Optimizing 4-bar crank-rocker mechanismOptimisation du mecanisme a quatre barres avec une manivelle et un balancier

Closed form equations are developed for the synthesis of the 4-bar crank-rocker mechanism in which the angle between dead-centre positions of the rocker and the corresponding angle turned by the crank are prescribed. All the four different situations are considered and the minimum transmission angle, for the complete rotation of the crank, is obtained for each case. The upper and lower bounds on the crank angle, corresponding to a dead centre position of the rocker, are obtained by using Grashof's criterion. The design is optimized by maximizing the minimum transmission angle. Each case is illustrated by providing a numerical example.     

Graphical synthesis of a 4-bar mechanismLa synthese graphique d'un mecanisme avec quatre barres

For a mechanism operating at steady state, the synthesis technique for specified coupler point location, velocity and acceleration is developed from the geometric nature of the acceleration pole. Two examples are presented. One example is based on a known site for the acceleration pole and the other depends on locating the pole from a specified acceleration.     

Axodes for the four-revolute spherical mechanismAxoides pour le mecanisme spherique a quatre couples cinematiques de rotation

This paper presents the relationships between the axodes and the geometric configuration of the spherical 4R mechanism. The order of the axodes of the spherical 4R mechanism is determined to be 16. The algebraic equations for the axodes of this mechanism are presented in terms of mechanism geometry. It is also shown that the order of the axodes of the simpler forms of the 4R spherical mechanism is lower than 16.     

Synthesis of position,path and function generating 4-bar mechanisms with completely rotatable driving linksSynthese de la position,de la trajectoire et de la generation de fonctions d'un mecanisme a quatre barres articulees

A unified treatment of the synthesis of position, path and function generating mechanisms with completely rotatable input links is presented in this paper. Algebraic-geometrical techniques are used to obtain all proper crank-rocker and drag-link linkage solutions with transmission angles in the range 45° ≤ μ ≤ 135°.     

Vector-network models for kinematics: The 4-bar mechanismModeles du reseau vectoriel pour la cinematique: Le mechanisme a quatre barres

The vector-network model has proved successful in the analysis of general, dynamic, 3-dimensional mechanical systems. In this paper, the application of this model is extended to the problem of kinematics. This unification of the modelling procedure has paved the way for the development of efficient computer programmers which can handle both dynamics as well as kinematics. Here, as an initial step, attention is focussed on the concepts underlying the vector-network model for mechanisms. The 4-bar mechanism has served as an illustrative example.     

Re-examination of a kempe linkageReexamen d'un mecanisme de kempe

More than a century ago, A. B. Kempe isolated several multiloop planar linkages, provoking considerable interest among mathematicians. Largely forgotten now, his work has not been followed up in the kinematics literature. One particularly fascinating solution lends itself more readilythan others to spatial analogues, but Kempe erred in its determination. Here, we present a fresh analysis of that solution, using an adaptation of closure equation algebra. Further insight is provided by means of some novel geometrical techniques. Attention is also given to the general matter of the mobility of multiloop linkages.     

Three position precessing mechanism synthesisLa synthese d'un mecanisme a preceder en trois positions

This paper presents a complex number development of a three position geared five-bar precessing mechanism synthesis.The methodology which is presented in this study is based on an extension of Burmester cycloidal circlepoint-centerpoint theory[2]. This paper presents the mathematical formulation of the synthesis process.A structured FORTRAN computer program was developed on a VAX 11/780 computer in order to implement the synthesis process. The synthesis program is capable of presenting the synthesis results on a graphical display. Typical results are shown.     

Dynamic force analysis of planar mechanismsAnalyse de force dynamique de mecanismes plans

A computer-oriented procedure for solving the dynamic force analysis problem for general planar mechanisms is presented. The procedure is based upon writing three equations of equilibrium for each link in the mechanism from free body diagrams. Inertia forces are included using d'Alembert's principle. A technique is shown for automatically reformulating these equations into matrix form so the joint constraint forces and the driving input force or torque can be readily solved for using Gaussian elimination. This computer-oriented technique operates directly on the equations written from body diagrams. The force analysis procedure discussed in this paper has been implemented in a computer program called KADAM, which also has a kinematic analysis capability. Because of the ease of problem formulation and since the technique is based upon first principles, it appears to have value as an educational tool. It is useful for the solution of practical industrial problems. Two illustrative examples are included.     

Coupled gyroscopic mechanisms for centerless gyrogrindersUn mecanisme gyroscopique pour une meule

A gyroscopic mechanism is developed as a centerless gyrogrinder. The mechanism maintains the proper relative positions of the grinder and the template during gyroscopic tracking. This is achieved through cross-coupling between the gimballed driving motor and a gimballed suspension system for the template. A mathematical model is developed for the analysis and synthesis of gyrogrinders. The model takes into account the various geometric, kinematic and dynamic aspects of the compound mechanism, and the possible inclusion of restoring springs and dashpots. Closed form expressions for the contact and tie-rod forces are developed using appropriate coordinate-transformations. A general computer routine is described and applied to study particular contours.It was found that the phenomenon of gyroscopic tracking, still persists even in the absence of the restoring springs and dashpots. Both provide extra controls on the values of the normal and tangential forces at the point of contact which may be required for the actual operation of the gyrogrinder.     

