bluuebunny/crossref_metadata_2025_split huggingface dataset:
A Procedure Using Manufacturing Variance to Design Gears With Minimum Transmission Error
Authors: Sundaresan S. , Ishii K. , Houser D. R. 
Published: April 2021

Abstract
This paper deals with the design of spur gears that have minimum transmission error and are insensitive to manufacturing variance. We address two stages of design: 1) generation of candidate designs (selection of number of teeth, pressure angle, etc.), and 2) tooth profile modification. The first stage involves a search of discrete combinations of design variables, while the second stage utilizes numerical optimization techniques. The key research issue is finding a candidate design and its profile modification that not only has low transmission error, but is insensitive to variations in the design values caused by the manufacturing process. To achieve this goal, the procedure applies Taguchi’s concept of parameter design. In this paper, we consider a design problem with a set specification: fixed center distance, speed ratio, and transmission torque. We seek to find a limited number of candidate designs by applying conventional design generation techniques and some design heuristics. For each candidate design, the procedure determines the optimum profile modification (linear tip relief) by linking the Load Distribution Program (LDP) for gears with an optimization program package (OPTPAK). From the resulting peak optimum, we further seek the statistical optimum using an algorithm developed in this paper. The statistical optimum shows a nominal increase in the transmission error, but is quite insensitive to typical process error associated with gear manufacturing. The developed algorithm readily applies to other gear designs as well as other types of machine elements. In particular, we foresee our procedure to be particularly effective for helical gears. We hope to further our method by developing a means to add statistical heuristics to the discrete design generation stage.
Determination of the Allowable Manipulator Link Shapes; and Task, Installation, and Obstacle Spaces Using the Monte Carlo Method
Authors: Rastegar J. , Tu Q. 
Published: April 2021

Abstract
The Monte Carlo method is used to solve a number of problems in manipulator link shape design, and in task space and obstacle placement. The shape of links of manipulators that are to operate within geometrically specified enclosures are determined. Within the enclosure, one or several obstacles may be present. The end effector operates within the task space, and may be required to reach points in different regions with different orientations. For a specified operating environment (enclosure geometry and obstacles), the spaces within which a given manipulator may be installed in order to perform the required tasks are identified. For a given enclosure, task space, and position of the fixed joint of the manipulator, regions within which obstacles may be placed are mapped. The developed methods are very simple, numeric in nature, and readily implemented on computer. Several examples are presented.
A Constrained Variational Method for Two-Dimensional Shape Optimization
Authors: West R. L. , Sandgren E. 
Published: April 2021

Abstract
A constrained variational method is presented for the formulation and solution of a class of two-dimensional continuous shape optimization problems with equality constraints. Conceptually, the method casts the shape optimization problem as an analogous application of the principle of virtual work. It is postulated that the optimal shape is that equilibrium shape distinguished by the stationary value of the systems “effective” virtual work. The resulting formulation leads to a direct variational statement of the shape optimization problem, yielding the optimality criteria consisting of the Euler-Lagrange equations, constraints and boundary conditions. The Euler-Lagrange equations are linearized about the current shape and transformed into a set of Poisson’s equations. A direct boundary integral formulation is developed for the solution of Poisson’s equation that results in a continuous expression for the shape in terms of the Lagrange multipliers. The numerical solution procedure involves discretizing the shape into boundary and domain elements and using the direct boundary element method and the linearized constraint set to form a set of matrix equations. The solution to the set of matrix equations yields new estimates of the shape and the Lagrange multipliers. Convergence of the method is achieved when successive iterations of the shape and Lagrange multiplier estimates fail to improve by some prescribed limit. The classical problem of finding the curve with minimum perimeter and a prescribed enclosed area is used to illustrate the method.
Modeling and Analysis of a Manipulator Joint Driven Through a Worm Gear Transmission
Authors: Mooring B. W. , May D. C. , Schulte M. S. 
Published: April 2021

Abstract
Worm gear transmissions are capable of high velocity ratios as well as redirection of rotation. Both of these features are desirable for some robot geometries. A problem has been encountered in several robot designs, however, where a self excited vibration occurs for some configurations of the manipulator in the joint containing the worm gear. In this work, a system which exhibits this type of undesirable motion is examined. The system consists of a DC servo motor which is used to position a flexible cantilever arm through a worm gear transmission. A nonlinear model is developed to describe the motion of the system. The model is then validated by comparing the predicted response to the observed response of an experimental system. It is demonstrated that the model accurately predicts the onset of the unstable vibration. The model is then linearized and it is shown that the linear model will predict the occurrence of the instability as well.
Transient Torque Produced in Arm Shaft of an Industrial Sewing Machine
Authors: Muramatsu N. 
Published: April 2021

