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RESEARCH PAPERS

J. Eng. Ind. 1969;91(1):1-12. doi:10.1115/1.3591517.

A hard look at the problems provoked by the quest for higher speeds of underwater craft shows that they can indeed be solved in a practical manner using the knowledge and principles derived in the evolution of the science of high-speed aerodynamics. Hydrodynamic heating, turbulent heat transfer and friction, boiling and cavitation, friction reduction by additives, normal and oblique shock waves, and rocket propulsion are topics brought under discussion. Propulsion remains the prime area of future endeavor in order to achieve the speeds demanded by modern times.

Commentary by Dr. Valentin Fuster
J. Eng. Ind. 1969;91(1):13-20. doi:10.1115/1.3591492.

The dependence of solar array energy on orbital parameters is given for cases that achieve optimum array pointing, and therefore, maximum performance. Optimum pointing requires continual array articulation and/or active spacecraft attitude control. Performance obtained in local-vertical attitudes with fixed or incrementally articulated arrays is compared with the maximum.

Commentary by Dr. Valentin Fuster
J. Eng. Ind. 1969;91(1):21-26. doi:10.1115/1.3591524.

A new method, herein referred to as the “Method of Linearly Independent Vectors,” is shown to permit the complete force balancing of certain planar linkages. This method consists of writing the equation describing the position of the total mechanism center of mass in such a way that the coefficients of the time-dependent terms may be set equal to zero. In this way, the total center of mass can be made stationary, and the shaking force vanishes. Derivations as well as practical applications are shown for four-bar and six-bar linkages with arbitrary link mass distributions.

Commentary by Dr. Valentin Fuster
J. Eng. Ind. 1969;91(1):27-36. doi:10.1115/1.3591544.

This article examines the plane hinged mechanisms with the aid of two original methods, i.e., a theoretical method and an experimental one. Each of these methods is based on the fact that the functions characterizing the motion of a large class of mechanisms are periodic functions. This fact determines the mathematical tools for the theoretical method; namely, complex Fourier series and the approximation exponential polynomial. For the experimental method this fact is of importance in the suitable choice of a system of successive derivatives of the electrical signal furnished by a polar mechanical transducer which represents the path of any point of the mechanism. The theoretical method of complex harmonic analysis represents the examination of binary structural groups with the aid of Fourier series expressed in complex form. The manner of applying this method to the investigation of plane hinged mechanisms is shown. In the case of the five-link mechanism of aspect I the method is brought to the level of a calculation algorithm which may be used on a digital computer. A numerical example is given with the aid of a CET-501 digital computer.

Commentary by Dr. Valentin Fuster
J. Eng. Ind. 1969;91(1):37-44. doi:10.1115/1.3591552.

Combinations of the inverted slider-crank linkage (i.e., the Whitworth quick-return mechanism) with another of the same sort, with a scotch-yoke mechanism or with a planetary gear, are able to produce excellent function generators having a stationary value of velocity ratio. Various forms are discussed, and graphs of their characteristic motions are shown.

Commentary by Dr. Valentin Fuster
J. Eng. Ind. 1969;91(1):45-54. doi:10.1115/1.3591553.

An algebraic method is presented for synthesizing the four-bar crank-rocker mechanisms in general, with the offset slider-crank mechanism as a special case, for coordinating the prescribed input and output link extreme positions. Solutions to the equations of constraint are derived for different cases. Among a large number of the available solutions, an optimal design is governed by a given parameter which is determined based on a design criterion. Numerous examples are provided.

Commentary by Dr. Valentin Fuster
J. Eng. Ind. 1969;91(1):55-65. doi:10.1115/1.3591554.

In this paper a geometrical solution is given to the problem of finding four-bar linkages having 5 given coupler-point positions coordinated with 4 given crank angles. It may also be possible to find solutions if one given coupler-point position together with a given crank angle, corresponding to this position, is replaced by two given link lengths. It has been found thus far that four-bar linkages, satisfying the stated conditions, are easy to obtain if the problem is related to Roberts’ law. To get a view of the possibilities, the degenerations of cognate circle-point curves and cognate center-point curves, linked to each other by the configuration (CR ) of Roberts, are investigated. As an example at the end of the paper a straight-line mechanism has been designed so that the coupler point moves along this line with an approximately uniform velocity.

Topics: Linkages , Mechanisms
Commentary by Dr. Valentin Fuster
J. Eng. Ind. 1969;91(1):66-74. doi:10.1115/1.3591555.

