Synthesis of cam-link mechanisms for exact path generationSynthese de mecanismes came-coulisse pour la generation exacte de trajectoires

In this paper, it is shown that there are a significantly large number of cam-link mechanisms that may be used for generating an exact path or for guiding a body through exactly specified infinite positions. Using Gruebler's mobility criterion, structural synthesis is performed to obtain several cam-link mechanisms for path and motion generation. A synthesis technique is also presented to design track-follower mechanisms. The technique utilizes the complex loop closure method and the envelope theory to find the centerline and the contact points of the track. The approach is general and may be applied to any cam-link mechanism used to generate exact paths or to guide a body through infinitely many positions. A method for finding the curvature of the track at the contact points is also given.     

Selective precision synthesis of planar mechanisms satisfying position and velocity constraintsSelective präzisions-sythese ebener getriebe für gegebene stellungen und geschwindigkeiten

For many path generating mechanisms used in today's machines, the tracer point velocity may be as critical as its generated position for adequate mechanism performance [1,2]. In this paper the recently developed Selective Precision Synthesis technique has been extended to include the synthesis of mechanisms whose tracer points satisfy velocity as well as position specifications. The mechanism designer now has the capability of determining the planar mechanisms whose tracer points generate the positions and velocities within specified limits of accuracy. The method is applicable to all planar mechanisms constructed from dyads—including 4-bar, slider-crank, multi-loop and multi-link mechanisms. The theory is programmed for digital computation and numerical examples are presented to illustrate the use of the method.     

Isometry in mechanism designIsometrie in der getriebesynthese

Isometric designs are those that carry the same linear dimensions. Unique specification of the motion requirements of a mechanism between skew axes, with the help of a suitable set of conventions, removes all alternative designs isometric to the original mechanism, with one exception: an isometric design satisfying exactly the same motion requirements is available but with the algebraic sign of the axis distance changed. The transformation is one of reflection and is called an opposite isometry. Extending the use of unique specification of motion requirements to the special case of two-position design with identical specification of motion derivatives at the two positions (as in the case of a crank-rocker design), one is left with an alternative isometric design, without change of sign of axis distance. The device consists of a change of direction of motion of the mechanism, coupled with an interchange of mechanism positions that correspond to the two distinct positions on the curve of motion relationship. There is, in this case, what is called a direct isometry. The two transformations are shown to be useful: (i) in reducing the extent of design cataloguing, and (ii) in reducing the area of search for suitable mechanism designs.     

A new approach to the synthesis of 4-bar function generatorsNeue methoden für die synthese viergliedriger funktionsgeneratoren

In the present work a new approach to the synthesis of 4-bar function generators has been presented. Using this graphical method quick and at the same time sufficiently accurate synthesis is possible in a large number of cases. The method is based on the principle of coordinating two positions and the corresponding velocities of the input and the output links. Thus four conditions are satisfied and better accuracy than that with three point synthesis may be expected. Positions of the proper accuracy points have been discussed and some guidance to the selection of the initial data has been presented in this paper. One problem has been solved as an example.     

Optimum synthesis of planar function generators by the linear partition of the dyadic loop equationsOptimale synthese ebener funktionsgetriebe durch linearisierung der dyaden-maschengleichungen

Introduction of optimum design techniques at the early stages of engineering programs for the timely transfer of engineering technology to industrial applications demands optimum design techniques in which satisfactory solutions can be reached by varying only a few parameters of a system without involving time consuming iterations. This article presents such a method of optimum synthesis of planar function generators, where the dimensions of an optimum mechanism are determined by minimizing the error in Freudenstein's input-output displacement equation of the mechanism at N design positions, where N is not limited by the number of unknowns of the system. Design equations are formed by partitioning Freudenstein's displacement equation into dyadic loop equations using the linear superposition technique, and they are linear in terms of the unknowns of the system. Hence, the solution requires no iteration. Equations for the optimum synthesis of the plane four-bar and slider-crank mechanisms are developed with three, four, and five unknown dimensions, which are also used for the optimum synthesis of multiloop mechanisms having series connected four-bar and slider-crank loops.     

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.     

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.     

Nine-link plane mechanisms for two-variable function generation—II. SynthesisNeunglieddrige ebene funktions getriebe für zwie unabhängige veränderliche: Tiel 2 - Synthese

Methods of synthesizing nine-link plane mechanisms for two-variable function generation are presented. These are simplified procedures which employ identical relative positions and identical absolute positions of links. These techniques split the problem into syntheses of two single-freedom linkages when proper mechanisms are chosen, out of the available nine-link mechanisms. Up to 16 precision points (specified) can be directly satisfied, depending on the mechanism chosen. Numerical examples demonstrate that nine-link mechanisms as two-variable function generators are a practical proposition, especially with the synthesis techniques presented.     

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.     

