp and manipulate a single object. Our method utilizes a divide-and-couquer type of heuristic and involves non-exhaustive mapping of configuration space. The method is applicable to all manipulators having any number of links and is suitable for path planning of single as well as cooperating robots. While there is no guarantee of finding a solution, the algorithm has been successfully applied to a variety of problems including two cooperating nine dof arms. Sample results are included.
Inverse Kinematic Solutions of a Rolling Disk Between Two Planar Manipulators
Authors: Agrawal Sunil Kumar , Pandravada R.
Published: March 2021

This paper describes the inverse kinematic solutions of a disk rolling between two planar manipulators. The problem, in essence, is to compute the joint angles of the manipulator links given the position and orientation of the rolling disk. An algebraic technique is used to find out the inverse solutions of the manipulator links and the maximum possible number of these solutions for a given position and orientation of the rolling disk. This problem is worthy of presentation due to the following reasons: (1) the inverse solutions are obtained after including the constraints of rolling between the disk and the manipulators, (2) the upper bound on the number of inverse solutions with rolling constraints is much higher than that demonstrated for structurally similar closed-chain manipulators without rolling, (3) the joint solutions are a function of the initial assembly configuration of the mechanism, (4) these solutions have potential use in the development of path-planning algorithms for planar manipulators with rolling constraints. From our study, we conclude that a disk manipulated by two planar 2R robots has a maximum of 24 feasible sets of joint angles for a given position and orientation of the disk.
Kinematic Analysis and Design of Articulated Manipulators With Joint Motion Constraints
Authors: Dwarakanath T. A. , Ghosal A. , Shrinivasa U.
Published: March 2021

This paper deals with kinematic analysis and design of articulated manipulators having constraints on joint motions. For an articulated manipulator with joint rotation constraints, the workspace is composed of several bounding surfaces and the number of bounding surfaces depend on the ranges and the mean positions of joint rotations. We show that the maximum workspace is not necessarily obtained for equal link lengths but is also determined by the range and mean positions of the joint motions. We present expressions for sectional area, workspace volume, overlap volume and work area in terms of link ratios, mean positions and ranges of joint motion.

To ensure maximum utilization of a manipulator in applications such as painting and welding, instead of the total workspace, it is often of more interest to obtain the maximum regular area or volume that can be embedded inside the workspace. In this paper, we present a numerical procedure to obtain the maximum rectangular area that can be embedded in the workspace of an articulated manipulator with joint rotation constraints.

The analytical expressions and the numerical plots are used for the kinematic design of an articulated manipulators with joint rotation constraints.
The Pole Curve Generated by Infinite Poles
Authors: Brady Michael H. , Peterson Steven W.
Published: March 2021

In this paper, a general expression for the pole curve equation was derived in the projective plane is applied to opposite-pole quadrilaterals that contain one or more infinite poles. Such infinite poles arise in four-position synthesis when a lamina moves from one position to another in pure translation. Classical derivations of the pole curve equation are not valid when a pole is infinite because these derivations depend upon distances between poles. However, this projective approach relies only upon the homogeneous coordinates of the poles. As infinite poles have finite coordinates in the projective plane, this derivation readily accommodates infinite poles.
Burmester-Theory for Band-Mechanisms
Authors: Luck Kurt , Modler Karl-Heinz
Published: March 2021

A band-mechanism includes inter alia a flexible band and a disk-profile. Such a mechanism can excellent be used for path-generation, better than a four-bar-linkage. Also several plane-positions additionally can be realized. This paper investigates the synthesis of four-bar-band-mechanisms by using the complex vector-algebra. Several technical tasks demonstrate the flexible application of such mechanisms. This tasks are formulated analogous to the wellknown BURMESTER-THEORY, but with higher claims and the solution is done by analytical methods. Further it is demonstrated that a four-bar-linkage is a special case of a four-bar-band-mechanism.
Software for Optimum Gear Design (DISENG)
Authors: Jáuregui Juan Carlos , Sansalvador Rodrigo López , Aparicio Alfredo Ramos , Contreras Isaías Regalado
Published: March 2021

