0


EDITORIAL

J. Mech. Des. 1982;104(4):679. doi:10.1115/1.3256406.
FREE TO VIEW
Abstract
Commentary by Dr. Valentin Fuster

BOOK REVIEWS

J. Mech. Des. 1982;104(4):680. doi:10.1115/1.3256407.
FREE TO VIEW
Abstract
Commentary by Dr. Valentin Fuster
J. Mech. Des. 1982;104(4):680-681. doi:10.1115/1.3256408.
FREE TO VIEW
Abstract
Topics: Fatigue
Commentary by Dr. Valentin Fuster
J. Mech. Des. 1982;104(4):681-682. doi:10.1115/1.3256409.
FREE TO VIEW
Abstract
Commentary by Dr. Valentin Fuster

RESEARCH PAPERS: Mechanisms Papers

J. Mech. Des. 1982;104(4):687-697. doi:10.1115/1.3256410.

This paper presents an analytical and computer-aided procedure on the kinematic synthesis of the planar two-gear drive. The drive is designed as a reversing mechanism and as a nonreversing mechanism either with or without dwell. Dwell characteristics of the mechanism are investigated using algebraic methods. It is found that the problem relates closely to the velocity-fluctuation of the four-bar linkage. Both general and specific dwell criteria are derived. An efficient computer-aided procedure can be used for the analysis of motion characteristics and for the development of a design chart. Numerical examples illustrate both analytical as well as graphical synthesis procedures.

Topics: Gears
Commentary by Dr. Valentin Fuster
J. Mech. Des. 1982;104(4):698-703. doi:10.1115/1.3256411.

The problem of stability of motion of elastic planar linkages is considered in the context of the classical Euler-Bernoulli equations of motion. The case of slider-crank mechanism is considered in detail and the critical values of the dimensionless parameters measuring slenderness, speed, and length ratio which may cause instability are determined. The start-up and the steady-state solution of the mechanism without viscous damping and the effects of flexibility on piston force and efficiency is evaluated.

Commentary by Dr. Valentin Fuster
J. Mech. Des. 1982;104(4):704-711. doi:10.1115/1.3256412.

This paper introduces some basic concepts regarding the workspaces of manipulators. The first part gives a general discussion regarding workspace shapes. Most of the rest of the paper focuses on manipulators with three orthogonal mutually intersecting axes. The structures of the primary and secondary workspaces for such systems are determined and the effects of hand size are examined in detail. Several specific examples are presented to illustrate the basic theory.

Topics: Design , Manipulators , Shapes
Commentary by Dr. Valentin Fuster

RESEARCH PAPERS: Power Transmission and Gearing Papers

J. Mech. Des. 1982;104(4):712-719. doi:10.1115/1.3256415.

The epicyclic differential gear has been known in modern times since 1575 when it appeared as a mechanism in a clock. Artifacts from an ancient shipwreck prove that it was known to the ancient Greeks at least 100 hundred years before Christ. The methods of kinematic analysis by either the relative angular velocity method or the instant center and linear velocity method, as given in the literature, are oriented toward specific solutions rather than general ones; they do not readily allow for parametric trend studies and they require a degree of imagination and intuition which may well be beyond the capabilities of those who are not practitioners of the art. The discussed methodology defines simple and compound epicyclic gears in terms of the overall ratio of a geometrically similar planetary gear. The kinematic analysis is derived in general terms for both the simple and compound epicyclic gear. It is shown that location of the point of zero tangential velocity of the velocity triangle relative to the system datum governs the characteristics of the gearset and whether it will perform as a differential gearset, or as a solar, star, or planetary gear. Simple mathematical relationships are given which define the proportions of the component gears, their speeds (rpm) and directions of rotations, and the resulting power splits. The formulas may be incorporated into simple computer programs oriented toward specific design requirements.

Commentary by Dr. Valentin Fuster
J. Mech. Des. 1982;104(4):724-730. doi:10.1115/1.3256419.

The paper studies the effect of bearing clearances in the dynamic analysis of gear mechanisms in high speed machinery. For this purpose, an analytical model is developed based on the interdependence between kinematics and kinetic relationships that must be satisfied when contact is maintained between the journal and its bearing. The contact modes are formulated such that the bearing eccentricity vector must align itself with bearing normal force at the point of contact. The analysis mainly relies on determining the direction of the bearing eccentricity vector defined as the clearance angles βi at the bearing revolutes for each contact mode of the gear teeth. The governing equations of the clearance angles are developed using the geometrical constraints of the contact point location and the velocity ratio. The clearance angles and their derivatives are subsequently used to systematically evaluate kinematic and dynamic quantities of each gear as well as the dynamic tooth load. A pair of rigid tooth spur gears with two revolute clearances is analyzed to illustrate the procedure. The model presented in the paper provides a design method for investigating the effect of bearing tolerances and wear on the evaluation of dynamic tooth load in high speed gearing systems.