Abstract
This study considered the effects of needle penetrating force, needle thread tightening tension, and pressing force of the presser foot on torque produced in the arm shaft of an industrial sewing machine. The results obtained are as follows.
(1) Penetrating force, especially the initial triangular wave fluctuation, induces noticeable transient vibration in torque.
(2) The torsional natural frequency of the arm shaft of the feed mechanism motion system is more than twice that of the thread take-up lever and needle bar mechanism motion system. Penetrating force, according to the relations with the natural period of the system, is considerably more transient than pressing force.
(3) Consequently, when estimating torque, it is necessary that the arm shaft of the thread take-up lever and needle bar mechanism motion system be considered as elastic. On the other hand, the arm shaft of the feed mechanism motion system can be treated as a rigid body.
Three-Dimensional Dynamic Simulation of Helical Compression Springs
Authors: Lin Y. , Pisano A. P. 
Published: April 2021

Abstract
The dynamic equations for general helical springs are solved and classified according to the number of energy terms used to formulate them. Solutions of several sets of dynamic equations, each with a different number of energy terms, are compared with experimental data. It is found that at higher compression speeds the numerical solution with a traditional, fixed boundary represents a physically impossible situation. A moving boundary technique is applied to improve the numerical solution and bring it into agreement with physical reality. Since a convergence proof for a numerical algorithm for nonlinear partial differential equations with a moving boundary is not available, a grid study has been performed to demonstrate convergence. The agreement between the solutions of different grid sizes and the experimental data is taken to show that the numerical algorithm was convergent. This three dimensional spring simulation model can be used in the simulation of high-speed mechanical machinery utilizing helical springs, and in particular, for design optimization of automotive valve springs.
Solution of Multibody Dynamics Using Natural Factors and Iterative Refinement: Part I — Open Kinematic Loops
Authors: Wehage R. A. 
Published: April 2021

Abstract
An O(n) methodology employing block matrix partitioning and recursive projection to solve multibody equations of motion coupled by a sparse connectivity matrix was developed in (Wehage 1988, 1989, Wehage and Shabana, 1989). These primitive equations, which include all joint generalized and absolute coordinates and constraint reaction forces, are easily obtained from free body diagrams. The corresponding recursive algorithms isolate the generalized joint accelerations for numerical integration and offer the best computational advantage when solving long kinematic chains on serial processors. Recursion, however, precludes effective exploitation of vector or parallel processors. Therefore this paper explores less recursive algorithms by applying the inverse of joint connectivity to eliminate absolute accelerations and constraint forces yielding a generalized system of equations. The resulting positive definite generalized inertia matrix is first represented symbolically as a product of sparse matrices, of which some are singular and then as the product of nonsingular factors obtained recursively. This algorithm has overhead ranging from O(n2) to O(n) depending on the degree of system parallelism. Incorporating iterative refinement and exploiting parallel and vector processing makes this approach competitive for many applications.
Mechanical States in Wound Capacitors: Part II — Optimization
Authors: Allen J. J. , Reuter R. C. 
Published: April 2021

Abstract
The winding process is encountered frequently in manufacturing, such as winding of polymer films and paper, laminated pressure vessel construction, and the manufacture of wound capacitors. The winding of capacitors will typically involve hundreds of plies of conductor and dielectric wound over a core. Due to the large number of layers, the calculation of the mechanical states within a wound capacitor is a significant computational task. Part I of this paper discussed methods for the calculation of the mechanical states within wound capacitor.
The focus of Part II of this paper is the formulation and application of optimization techniques for the design of wound capacitors. The design criteria to be achieved is a specified uniform wound tension in a capacitor. The paper will formulate an optimization statement of the wound capacitor design problem, develop a technique for reducing the numerical calculation required to repeatedly analyze the capacitor which is required by the optimization algorithm, and apply the technique to an example. The following effects will be investigated using the example.
1. The ability of low order winding tension profiles, such as constant, linear, or bilinear profiles, to meet the optimization objective.
2. The usefulness and practicality of high order winding tension profiles, which require a significant number of design variables to meet the optimization objective.
3. Differential weighting of the aluminum and mylar layer wound tensions in the objective function will be investigated as a technique for achieving the optimization/design goal.
Design of the Ball Screw Mechanism for Optimal Efficiency
Authors: Lin M.-C. , Velinsky S. A. , Ravani B. 
Published: April 2021