A new method has been developed to derive the 10 Hackmüller conics going through the four Burmester points of five positions of a moving plane, and each going through another virtual center of rotation. The calculation and graphical construction of the Burmester points in this paper are based upon this development. The calculation itself has been translated into the ALGOL computer-language and is available at the University of Eindhoven.

Commentary by Dr. Valentin Fuster
J. Eng. Ind. 1969;91(1):75-82. doi:10.1115/1.3591556.

The optimal design of crank and rocker mechanisms satisfying four prescribed multiply separated positions of the moving plane is considered. The constraints are obtained from pairs of corresponding points on the generalized Burmester curves. Sorting the ∞2 linkages which result is accomplished by zones and weighting factors as applied to necessary design criteria.

Commentary by Dr. Valentin Fuster
J. Eng. Ind. 1969;91(1):83-90. doi:10.1115/1.3591557.

A new method is presented by which positions of peculiar kinematic interest, such as ends of travel, locking positions and points of “uncertainty,” in certain types of spatial mechanisms can be readily ascertained. This method is based upon an analysis of the curves of intersection of the surfaces generated by points in the mechanisms, and is there related in such a manner as to render it useful both in determining the positiona interrelationships of components of the mechanisms, and in classifying the mechanism according to its motion.

Commentary by Dr. Valentin Fuster
J. Eng. Ind. 1969;91(1):91-96. doi:10.1115/1.3591558.

Cycloidpoints were recently introduced [1]. The present paper demonstrates the existence of Burmester point trios at which the rotation of the moving plane between precision positions is a constant multiple of the rotation of the circlepoint centerpoint vector. A new geared linkage is introduced to mechanize this commensurate relationship. Equations for finite-motion generation and for both finite and infinitesimal path generation are developed. Cognates of this mechanism are shown to exist.

Commentary by Dr. Valentin Fuster
J. Eng. Ind. 1969;91(1):97-102. doi:10.1115/1.3591559.

Some methods have been investigated both theoretically and experimentally to reduce the fluctuating torques in the driving shafts caused by the inertia forces in the crank-and-rocker mechanisms; the spatial four-bar mechanism having two revolute and two spheric pairs is cited as an example. The fluctuating torque has been actually reduced to 1/20–1/3 .

Commentary by Dr. Valentin Fuster
J. Eng. Ind. 1969;91(1):103-113. doi:10.1115/1.3591479.

Algebraic, geometric and some kinematic properties are derived for the paths generated by points on representative single degree-of-freedom spatial motions of four and fewer members. The motions considered are spherical rolling, spatial three-link motion, spherical four-bar motion, skew four-bar motion (three types), Bennett’s mechanism, and one type of spatial four-bar motion.

Commentary by Dr. Valentin Fuster
J. Eng. Ind. 1969;91(1):115-121. doi:10.1115/1.3591482.

One of the key concepts in a general method of spatial kinematic synthesis is a stretch-rotation operator applied to members of a general spatial kinematic chain. The latter consists of one or more interconnected loops of successively ball-jointed bar-slideball members. Each member is represented by a vector free to stretch-rotate with the motion of the chain. In the mathematical model of the general chain, displacement is simulated by means of stretch-rotation tensors operating on each member vector. Appropriate mathematical constraints render the general chain and its mathematical model equivalent to a particular mechanism. With this approach and by taking derivatives, first, second, and higher-order loop equations can be developed which form the basis for a general method of spatial kinematic synthesis, applicable to path, function and motion generation (body guidance) with first, second, and higher-order as well as for combined “point-order” approximations.

Commentary by Dr. Valentin Fuster
J. Eng. Ind. 1969;91(1):123-127. doi:10.1115/1.3591485.

Thirty space, four-link mechanisms with two general constraints are investigated to study the existence of their coupler-curve cognates (Roberts’ cognates). The present study shows that the space-cognate mechanisms neither necessarily require the same pair order nor the same types of kinematic pairs.

Topics: Mechanisms
Commentary by Dr. Valentin Fuster
J. Eng. Ind. 1969;91(1):129-134. doi:10.1115/1.3591490.

The present paper intends to report a discovery of geometric invariant in finite synthesis of space mechanism called “the duality of R-R link.” The duality itself is first proven here by using the screw geometry to give it a simple and intuitive form. Second, proving the 4-bar mechanism made by the dual R-R links is a Bennett mechanism it is made possible to synthesize the Bennett mechanisms for rigid-body guidance and function generation. Synthesizing the Bennett mechanisms the first time, for these practical uses, is important in itself. However, from the point of view of “the duality” it is only one special application.