Commentary by Dr. Valentin Fuster
J. Mech. Des. 1982;104(4):731-742. doi:10.1115/1.3256420.

In this paper a method is described for the calculation of the dished and pencil grinding wheel profiles for relief grinding of hobs for manufacturing spur, helical, and worm gears. Archimedean, convolute, involute, and ground worm gear drives are dealt with. For the purposes of control of the calculated grinding wheel profiles and of the determination of the generation error in the case of the profile curve approximation to a straight-line or a circular arc, the method contains the calculation of the hob tooth profile, relief ground with a grinding wheel of the calculated or approximated axial profile.

Commentary by Dr. Valentin Fuster
J. Mech. Des. 1982;104(4):743-748. doi:10.1115/1.3256421.

An analysis of the surface geometry of spiral bevel gears formed by a circular cutter is presented. The emphasis is upon determining the tooth surface principal radii of curvature of crown (flat) gears. Specific results are presented for involute, straight, and hyperbolic cutter profiles. It is shown that the geometry of circular cut spiral bevel gears is somewhat simpler than a theoretical logarithmic spiral bevel gear.

Topics: Gears , Geometry
Commentary by Dr. Valentin Fuster
J. Mech. Des. 1982;104(4):749-757. doi:10.1115/1.3256424.

The design of a standard gear mesh is treated with the objective of minimizing the gear size for a given ratio, pinion torque, and allowable tooth strength. Scoring, pitting fatigue, bending fatigue, and the kinematic limits of contact ratio and interference are considered. A design space is defined in terms of the number of teeth on the pinion and the diametral pitch. This space is then combined with the objective function of minimum center distance to obtain an optimal design region. This region defines the number of pinion teeth for the most compact design. The number is a function of the gear ratio only. A design example illustrating this procedure is also given.

Commentary by Dr. Valentin Fuster
J. Mech. Des. 1982;104(4):759-764. doi:10.1115/1.3256429.

A method of selecting grid size for the finite element analysis of gear tooth deflection is presented. The method is based on a finite element study of two cylinders in line contact, where the criterion for establishing element size was that there be agreement with the classic Hertzian solution for deflection. Many previous finite element studies of gear tooth deflection have not included the full effect of the Hertzian deflection. The present results are applied to calculate deflection for the gear specimen used in the NASA spur gear test rig. Comparisons are made between the present results and the results of two other methods of calculation. The results have application in design of gear tooth profile modifications to reduce noise and dynamic loads.

Commentary by Dr. Valentin Fuster
J. Mech. Des. 1982;104(4):767-774. doi:10.1115/1.3256434.

A method to calculate spur gear system power loss for a wide range of gear geometries and operating conditions is used to determine design requirements for an efficient gearset. The effects of spur gear size, pitch, ratio, pitch-line-velocity, and load on efficiency are shown. A design example is given to illustrate how the method is to be applied. In general, peak efficiencies were found to be greater for larger diameter and fine pitched gears and tare (no-load) losses were found to be significant.

Topics: Design , Gears , Spur gears , Stress
Commentary by Dr. Valentin Fuster
J. Mech. Des. 1982;104(4):775-777. doi:10.1115/1.3256435.

Finding the number of teeth for each gear in a gear train required to provide a specified noninteger ratio (or its inverse) of angular velocity between input and output shafts has been a troublesome problem throughout the history of gearing. A direct method for finding the required number of teeth is presented, along with a program for its implementation on a programmable pocket calculator.

Topics: Gears , Trains
Commentary by Dr. Valentin Fuster

RESEARCH PAPERS: Design Automation Papers

J. Mech. Des. 1982;104(4):778-784. doi:10.1115/1.3256436.

A method is presented for dynamic analysis of systems with impulsive forces, impact, discontinuous constraints, and discontinuous velocities. A method of computer generation of the equations of planar motion and impulse-momentum relations that define jump discontinuities in system velocity for large scale systems is presented. An event predictor, working in conjunction with a new numerical integration algorithm, efficiently controls the numerical integration and allows for automatic equation reformulation. A weapon mechanism and a trip plow are simulated using the method to illustrate its capabilities.

Commentary by Dr. Valentin Fuster
J. Mech. Des. 1982;104(4):785-791. doi:10.1115/1.3256437.