Coupler point-paths and line-envelopes of 4-bar linkages in asymptotic configurationsTrajectoires de la bielle d'accouplement et enveloppes de lignes des chaines a quatre barres en configuration asymptotique

This paper describes some of the properties of coupler point-paths and line-envelopes when the instantaneous centre approaches infinity. The degeneration of the cusp circle and inflexion circle leads to interesting properties of the loci of certain points and lines on the moving lamina. Finally, the conditions for the existence of a point of inflexion in a mechanically traced planar line-envelope are established.     

The design of an adjustable,three dimensional slider crank mechanismLa conception du mecanisme manivelle coulissante ajustable a trois dimensions

This paper presents a technique for the design of an adjustable spatial slider crank mechanism to be used as a variable displacement pump or compressor. The design method considers velocity fluctuation, force transmission effectiveness and mechanism geometric proportions. An example application is provided.     

Synthesis of an involute based dwell mechanismSynthese eines evolventenrastgetriebes

A dwell mechanism has been developed based on a coupler curve approximating an involute and utilising a rack and pinion arrangement. The proportions of the basic linkage have been synthesised and the dwell characteristics of the output link have been computed and presented.     

Computer optimization of trailer suspensionsOptimisation par ordinateur des suspensions de remorque

This paper presents an optimization procedure which has been developed to select appropriate suspension design parameters for a simple two wheel trailer. A modern approach to the optimization problem has been used applying non-linear programming to the constrained search for the minimum of an objective function. The acceleration response to roadway input of selected points on the load of the trailer has been designated for minimization. This acceleration has an important significance to the trailer design because of its effect on the stable and smooth ride of the trailer. Two computational procedures have been used and the results compared. The first approach involves the linear superposition of responses to a series of discrete sinusoidal inputs while the second applies more contemporary random vibration theory using power spectral density curves to simulate the actual road surfaces. The results of the optimization procedure are then compared with the response characteristics of the original trailer design and demonstrate that a substantial improvement has been made.     

An analysis of goldberg's anconoidal linkageUne analyse du mecanisme anconoidal de Goldberg

Among Goldberg's pioneering works is his introduction of spatial networks of Bennett linkages, inspired partially by Kempe's planar networks. Presented more than 35 yr ago, his innovatory chains have never been correctly nor fully analysed. This paper is intended to remedy that situation and to put Goldberg's multiloop linkages into perspective against related recent advances.     

Kinematics and dynamics of the RSSR mechanismCinematique et dynamique du mechanisme RSSR

A kinematic analysis of the RSSR mechanism is developed using rectangular co-ordinates. The dynamic response and certain constraint forces are calculated using equimomental point-mass systems and the principle of virtual work, on the assumption that the coupler is a solid of revolution.     

A note on the optimum design of four bar crank-rocker mechanismsNote sur le calcul optimum des mécanismes a quatre barres avec une manivelle

In this paper, the classical transmission angle problem is discussed from a general approximation point of view. It is shown that the least square and Chebyshev optimizations are two closely related approaches to this problem. A least square optimum solution to this problem is investigated by means of a parametric representation for the link lengths, and results are compared with those available in literature. It is found that the computations for the least square method can be easily performed by using a pocket calculator.     

A note on position analysis of manipulatorsUne note sur l'analyse de la position des manipulateurs

The notion of zero position of a manipulator is introduced and used in conjunction with the principle of similarity to derive analysis equations. The usual link coordinate systems are not defined and the base coordinate system is the only one used in analysis.     

Mechanisms with discontinuous transmission ratiosMecanismes a rapport de transmission discontinus

A 6-bar linkage with certain dimensions can provide an instantaneous reversal in the sign of the transmission ratio between input and output. By adding further components, it is possible to construct mechanisms that provide discontinuous transmission ratios without reversal, and without using edge-contacts or deformable members.     

Analysis of roller chain sprocket pressure anglesL'analyse des angles de pression d'un pignon avec une chaine a rouleax

An analysis is presented for determining the effect of pitch difference on roller chain articulation angles and pressure angles. Basic formulas and strategies are given for locating contact points. Results are presented and compared with those from a graphical solution.     

Closed-form analytic synthesis of a five-link spatial motion generatorLa synthese analytique non-iterative d'un generateur de mouvement spatial avec cinq barres

In the synthesis of motion generating mechanisms we seek to determine the key dimensions of a preconceived type of single-degree-of-freedom mechanism which will guide one of its links through a sequence of finitely or infinitesimally separated arbitrarily prescribed positions. In space, each such finitely separated precision position can be specified by the radius vector of the origin and the Euler angles of orientation of a coordinate system, embedded in the guided link, with respect to a fixed coordinate system of reference.The motion generator mechanim considered here consists of two grounded S-S links, ⁵ one grounded C-S link, a ternary S-S-S coupler and the R-R-C fixed frame. Motion of the coupler is to prescribed. Each equation of synthesis is written by expressing the closure of the vector polygon covering the starting and one displaced position of one dyad formed by a grounded link and the coupler. The resulting system can be solved for unknown vectors defining the dyad in its starting position, in closed form for up to three precision positions.