Topics: Screws , Geometry , Mechanisms
Commentary by Dr. Valentin Fuster
J. Eng. Ind. 1969;91(1):135-141. doi:10.1115/1.3591491.

Cardan motion has been treated in the literature principally in terms of infinitesimally separated positions. Here Cardan motion is synthesized for all combinations of up to five infinitesimally and finitely separated positions of the moving plane. For each of the five distinct combinations which exist for four positions, the circle point curve is shown to degenerate into a circle and a line and the center point curve into a line at infinity and a hyperbola. Elementary analytical and graphical design procedures are provided and supported by examples. The five position problem is shown to be constrained only by the well-known Scott-Russell mechanism or a double-slider mechanism.

Topics: Motion , Mechanisms , Design
Commentary by Dr. Valentin Fuster
J. Eng. Ind. 1969;91(1):143-146. doi:10.1115/1.3591495.

If a plane oscillating cylinder mechanism is in the position where the slider and the crank are aligned, it has a Ball point on the slider. This Ball point coincides with the inflexion-pole. The said point has the excess two if and only if the mechanism is suitably dimensioned. In this paper, extensions of these theorems are given for a spherical oscillating cylinder mechanism. It is shown that the theorems for the plane mechanism can be obtained from the spherical ones by a limiting process. Moreover, some theorems on the spherical mechanism are given without proofs.

Commentary by Dr. Valentin Fuster
J. Eng. Ind. 1969;91(1):147-150. doi:10.1115/1.3591496.

In plane kinematics there is in general in a given position of the moving plane one point J in this plane (the acceleration pole) which has the acceleration zero. Moreover, if A ≠ J is a point in the moving plane, the angle γ between AJ→ and the acceleration AA→j of A does not depend on the choice of A. We give in this paper a generalization of this theorem to spatial motions.

Commentary by Dr. Valentin Fuster
J. Eng. Ind. 1969;91(1):152-156. doi:10.1115/1.3591499.

A closure equation, in terms of matrices with dual-number elements, for spatial five-link mechanisms, is presented in this paper. From the equation, a set of displacement equations for a RCRCR mechanism with general proportions is obtained; the input-output relationship is expressed as a fourth-degree algebraic equation and formulas to determine other linkage variables are expressed in closed form.

Commentary by Dr. Valentin Fuster
J. Eng. Ind. 1969;91(1):158-162. doi:10.1115/1.3591502.

A study is made of the mobility of linkages with line and plane symmetry. The symmetry conditions are shown to give rise to several very general classes of overconstrained linkages.

Topics: Linkages
Commentary by Dr. Valentin Fuster
J. Eng. Ind. 1969;91(1):165-171. doi:10.1115/1.3591505.

The problem of involute helical gear noise is studied by running a pair of 6 DP gears in a power circulating rig inside an anechoic room. More than 3500 magnetic tape recordings were taken and analyzed, for gears running at different speeds and transmitting different loads. A pair of 14 DP nickel steel gears of finished, ground, and shaved teeth was also tested to study the effect of surface finish on gear noise. Experimental results revealed that the main sources of gear noise are impact between gear teeth and friction. A sudden rise in noise level has been noticed when a whole number of teeth are in contact. This paper presents experimental results and study of noise of involute helical gears of different facewidths and pitches, running at different speeds, and transmitting different loads. The source of gear noise and noise generating mechanisms are also discussed.

Commentary by Dr. Valentin Fuster
J. Eng. Ind. 1969;91(1):172-178. doi:10.1115/1.3591506.

A design technique which makes use of the unique inflection circles that result when the instant center (pole) falls at a fixed pivot or at a link pivot is developed to synthesize a 4-bar linkage which has a point or points on its coupler plane which trace two straight-line motions of specified angular displacements for two adjustments of a “fixed” pivot. When combined with an adaptation of the Euler-Savary equation, this technique can be used to synthesize a 4-bar linkage having a coupler point which traces three straight-line motions for three specified adjustments of a fixed pivot.

Commentary by Dr. Valentin Fuster
J. Eng. Ind. 1969;91(1):179-184. doi:10.1115/1.3591509.
Abstract
Topics: Screws
Commentary by Dr. Valentin Fuster
J. Eng. Ind. 1969;91(1):186-191. doi:10.1115/1.3591512.