This paper presents a computer-based method for formulation and efficient solution of nonlinear, constrained differential equations of motion for spatial dynamic analysis of mechanical systems. Nonlinear holonomic constraint equations and differential equations of motion are written in terms of a maximal set of Cartesian generalized coordinates, three translational and four rotational coordinates for each rigid body in the system, where the rotational coordinates are the Euler parameters. Euler parameters, in contrast to Euler angles or any other set of three rotational generalized coordinates, have no critical singular cases. The maximal set of generalized coordinates facilitates the general formulation of constraints and forcing functions. A Gaussian elimination algorithm with full pivoting decomposes the constraint Jacobian matrix, identifies dependent variables, and constructs an influence coefficient matrix relating variations in dependent and indpendent variables. This information is employed to numerically construct a reduced system of differential equations of motion whose solution yields the total system dynamic response. A numerical integration algorithm with positive-error control, employing a predictor-corrector algorithm with variable order and step size, integrates for only the independent variables, yet effectively determines dependent variables.

Commentary by Dr. Valentin Fuster
J. Mech. Des. 1982;104(4):792-798. doi:10.1115/1.3256438.

Problems of optimal design of mechanisms are formulated in a state space setting that allows treatment of general design objectives and constraints. A constrained multi-element technique is employed for velocity, acceleration, and kineto-static analysis of mechanisms. An adjoint variable technique is employed to compute derivatives with respect to design of general cost and constraint functions involving kinematic, force, and design variables. A generalized steepest descent optimization algorithm is employed, using the design sensitivity analysis methods developed, as the basis for a general purpose kinematic system optimization algorithm. Two optimal design problems are solved to demonstrate effectiveness of the method.

Commentary by Dr. Valentin Fuster
J. Mech. Des. 1982;104(4):799-805. doi:10.1115/1.3256439.

The application of mathematical structural optimization methods to automotive structures is discussed. The global structures are typically simultaneously frequency and stress constrained. In addition, bending effects in the components cannot be ignored. Therefore, it is necessary to develop a very general approach while still retaining computational efficiencies. It has been found that approximation techniques coupled with mathematical programming allow the optimization of moderately realistic structures. In addition, there is a class of problems which must be characterized in terms of their boundary shape. This imposes a new set of difficulties primarily of insuring model integrity during the optimization.

Commentary by Dr. Valentin Fuster
J. Mech. Des. 1982;104(4):806-812. doi:10.1115/1.3256440.

An interactive computer program to aid a designer in selecting candidate manufacturing process and material combinations for a part is described. The program uses a twelve-digit code to eliminate unsuitable combinations from consideration and to rank the remainder using numerical figures of merit.

Commentary by Dr. Valentin Fuster
J. Mech. Des. 1982;104(4):813-816. doi:10.1115/1.3256441.

Three dimensional construction techniques are described along with the detailed description of several derivations. The resultant algorithms allow construction of points, lines, and conics directly in 3-space. These pieces of geometry are constructed relative to existing lines, conics, and splines which are represented as parametric rational cubics. The generality of these algorithms allows a single routine to handle construction relative to all curve types in the system. This characteristic reduces the amount of code and thus the implementation and maintenance costs of the CAD system. These techniques are being incorporated into a Computer-Aided Design system.

Commentary by Dr. Valentin Fuster
J. Mech. Des. 1982;104(4):817-824. doi:10.1115/1.3256442.

The design and visualization of three-dimensional objects with curved surfaces have always been difficult. This paper describes a computer system that facilitates both the design and visualization of such surfaces. The system enhances the design of these surfaces by virtue of various interactive techniques coupled with the application of B-Spline theory. Visualization is facilitated by including a specially built model-making machine that produces three-dimensional foam models. Thus the system permits the designer to define an object and, with little additional effort, produce an inexpensive model of the object which is suitable for evaluation and presentation.

Commentary by Dr. Valentin Fuster
J. Mech. Des. 1982;104(4):825-830. doi:10.1115/1.3256443.

An optimality criteria approach for the stiffness design problem is developed for the case of two elastic bodies in frictionless contact. The contact problem is analyzed by appending the nonpenetration constraint to the system potential energy. Necessary and sufficient conditions for stiffness maximization are derived. A computational method for design problem solution is developed and numerical results for a beam on a foundation are displayed.

Commentary by Dr. Valentin Fuster
J. Mech. Des. 1982;104(4):831-836. doi:10.1115/1.3256444.

A design procedure for a car trunk deck-lid using an approximate optimization technique is presented. Selecting the deck-lid gages and deck-lid inner panel configuration as design variables and overall stiffnesses as constraints, a possible weight reduction of 20 percent is demonstrated, compared with the base production deck-lid design. Although other practical design constraints might not allow one to achieve this goal, the potential value of optimization techniques is clearly demonstrated by this study. It is concluded that it could be useful to develop and apply such a procedure to components such as hoods, deck-lids, doors, and fenders, which are isolatable as structural components.

Commentary by Dr. Valentin Fuster
J. Mech. Des. 1982;104(4):837-843. doi:10.1115/1.3256445.