In this paper, a specialized software for optimum gear design is presented. This optimum is found through a logical solution search algorithm, rather than general optimization techniques. The logical search is based upon the constraints and needs set by the user, who defines the solution space and the search trajectory. For each problem, the solution will be the less expensive according to specific constraints. Calculation routines were based on AGMA standards, and input data routines were conceived to be as helpful as possible. A complete help routine is included on each part of the software and every input data is foolproof. It also includes a routine for intermediate results analysis that allows the user to verify every iteration.
Torque Resolver Design for Tendon-Driven Manipulators
Authors: Lee Jyh-Jone , Tsai Lung-Wen
Published: March 2021

Given a set of desired joint torques in an n-DOF tendon-driven manipulator with n + 1 control tendons, the determination of tendon forces is an indeterminate problem. Usually, the pseudo-inverse technique is used to solve for such a problem. In this paper, rather than using the pseudo-inverse technique, an efficient methodology for transforming joint torques (n elements) to motor torques (n + 1 elements) has been developed. This technique, called “torque resolver”, utilizes two circuit-like operators to transform torques between the two different vector spaces. It can be easily programmed on a digital computer or implemented into an analog-circuit system. It is hoped that this technique will make real-time computed-torque control feasible. The technique has been demonstrated through the dynamic simulation of a three-DOF manipulator.
Position-Force Synthesis of Closed-Loop Linkages
Authors: Huang Chintien , Roth Bernard
Published: March 2021

The dimensional synthesis of spatial closed-loop linkages to match both force and position specifications is investigated. An efficient means of formulating force equations is introduced through the application of linear algebra to screw theory. The synthesis of spatial four-bar linkages is discussed in detail; it is shown that the maximum number of allowable design positions is not decreased after force constraints are imposed on classical position synthesis problems.
Directional Probabilistic Design of Three-Coupler-Point Four-Bar Mechanisms
Authors: Schade George R. , Korbel Douglas R. , Shanmugam Deena D.
Published: March 2021

A standard four-bar coupler-point position synthesis technique is augmented with a probabilistic model of randomness coupler-point position caused by production variations in link dimension. The synthesis is optimized to reduce the variations in a chosen direction. The probabilistic optimum is verified by Monte-Carlo test.
Computer Aided Design and Analysis of the Rack and Pinion Mechanism
Authors: Srinivas D. , Kramer Steven N.
Published: March 2021

The general procedure for synthesizing the rack and pinion mechanism for six precision conditions is developed. To illustrate the method, the mechanism has been synthesized in closed form for generating both four prescribed path points with input coordination and two positions of function generation. This is the extension of the work reported earlier on this mechanism where only three path precision points were satisfied. The rack and pinion mechanism has a number of advantages over the conventional four bar linkage mechanism. First, since the rack is always tangent to the pinion, the transmission angle has a constant optimum value of 90 degrees minus the pressure angle of the pinion. Second, because both translation and rotation of the rack are possible, multiple outputs are available. Generation of monotonic functions for a wide variety of motion, and nonmonotonic functions for the full range of motion as well as nonlinear motions, are other advantages of this mechanism. The rack and pinion mechanism has applications in the packaging industry, in toys, and automotive steering mechanisms. In this work, the mechanism is made to satisfy a number of practical design constraints such as a completely rotatable input crank and others. Also, structural errors for function generation are calculated to give an estimate of the accuracy of the mechanism. The method of solution developed in this work uses the complex number method of mechanism synthesis and a FORTRAN program is written to find the solutions for any input.
Complete Solutions to Synthesis of Six-Link, Slider-Crank and Four-Link Mechanisms for Function, Path and Motion Generation Using Homotopy With M-Homogenization
Authors: Dhingra Anoop K. , Cheng Jyun-Cheng , Kohli Dilip
Published: March 2021

This paper presents complete solutions to the function, motion and path generation problems of Watt’s and Stephenson six-link, slider-crank and four-link mechanisms using homotopy methods with m-homogenization. It is shown that using the matrix method for synthesis, applying m-homogeneous group theory, and by defining compatibility equations in addition to the synthesis equations, the number of homotopy paths to be tracked can be drastically reduced. For Watt’s six-link function generators with 6 thru 11 precision positions, the number of homotopy paths to be tracked in obtaining all possible solutions range from 640 to 55,050,240. For Stephenson-II and -III mechanisms these numbers vary from 640 to 412,876,800. For 6, 7 and 8 point slider-crank path generation problems, the number of paths to be tracked are 320, 3840 and 17,920, respectively, whereas for four-link path generators with 6 thru 8 positions these numbers range from 640 to 71,680. It is also shown that for body guidance problems of slider-crank and four-link mechanisms, the number of homotopy paths to be tracked is exactly same as the maximum number of possible solutions given by the Burmester-Ball theories. Numerical results of synthesis of slider-crank path generators for 8 precision positions and six-link Watt and Stephenson-III function generators for 9 prescribed positions are also presented.
An Application of Generalized Kinematic Chains to the Structural Synthesis of Nonfractionated Epicyclic Gear Trains
Authors: Hsu Cheng-Ho
Published: March 2021