可调节型空间RRSS机构刚体导引综合

提出了可调节型空间RRSS机构刚体导引综合的方法,分杆组分任务独立求解导出了相应综合方程,其中R-R杆组综合时运用了共面和反位移原理,简化了求解的复杂度。通过调节机构部分参数可实现多任务刚体导引综合,给定了任务与最大精确导引位置数之间的关系。运用混沌分形方法求出了综合方程组全部解,并给出了一个数字实例。     

On a general method for the synthesis of the path approximation mechanismsAllgemeines entwurfsverfahren für getriebe zur angenäherten erzeugung von kurven

The purpose of this paper is to give a general method for the synthesis of the path approximation mechanisms. The method is based on matrix algebra and is adjusted for use with a digital computer. The procedure described for applying the proposed method of synthesis is made on the one-loop spatial mechanism with seven links having constrained motion, but it may be employed for the synthesis of any type of simple closed or poly-loop mechanism.     

基于DE优化方法的混合驱动平面五杆机构实现点位对应综合

主要研究了利用混合驱动平面五杆机构再现给定轨迹曲线的问题,在分析了五杆机构的误差、可动性、构形 选择和伺服电机的选择与控制的基础上,提出了该五杆机构的优化模型。并用DifferentialEvolution(DE)算法进行 优化设计。最后给出了设计示例,证明该优化方法是可行的。     

Dimensional synthesis of linkages by multifactor optimizationSynthèse dimensionnelle de coulisse par optimisation à facteur multiples

The linkage dimensional synthesis problem is posed as a multifactor optimization problem with constraints. A new concept of inverse utilities is used to formulate an objective function combining the contributions of kinematic structural error, mechanical error and link length to indicate the desirability of the design.The concept has been applied to a user oriented computer program for synthesizing the RRRR and RRRP linkages as function and path generators, and the RGGR linkage as a function generator.     

Conjugate positions for planar four-bar mechanisms and corresponding special forms of the coupler-curvesKonjugierte stellungen bei ebenen viergelenkgetrieben und die zugenhörigen sonderformen der koppelkurven

Four-bar mechanisms and their variations yield two positions for which the output angle β or the coupler angle γ is identical. These positions are called “conjugate positions” and their significance is discussed. The kinematic inversions of mechanisms in certain conjugate positions leads to new mechanisms with special coupler curves. Coupler points which trace a path with two cusps are easily determined. A similar treatment of the non-turnable double rocker yields coupler curves with three cusps. Requirements for symmetrical coupler curves with two or three cusps can be satisfied.     

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°.     

On the synthesis of certain straight-line mechanismsSur la synthese des mechanismes reproduisant des droites

A direct method is presented for the synthesis of a large class of approximate straight line mechanisms based on a set of two equations describing the center of curvature of the path (the coupler curve) of an arbitrary point on the coupler of a crank-slider mechanism with an off-set. Several examples are discussed to establish the capability of the proposed set of equations to incorporate the classical approximate straight-line mechanisms (e.g. Watt, Chebyshev and Scott-Russell) as the special cases of the synthesis which can be constructed directly based on graphical considerations. A straightforward design of a luffing-crane mechanism and a graphical construction of a special mechanism which generates two mutually orthogonal straight lines are also presented to further illustrate the general versatility of the proposed method of synthesis.     

Function-cognate mechanisms: General theory and applicationGleichwertige Übertragungsgetriebe: Allgemeine theorie und ihre anwendung

A general algebraic approach using comparison of coefficients in the input-output displacement equation with appropriately grouped terms is developed rigorously for the identification of function-cognate mechanisms. These are mechanisms that give exactly the same relationship between the displacements of the input and output links. Several single-loop mechanisms are investigated to establish the existence or nonexistence of function cognates.     

Computer method for kinematic analysis of lower-pair mechanisms—I velocities and accelerationsEine neue methode zur analyse von mechanismen teil 1: Geschwindigkeit und beschleunigung

This work presents a new method for the analysis of lower pair mechanisms with the help of a computer. This method make use of the coordinates of the pairs and of those of other points of interest as Lagrangian coordinates of the problem. It also makes use of link constraint equations. Perhaps, the most attractive features of this method are its conceptual simplicity and the ease with which it can be programmed in a digital mini-computer. This work is divided into two parts. The first part describes the coordinates and constraint equations made use of, with emphasis on the analysis of velocities and accelerations. The second part presents the resolution of three typically non-linear problems: initial position, finite displacements, and static equilibrium position of a mechanism with elastic connections. It presents an iterative method of rapid convergence and demonstrates that a good initial estimate is not required.     

On the kinematic synthesis of 5-axis spatial mechanisms

In the present study the possibilities of kinematic synthesis of 5-axis spatial mechanisms are explored, in order to elaborate a design method for achieving associated positions and velocities imposed on input and output links. Structural schemes of 3R-2C mechanisms together with the appropriate mathematical algorithms for their synthesis are suggested. In completion one presents a computer-aided procedure for the kinematic systhesis, directly usable by the designer.