Abstract
This paper develops theories for evaluating the efficiency of the ball screw mechanism and additionally, for designing this mechanism. Initially, a quasi-static analysis, which is similar to that of the early work in this area, is employed to evaluate efficiency. Dynamic forces, which are neglected by the quasi-static analysis, will have an effect on efficiency. Thus, an exact theory based on the simultaneous solution of both the Newton-Euler equations of motion and the relevant kinematic equations is employed to determine mechanism efficiency, as well as the steady-state motion of all components within the ball screw. However, the development of design methods based on this exact theory is difficult due to the extensive computation necessary and thus, an approximate closed-form representation, that still accounts for the ball screw dynamics, is derived. The validity of this closed-form solution is proven and it is then used in developing an optimum design methodology for the ball screw mechanism based on efficiency. Additionally, the self-braking condition is examined, as are load capacity considerations.
Cyclic Symmetric Analysis of Fabricated Gear Wheels
Authors: Ramamurti V. , Subramaniam M. , Shanker B. 
Published: April 2021

Abstract
A computer aided method of analysis of the web portion of a spur gear is presented. The cyclic symmetric concept is used for solving the problem of the steady state stress analysis (asymmetric loading) when the gear is subjected to a concentrated edge load due to the mating tooth. The effect of cut-outs in the web is studied. The response of the web to a moving load is investigated. The ratio of the forcing frequency to the fundamental frequency of the gear wheel being small, the moving load is approximated as a static load acting at different points. The influence of radial ribs on the behaviour of the gear is also studied.
Curvature Constraints in the Design of Cam Mechanisms: Part I — Translating Flat-Face Followers
Authors: Angeles J. , Lopez-Cajun C. S. , Saha S. K. 
Published: April 2021

Abstract
The optimization of cam mechanisms with translating flat-face followers, upon consideration of curvature constraints, is discussed here. In fact, when minimizing the size of the cam disk, cam profiles with cusps arising from discontinuities in the curvature of the profile, can appear. On the other hand, cusps are undesirable because they give rise to inadmissibly large contact stresses and hence, should be prevented from occurring. Conditions under which these discontinuities appear, although available in the literature, are not readily applicable, for they are highly problem-dependent. However, if both the follower-displacement program and the profile are determined based on the normal spline, a design tool introduced elsewhere, then readily applicable design formulae, leading to unconstrained optimum designs, are derived. As well, design charts are derived, which produce the cusp-free, minimum-size profile for a given displacement program. The same problem for oscillating flat-face followers is addressed in an accompanying paper.
Curvature Constraints in the Design Optimization of Cam Mechanisms: Part II — Oscillating Flat-Face Followers
Authors: Angeles J. , Saha S. K. , Lopez-Cajun C. S. 
Published: April 2021

Abstract
This paper follows an accompanying one on the constrained minimization of cam profiles with translating flat-face followers. Here, the corresponding problem for oscillating flat-face followers is addressed. The unconstrained optimization of this type of cam mechanisms, aimed at the minimization of the area of the cam disk, has been reported elsewhere. In this paper we recognize that unconstrained cam-size minimization can lead to profiles with curvature discontinuities, i.e.. cusps, which should be eliminated, for they give rise to inadmissibly large contact stresses. The conditions under which curvature discontinuities arise are derived. These conditions lead to a simple constrained minimization procedure, whose application is illustrated with a fully solved numerical example.
Modeling, Simulation, and Modal Analysis Hydraulic Valve Lifter With Oil Compressibility Effects
Authors: Hatch T. , Pisano A. P. 
Published: April 2021

Abstract
A two-degree-of-freedom (2-DOF), analytical model of a hydraulic valve lifter is derived. Special features of the model include the effects of bulk oil compressibility, multi-mode behavior due to plunger check valve modeling, and provision for the inclusion of third and fourth body displacements to aid In the use of the model in extended, multi-DOF systems. It is shown that motion of the lifter plunger and body must satisfy a coupled system of third-order, non-linear differential equations of motion. It is also shown that the special cases of zero oil compressibility and/or 1-DOF motion of lifter plunger can be obtained from the general third-order equations. For the case of zero oil compressibility, using Newtonian fluid assumptions, the equations of motion are shown to reduce to a system of second-order, linear differential equations. The differential equations are numerically integrated in five scenarios designed to test various aspects of the model. A modal analysis of the 2-DOF, compressible model with an external contact spring is performed and is shown to be in excellent agreement with simulation results.
Optimization of Dynamic Forces in the Design of Mechanical Hands
Authors: Nahon M. A. , Angeles J. 
Published: April 2021

Abstract
Mechanical hands have become of greater interest in robotics due to the advantages they offer over conventional grippers in tasks requiring dextrous manipulation. However, mechanical hands also tend to be more complex in construction and require more sophisticated design analysis to determine the forces in the system. A mechanical hand can be described as a kinematic chain with time-varying topology which becomes redundantly actuated when an object is grasped. When this occurs, care must be exercised to avoid crushing the object or generating excessive forces within the mechanism. In the present work, this problem is formulated as a constrained quadratic optimization problem. The forces to be minimized form the objective, the dynamic equations of motion form the equality constraints and the finger-object contacts yield the inequality constraints. The quadratic-programming approach is shown to be advantageous due to its ability to minimize ‘internal forces’ A technique is proposed for smoothing the discontinuities in the force solution which occur when the toplogy changes.
A New Probabilistic Method for the Performance Evaluation of Manipulators: Part II — Application to Task Placement
Authors: Rastegar J. , Singh J. R. 
Published: April 2021