This paper presents a systematic approach, which is based on the concept of generalization for the structural synthesis of geared kinematic chains for epicyclic gear trains with any number of degrees of freedom. First, the fundamental rules of generalized kinematic chains for nonfractionated epicyclic gear trains are investigated. Next, according to the numbers of gear pairs and degrees of freedom, acceptable kinematic chains for nonfractionated epicyclic gear trains are identified from an atlas of basic kinematic chains. Then, each acceptable kinematic chain is specialized to be epicyclic gear trains. Finally, geared kinematic chains for nonfractionated epicyclic gear trains with up to three degrees of freedom and four gear pairs have been susscessfully constructed.
A Proposed Method to Group the Solutions From Dimensional Synthesis: Planar Triads for Six Precision Position
Authors: Lu Xiancheng , Lin Chuen-Sen
Published: March 2021

In this paper, a method has been proposed to group into six sets the infinite number of solutions from dimensional synthesis of planar triads for six precision positions. The proposed method reveals the relationships between the different configurations of the compatibility linkage and the sets of numerical solutions from dimensional synthesis. By checking the determinant signs and the contunities of values of the sub-Jacobian matrices and their derivatives with respect to the independent angular displacement for all constraint sets in the compatibility linkage, it enables the computer to identify and group the synthesized solutions.

Numerical examples have been given to verify the applicability of this method. Six sets of the partial triad Burmester curves have been plotted based on grouped solutions. Suitable solutions can be easily found from the partial triad Burmester curves and utilized for the prescribed design task. This method provides a useful tool to group the dimensional synthesis solutions and enhances the computer automation in the design of linkage mechanisms.
Four-Position Synthesis for Spatial Mechanisms With Two Independent Loops
Authors: Chiang Chien H. , Chieng Wei Hua , Hoeltzel David A.
Published: March 2021

Mathematical models that have been employed to synthesize spatial mechanisms for rigid body guidance have been found to be too complicated to implement in practical applications, especially for four-position guidance synthesis. This paper describes simple analytical methods for synthesizing single degree-of-freedom spatial mechanisms having two independent loops for four precision positions. In addition, prescribed timing has been simultaneously considered for several spatial mechanisms.
Tool Path Geometry for Multi-Axis Kinematics Conversion in CAD-CAM Integration
Authors: Chou Jui-Jen , Yang D. C. H.
Published: March 2021

In the integration of CAD and CAM, it is necessary to relate machine tool kinematics and control in a CAM process to the geometrical data in a CAD model. The data stored in a CAD model is usually static in nature and represented by unitless parameters. Yet, in machine tool motion and control, the data should be transformed into a time dependent domain. In this paper, a general theory on the conversion from desired paths to motion trajectory is analytically derived. The geometrical properties of a desired path, including position, tangent, and curvature are related to the kinematics of coordinated motion including feedrate, acceleration, and jerk. As a result, the motion commands used as control references to track arbitrary space curves for five-axis computer-controlled machines can be generated in a rather straight-forward as well as systematic way.
Automatic Generation of Piecewise Constant Speed Motion for Multi-Axis Machines
Authors: Yang D. C. H. , Chou Jui-Jen
Published: March 2021

This paper presents a general theory on the generation of smooth motion profiles for the coordinated motion of multi-axis manipulators with orthogonal regional structures. Motion with constant speed is important and required in many manufacturing processes, such as milling, welding, finishing and painting. In this paper, a piecewise constant speed profile is constructed by a sequence of Hermite cuves to form a composite Hermite curve in parametric domain. Due to the continuity of acceleration in the proposed speed profile, it generates relatively better product quality than traditional techniques. Besides, we also provide a method for the feasibility study of manufacture capability in terms of the given manipulator, the desired path, and the assigned speed. This includes the consideration of manipulator dynamics, actuator limitation, path geometry, jerk constraints and motion kinematics. The result is a general one and is applicable to all curves tracked by multi-axis manipulators with orthogonal regional structures.