The rolamite is a precision roller-band mechanism which was recently developed. The looseness of the rolamite geometry is a function of the band tension. The tight geometry and the slightly loose (small-deflection) geometry may be described by simple equations. Typical digital computer results are presented for the interroller clearance in the very loose (large-deflection) geometry. The rolamite may be made to generate forces if the band flexural rigidity is varied, or if it is precurved. An energy method is used to derive a general form of the force equation.

Commentary by Dr. Valentin Fuster
J. Eng. Ind. 1969;91(1):193-197. doi:10.1115/1.3591515.

A method intended for programming on a computer is presented for designing four bar function generators based on infinitesimal kinematic synthesis. By using the outlined procedure, one can obtain mechanism linkage specifications and tables of performance of a large number of the possible mechanisms for a single design point. Selection of the most suitable mechanism by inspection of the tables is then possible.

Commentary by Dr. Valentin Fuster
J. Eng. Ind. 1969;91(1):198-202. doi:10.1115/1.3591516.

In designing a linkage to transform one motion into another motion, consideration is given to the design sensitivity by analyzing the difference between the function generated by an ideal model of the mechanism and a model which incorporates manufacturing tolerances and clearances. The effects of these tolerances and clearances are presented in the form of mobility bands for the linkages.

Commentary by Dr. Valentin Fuster
J. Eng. Ind. 1969;91(1):203-208. doi:10.1115/1.3591522.

A rigid body is studied in a series of different positions. These positions can be finitely separated, infinitesimally separated, or a combination of the two. A general method for determining the locations of points or lines (in the rigid body) which have their different multiple positions satisfying the constraints of binary links or combined link chains is developed. In a companion paper [10] equations governing the locations of these special points and lines are derived.

Commentary by Dr. Valentin Fuster
J. Eng. Ind. 1969;91(1):209-219. doi:10.1115/1.3591523.

A general method for synthesizing spatial linkages (derived in a previous paper [1]) is applied to the design of various types of binary links and combined link chains. Equations governing those special points and lines which define the link dimensions are derived. Types and order of loci of such special points and lines and the maximum number of design positions for each link are given. Numerical method for computing these special points and lines are discussed, and a numerical example is presented.

Commentary by Dr. Valentin Fuster
J. Eng. Ind. 1969;91(1):220-223. doi:10.1115/1.3591525.

With the aid of the geometrical surface described by the relative motion of a spatial link dyad, rules are derived for the determination of type (crank-and-rocker, drag link, and double rocker) of the skew four-bar mechanism. The results are closely related to Grashof’s rule for plane four-bar linkages.

Commentary by Dr. Valentin Fuster
Commentary by Dr. Valentin Fuster
J. Eng. Ind. 1969;91(1):228-233. doi:10.1115/1.3591529.

An energy method given by Quinnfor determining the dynamic characteristics of planar mechanisms under the action of displacement-related forces is extended to spatial linkages. These linkages may, in addition, be subjected to time-related forces or to velocity-related damping forces. Recently developed matrix methods are used in the linkage analysis resulting in a method well suited to digital computation.

Commentary by Dr. Valentin Fuster
J. Eng. Ind. 1969;91(1):235-239. doi:10.1115/1.3591533.

In the following paper, Lagrange’s equation is used to derive an equation of motion for the rolamite mechanism in the ideal tight configuration; the effects of band inertia, force generation by bands of varying bending stiffness, and nonconservative forces are considered. An experimental system for investigating the dynamic response of rolamite is described. The effects of friction on the rolamite mechanism are discussed and experimentally determined values of coefficients of friction are presented.

Commentary by Dr. Valentin Fuster
J. Eng. Ind. 1969;91(1):240-249. doi:10.1115/1.3591536.

The structural permutation method (the “number” synthesis) of linkages is used to produce a collection of linkage forms with mobility 4. The steps of the procedure are carefully explained in detail; Franke’s notation is used. From the collection, a few promising forms are selected for dimensional sizing, so that the mechanism be capable of adding any of the numbers 1, 2, 4, and 8 to obtain a sum N with 0 ≤ N ≤ 15. The study provides an example of this design procedure.

Topics: Mechanisms , Linkages , Design
Commentary by Dr. Valentin Fuster
J. Eng. Ind. 1969;91(1):251-265. doi:10.1115/1.3591539.

