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 transmission angle control in planar linkage synthesisControle graphique de l'angle de transmission dans la synthese de liaisons planes

Graphical techniques are presented which permit control of the maximum transmission angles (the transmission angle is here taken as the angle between the coupler and the normal to the driven crank) in the design positions for precision position linkage synthesis. This method does not directly control the maximum transmission angle magnitude throughout a motion cycle. It does permit elimination of all solutions whose transmission angle magnitude exceed nominated limits in the design positions. The constructions involve only circles and lines. They would seem well suited to implementation in interactive computer graphic synthesis programs.     

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.     

Synthesis of fully rotatable R-S-S-R linkagesCинтeз кpивoшипнoгo B-C-C-B pычaжнoгo мeнизмa

Algebraic-geometrical techniques to design fully rotatable R-S-S-R linkages with transmission angle control are presented. The concept of upper bounding Cos μ where μ is the transmission angle, is used to obtain feasible regions for linkages with full input-link rotatability. The proposed feasible regions have algebraic boundaries. This concept was developed earlier for the precision synthesis of planar four-bar linkage and it has now been extended to the precision synthesis of R-S-S-R linkage.     

Graphical synthesis of the RSSR crank-rocker mechanismGraphische synthese der RSSR-kurbelschwinge

Four different graphical constructions are put forward for the synthesis of the RSSR crank-rocker mechanism for prescribed oscillation angle and quick-return ratio. All these graphical constructions exhibit a series of designs, enabling some amount of direct choice. Checks for crankrocker action and for oscillation between the prescribed positions and in the prescribed direction are included along with a consideration of the transmission angle. These graphical procedures are believed to be useful when critical demands are not being made or while deviating somewhat from a limited set of catalogued designs.     

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 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°.     

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.     

Pantograph mechanism as a non-traditional manipulator structureMecanisme a pantographe comme structure non traditionnelle de manipulateur robotique

This paper presents a study on the design, motion and force transmission characteristics of a non-traditional robot structure, the pantograph mechanism. Although the pantograph mechanisms has been known for about four hundred years, the comprehensive study of its potential advantages and limitations when used as a robot is believed to be new. In this paper, the kinematic linearity and dynamic nonlinearity between inputs and outputs are investigated. It is also proven that the two rectilinear input motions which exist in a pantograph structure are not coupled, and therefore are suitable for being adopted as generalized coordinates in control. In addition, a set of physically meaningful dimensionless parameters has been identified. Based on these parameters, kinematic properties for obtaining optimum motion range and workspace are suggested.     

Kinematic design and analysis of the rack-and-gear mechanism for function generationKinematische synthese und analyse des Zahnstangen-Räderkoppelgetriebes zur funktionserzeugung

The complex number method is applied to the kinematic design and analysis of the rack-and-gear function generating mechanism for three finely separated positions. The rack-and-gear mechanism is a useful planar mechanism that can be used to generate many functions that the four-bar mechanism can generate plus a great deal more. Due to the extra complexity of the rack-and-gear both monotonic and non-monotonic functions, as well as non-linear amplified motions, can be generated. A major advantage of the rack-and-gear mechanism is that the transmission angle always remains at its optimal value since the rack is always tangenial to the gear. Both the design and analysis have been programmed for use on the PDP 11/70 and are available to interested readers.     

Bevel-carrier logic in a variable-ratio transmissionTransmissions aux engrenages non-circulaires et rapport de vitesse variable infiniment

This paper describes several methods of combining non-circular gears to make an infinitely-variable transmission. The gears are affixed to the bevel and carrier of a differential which may be asymmetrical. This has a significant effect on the shape of the non-circular gears and on the performance characteristics of a transmission which uses such gears.     

An unsymmetrical watt-1 linkage generating a family of symmetrical curvesEin unsymmetrisches watt-1 gelenkgetriebe,dass trotzdem eine familie von symmetrische kurven erzeugt

The two minimum transmission angles, 2μ₁ and 2μ₂, and the coupler angle β of a four-bar, determine a family of symmetrical 6-bar curves, traced by non-symmetrical Watt-1 mechanisms, obtained through cognation and generalization of Kempe's focal linkage.The 6-bar linkages obtained, contain a bar that moves in a completely symmetric wayA geometric derivation of these highly useful linkages is presented in the paper in conjunction with a set of expressions for their dimensions. A set of examples, obtained through variation of the three determining parameters and two “double numbers” (δ₁ and δ₂ = ± 1) demonstrates the topological change in the shape of the curves that are traced by a set of points chosen on the symmetrical movinb bar.     

Synthesis of double-rocker mechanism with optimum transmission characteristicsSynthese du double mecanisme oscillant a bielle avec caracteristiques optima de transmission

A simple analytical procedure is presented for the synthesis of the planar 4-bar double-rocker mechanism for coordinating the prescribed extreme positions. For optimum transmission characteristics, the design criterion used is the equal deviation of the transmission angles from 90° at the two dead-centre positions. Numerical examples are provided to illustrate the method.     

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.     

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.     

Intrinsic transmission functions of plane single-loop kinematic chains with revolute or prismatic jointsFonctions de transmission intrinseques d'une chaine cinematique plane a une boucle ayant des joints articules ou a glissiere

Expressions for the intrinsic transmission functions of a plane single-loop kinematic chain, with revolute or translation joints and many degrees of freedom are found using the vector analysis. They are shown to represent a ratio of the oriented areas of triangles, or a combination of such rations for transmission functions of a higher orders. A set of equations is formed which establishes the relation between the intrinsic and absolute transmission functions.     

Synthesis of optimum slider-crank mechanismsCИ

For the spatial slider-crank mechanism formulas are obtained to allow the user determine the link sizes and slider offset for a predetermined stroke with an acceptable pressure angle at the extremes of slider travel as well as by a given angle between the crosshead guide of the slider and a plane in which the crank revolves. Formulas for determining the sizes of links of the plane slider-crank mechanism as a special case of the spatial mechanism are also presented. The particular cases of mechanisms havingequal angles of pressure as well as at extreme values of an angle between crosshead guide and the revolution plane of the crank are discussed. It is shown, that the plane mechanism case provides maximum slider travel when other things are equal.     

Choice of the law for a position control system

A problem is discussed concerning the structural and parametric synthesis of the control unit of a mechatronic (positional) system, consisting of an engine, a transmission mechanism, and a control unit. The technical characteristics of several control laws are analyzed. The advantages and deficiencies of each law in controlling the process of positioning are examined.     

一种摆杆极位五阶停歇机构的设计

停歇机构的设计理论是机构设计理论中的重要分支之一,数学分析表明,复合函数中第一个基本函数在某时刻的一、二阶导数为零,第二个基本函数的一阶导数在对应时刻为零,导致复合函数的一至五阶导数在对应时刻为零。此原理开创了一种崭新的基于基本机构之组合的高阶停歇机构的设计方法。为此,设计了一种基于行星轮系的摆杆在极限位置具有直到五阶停歇的平面七杆机构,研究了它的尺寸设计与高阶传动特征。该种组合机构结构较简单,容易设计,传动角大。     

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.