Abstract
A probabilistic method for optimal placement of a prescribed task space in the workspace of a robotic manipulator is presented. Velocity and force transmission (alone and in combination) are used as optimality criteria. Complex task space and manipulator workspace geometries are readily handled. The distribution of the tasks within the task space, and the velocity and force transmission requirements may assume any arbitrary form. The method is extremely simple, does not require inverse calculations, is numerical in nature, and is readily implemented on computers. In many cases, the best location of the task space within the manipulator workspace can be visually ascertained. Minimal analytical formulations are required. Several examples are presented.
The Optimum Design of a 6 DOF Fully-Parallel Micromanipulator for Enhanced Robot Accuracy
Authors: Han C.-S. , Tesar D. , Traver A. E. 
Published: April 2021

Abstract
The micromanipulator is a small amplitude, high resolution motion device to enhance robot accuracy by providing fine adjustments for precise error compensation and delicate force control. This paper addresses design objectives and optimization procedures for design of a unique 6 degree-of-freedom (DOF) fully-parallel micromanipulator. Using kinematic and dynamic modeling analysis, optimum geometric parameters are found which satisfy the desired motion range, effective force and velocity transmission and minimum input loading due to the bending of flexural joints. Computer simulations, optimization theory, and the finite element method are used to model, synthesize, and analyze micromanipulator components. Internal force analysis is performed to design the hardware components for critical load conditions. Using a CAD/CAM system, a full scale model of the mechanism has been created, and local stress and deflection analysis has been performed on the critical components.
Sensitivity Analysis of the Burmester Equations of Planar Motion
Authors: Mahableshwarkar S. V. , Kramer S. N. 
Published: April 2021

Abstract
In this paper the sensitivity of the configuration of a mechanism to small variations in the precision point locations and corresponding coupler rotations is presented. The changes in the locations of the centerpoints and circlepoints, hence the dyads constituting the mechanism, due to these variations are determined by evaluating the total differentials of these quantities. The method is applied to mechanisms designed by the Burmester Theory of Planar Motion for four precision and five precision points. This additional information on sensitivity is shown to be useful in the process of mechanism design (Mahableshwarkar, 1989). Numerical examples are included to illustrate the formulation.
Geometrically Approximated Grashof-Type Movability Conditions for Spatial RSRC Mechanisms With Transmission Angle Limitations
Authors: Rastegar J. , Tu Q. 
Published: April 2021

Abstract
For closed-loop spatial RSRC mechanisms, Grashof-type movability conditions (i.e., conditions for the existence of crank-rocker and drag link types of mechanisms) are derived using geometrical approximation. The movability conditions are derived in the presence and absence of transmission angle limitations. The mechanism has two branches (configurations). Without transmission angle limitations, both configurations have identical movability conditions. However, by including transmission angle limitations, the movability conditions become different for each configuration of the mechanism. The movability conditions eliminate the possibility of changeover from one configuration to the other.
Solving a Planar Four-Bar Design Problem Using Continuation
Authors: Morgan A. P. , Wampler C. W. 
Published: April 2021

Abstract
The problem of synthesizing a planar 4-bar with given pivots such that the coupler curve passes through live precision points is considered. It is shown that the design parameters must satisfy a system of 4 fourth-degree polynomial equations in 4 unknowns which has at most 36 nonzero real solutions.
This polynomial system is solved using a continuation method, which thereby generates the collection of all designs that meet the precision-point specification. A computer program that implements this continuation method has been tested on a number of problems. It is reliable and fast enough for the purposes of design.
The approach to kinematic design represented by this work is completely general, subject only to computer-time limitations that may arise for problems with many design elements.
Coupler-Point-Curve Synthesis Using Homotopy Methods
Authors: Tsai L.-W. , Lu J.-J. 
Published: April 2021

Abstract
A numerical method called “Homotopy Method” (or Continuation Method) is applied to the problem of four-bar coupler-point-curve synthesis. We have shown that: for five precision points, the “General Homotopy method” can be applied to find the link lengths of a number of four-bar linkages, and for nine precision points, a heuristic “Cheater’s Homotopy” can be applied to find some four-bar linkages. The nine-coupler-points synthesis problem is highly non-linear and highly singular. We have found that Newton-Raphson’s method and Powell’s method tend to converge to the singular solutions or do not converge at all, while the Cheater’s Homotopy always finds some non-singular solutions although sometimes the solutions may be complex.