The optimum design problem is formulated for the selection of pipe sizes in a hydraulic network such as a power plant service water or bearing cooling water system. The flows in each branch of the network are taken to be known, which makes the design problem linear in the variables. The optimization problem is formulated as a mixed integer linear programming problem. A design example is given. The role of this problem formulation and solution method in an interactive computer aided design (CAD) system is discussed.

Commentary by Dr. Valentin Fuster
J. Mech. Des. 1982;104(4):844-848. doi:10.1115/1.3256446.

A problem class is identified and characterized: The problem is to optimally select variables of a multi-segment activity or design where there is an overall limiting constraint. A number of problems have been individually solved, but it is shown that a wide variety of practical problems can be formulated thusly and that a general solution technique is effective.

Commentary by Dr. Valentin Fuster
J. Mech. Des. 1982;104(4):849-854. doi:10.1115/1.3256447.

The optimal design of marine risers used for drilling and production of oil in offshore operations is studied. The optimization problem is formulated on a two-dimensional model for bending of circular tubular beams under tension and internal and external static pressure. A general polynomial expression describes the external hydrodynamic loads. Monotonicity analysis is used to identify active constraints, determine design rules, and reduce the size of the problem.

Commentary by Dr. Valentin Fuster
J. Mech. Des. 1982;104(4):855-860. doi:10.1115/1.3256448.

This paper proposes an approach that integrates the relationship between design and production engineers through the theory of nonlinear optimization. It attempts to cope with the problem of optimally allocating tolerances in a manufacturing process. The upper and lower limits of the random variables of an engineering system are allocated so as to minimize production cost, with allowance for the system scrap percentage. The approach is illustrated by an example, and the general mathematical theory is also provided. An important distinction between the design and the manufacturing scrap is introduced, and the cell technique is utilized to estimate efficiently the system scrap.

Commentary by Dr. Valentin Fuster
J. Mech. Des. 1982;104(4):861-868. doi:10.1115/1.3256449.

In this paper, the problem of fail-safe design of complex structural systems is considered. A substructural formulation for this class of design problems is presented. Constraints are imposed on stresses, deflections, natural frequency, and member sizes. It is shown that a structure can be designed to withstand the projected future damage. It is also shown that the substructural formulation offers computational advantage for both structural analysis and design sensitivity analysis parts of an optimal design algorithm. Fail-safe designs of open truss and closed helicopter tailbooms are obtained using a program developed based on the substructural formulation.

Commentary by Dr. Valentin Fuster
J. Mech. Des. 1982;104(4):869-874. doi:10.1115/1.3256450.

In this paper, a new method for the numerical solution of the finite displacement problem in spatial mechanisms with revolute (R), cylindrical (C), spherical (S), and prismatic (P) pairs is presented. It is based on the use of special points’ coordinates as Lagrangian coordinates of the mechanism. The kinematic constraint equations are imposed as constant distances, areas, and volumes of segments, triangles, and tetrahedrons determined by those points. The system of nonlinear equations is solved via the Gauss-Newton variation of the Least Squares Method. Finally, three examples are presented in which the good convergence properties of the method can be seen.

Commentary by Dr. Valentin Fuster
J. Mech. Des. 1982;104(4):875-880. doi:10.1115/1.3256451.

A method is developed to design for optimal unbalance distribution in a rotor system which has elements that are assembled on the shaft and operates above the first critical speed. This method can also be used for computing the optimal selection of balance weights in specified planes for a rotor with a known distribution of unbalance—the classic balancing problem. The method is an optimization problem where the strain energy of the rotor and its supports are minimized subject to the constraints of the equations of motion of the rotor system at a particular balancing speed. The problem is a quadratic program that has a unique minimum.

Commentary by Dr. Valentin Fuster
J. Mech. Des. 1982;104(4):881-884. doi:10.1115/1.3256452.

Minimum squared error mechanism synthesis can be done relatively easily by Error Linearization, a nonlinear regression procedure long known to statisticians. It has a descent property not possessed by the Newton-Raphson method, which consequently tends more readily to converge to unwanted stationary points. Applied to a four-bar function generator, error linearization yields, for the Freudenstein linear displacement equation, a least-squares design as a direct solution of three linear equations, whatever the number of design angle pairs. For the particular example considered, this design is mechanically unacceptable, but a good configuration is produced by a more natural nonlinear model in which angular error is the measure of performance. Here error linearization avoids nonoptimal local minima to which the Newton-Raphson method converges.

Commentary by Dr. Valentin Fuster

DISCUSSIONS

Commentary by Dr. Valentin Fuster
Commentary by Dr. Valentin Fuster
Commentary by Dr. Valentin Fuster

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In