Part 1: Over the past several years, the matrix method of linkage analysis has been developed to give the kinematic, static and dynamic force, error, and equilibrium analyses of three-dimensional mechanical linkages. This two-part paper is an extension of these methods to include some aspects of dynamic analysis. In Part 1, expressions are developed for the kinetic and potential energies of a system consisting of a multiloop, multi-degree-of-freedom spatial linkage having springs and damping devices in any or all of its joints, and under the influence of gravity as well as time varying external forces. Using the Lagrange equations, the exact differential equations governing the motion of such a system are derived. Although these equations cannot be solved directly, they form the basis for the solution of more restricted problems, such as a linearized small oscillation analysis which forms Part 2 of the paper. Part 2: This paper is a direct extension of Part 1 and it is assumed that the reader has a thorough knowledge of the previous material. Assuming that the spatial linkage has a stable position of static equilibrium and oscillates with small displacements and small velocities about this position, the general differential equations of motion are linearized to describe these oscillations. The equations lead to an eigenvalue problem which yields the resonant frequencies and associated damping constants of the system for the equilibrium position. Laplace transformations are then used to solve the linearized equations. Digital computer programs have been written to lest these methods and an example solution dealing with a vehicle suspension is presented.

Commentary by Dr. Valentin Fuster
J. Eng. Ind. 1969;91(1):266-272. doi:10.1115/1.3591540.

Solutions are developed for bending and buckling of a circular ring with an arbitrary section under several types of loading. It is found that in-plane and out-of-plane deformations are coupled. In-plane loads cause out-of-plane deformations, and loads normal to the plane of the ring cause in-plane deformations. The solutions reduce to known results from strength of materials in special cases.

Commentary by Dr. Valentin Fuster
J. Eng. Ind. 1969;91(1):273-281. doi:10.1115/1.3591543.

The small, highly efficient, thermal regenerators used in cryogenic refrigerators present a very complex problem in analysis and design. Many effects which are negligible in larger, less efficient, regenerators produce sizable thermal losses in these small units and must be considered if their performance is to be calculated accurately. Included among these are longitudinal heat conduction, temperature-dependent property variations, surface, feed gas flow, and end effects. This paper describes these effects and presents the results of an analytical and experimental investigation conducted to determine the magnitude and physical nature of the resulting thermal losses. Included also is a description of the mathematical parallel flow analogy that was used to overcome the poor computational time accuracy characteristics of the finite difference method used to calculate regenerator performance.

Commentary by Dr. Valentin Fuster
J. Eng. Ind. 1969;91(1):282-287. doi:10.1115/1.3591545.

The analysis of parallel damped dynamic vibration absorbers is presented. The system considered is essentially a modification of the conventional damped vibration absorber and consists of adding, in parallel, a subsidiary undamped absorber mass in addition to the damped absorber mass. The analysis clearly shows that it is possible to obtain an undamped antiresonance in a dynamic absorber system which exhibits a well-damped resonance. While the bandwidth of frequencies between the damped peaks is not significantly increased, the amplitudes of the main mass are considerably smaller within the operational range of the absorber. The damped absorber mass and the main mass attain null simultaneously so that the vibratory force is transmitted directly to the undamped absorber. Numerical results are presented for the special case when the absorber masses have the same magnitude. Two cases of tuning have been considered: (a) when the absorber masses are tuned to the frequency of the main mass, and (b) when the absorber masses are tuned to the so-called favorable tuning frequency. Comparison of the results with those of the conventional absorber indicates that the parallel damped dynamic vibration absorber has definite advantages over the conventional damped vibration absorber.

Commentary by Dr. Valentin Fuster

DISCUSSIONS

Commentary by Dr. Valentin Fuster
Commentary by Dr. Valentin Fuster
J. Eng. Ind. 1969;91(1):141-142. doi:10.1115/1.3591494.
FREE TO VIEW
Abstract
Commentary by Dr. Valentin Fuster
J. Eng. Ind. 1969;91(1):162-163. doi:10.1115/1.3591503.
FREE TO VIEW
Abstract
Topics: Linkages
Commentary by Dr. Valentin Fuster
Commentary by Dr. Valentin Fuster
Commentary by Dr. Valentin Fuster
J. Eng. Ind. 1969;91(1):191-192. doi:10.1115/1.3591514.
FREE TO VIEW
Abstract
Topics: Force , Geometry
Commentary by Dr. Valentin Fuster
Commentary by Dr. Valentin Fuster

TECHNICAL BRIEFS

J. Eng. Ind. 1969;91(1):290-292. doi:10.1115/1.3591551.

A solution based upon the theory of elasticity is found for the maximum allowable bolt spacing in a flange assembly. The flanges are assumed to have flat faces and no gasket.

Commentary by Dr. Valentin Fuster

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