Designing polycentric mechanisms by curve matchingLe calcul de mecanismes polycentriques par appariement de courbes

This paper presents a new method for the design of a slider-crank mechanism to satisfy specified behavior of the moving centrode. The method is based on the technique of curve matching using a series of design curves. The various families of centrode curves possible from the slider-crank mechanism are discussed. An example of the use of the curve matching method is presented.     

Coulomb friction in mechanism sliding jointsFrottement sec et dynamique des mecanismes

Shortcomings in method of solutions of the Coulomb friction problem by other researchers are discussed and a direct method is proposed for introducing the non-linearities of this type of friction into sets of dynamic equations of motion for mechanical systems. The proposed method is free of iterations and repeats its calculations only once at each change of sign of reaction force. Numerical results demonstrate the efficiency of this direct method. The method also shows up the existence of regions of “exceptional” solutions to the dynamic equations.     

Optimum synthesis of function generators involving derivative constraintsLa synthese optimale de generateurs de fonction impliquant des derivees comme contraintes

Presented in this article is the method of optimum synthesis of mechanisms satisfying derivatives of the generated displacements along with the displacements at a discrete set of design positions. Although the method is illustrated for the synthesis of four-bar function generators, where the first and second derivatives of the generated functions are also generated at all or some of the design positions in order to increase the efficiency of approximating the generated function, the method is readily applicable for the synthesis of mechanisms to generate paths and rigid-body positions satisfying path velocities, path accelerations, and rigid-body angular velocities. Mechanisms of precision control units, vibratory feeders and conveyors, transfer robots and mechanical arms, and linkages replacing noncircular gear drives require the application of such synthesis techniques involving derivatives of the generated displacements.     

Finite element analysis of high-speed flexible mechanismsAnalyse de mecanismes flexibles de grande vitesse

A procedure is presented for determining the governing equations of a mechanism with physically undamped flexible links and distributed mass, operating at a prescribed input rotational speed. The procedure is illustrated by a detailed analysis of a planar 4-bar angular function generating mechanism. The set of governing equations for the deflections about the rigid body trajectory of mechanism members is derived using the Lagrange equation. These equations are discretized by the finite element method. The equations derived in this paper give a more refined mathematical model by including additional terms as compared to previous methods which represented mechanisms as a sequence of instantaneous structures. The element equations are transformed and assembled to generate the governing differential equations for the mechanism, using a connection procedure suitable for elements which are assumed axially rigid. In this manner a smaller set of global equations than those previously used is obtained.     

The analysis of planar linkages using a modular approachAnalyse des mecanismes plans par approche modulaire

Most complex planar linkages with lower pairs are actually made up of several simple mechanism components in series. When this is the case, it is possible to analyze the complex linkages by sequentially analyzing each of the simpler mechanism components. This procedure was described by Suh and Radcliffe[1], who have developed positive, velocity and acceleration equations for the component modules: rigid body, oscillating slider, two-link dyad, and rotating guide. The mechanism input module must be a driving crank.In this paper, this kinematic analysis technique is extended by incorporating dual slider, slider-crank, and inverted slider-crank modules, permitting mechanisms to be analyzed when a slider input, e.g. hydraulic or pneumatic cylinder, is involved.With this extension, most of the common compound planar mechanisms with lower pairs can be analyzed. However, there is still a class of mechanisms which cannot be analyzed in a direct fashion using the modular approach. These are mechanisms, such as the Watt “walking beam”, with more than two links between the moving end of the driver link and the frame. Such mechanisms can be analyzed using an inversion technique developed by Goodman[2], however; and the use of this technique with the modular technique is also discussed.The procedure developed is noniterative in nature and therefore can be conveniently programmed and executed on a minicomputer.     

Kirchhoff's circulation law applied to multi-loop kinematic chainsApplication de la loi de Kirchhoff aux chaines cinematiques

Kirchhoff's circulation law for potential difference is adapted to the purpose of finding a set of independent instantenous screw motors associated with any two bodiesin a kinematic chain when the configuration of the kinematic chain is given. Every possible instantaneous relative motion of two bodies can be found from linear combinations of the screw motors of the set. The procedure is applicable to any kinematic chain: it does not require special cases to be identified. It leads to a matrix formulation for which well-established numerical methods of solution are available.     

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.     

A linearized lumped parameter approach to vibration and stress analysis of elastic linkagesAnalyse des contraintes et des vibrations des mecanismes aux barres flexibles par la methode de discretisation lineare des parametres

Nonlinear equations of motion resulting from the lumped-mass modeling of mechanism links are linearized and decoupled by using the concept of kinematic influence coefficients. Effect of rotatory inertia of elements and end masses of moving links is investigated. Equations of motion are solved by way of the central finite difference method. The model is applied to a planar four-bar linkage corresponding to an actual mechanism that has been examined experimentally and analyzed by non-linear lumped parameter method. The results show that the error due to linearization is small and that rotatory inertia has significant effect on the elastic response of the mechanism.     

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.     

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.     

Synthesis of position generating crank-rocker or drag-link mechanismsSynthese de generateurs de position par des mecanismes a manivelle oscillante ou a manivelle double

A method is presented to synthesize crack-rocker or drag-link mechanisms which exactly generate a given set of finitely separated positions of a moving plane with a complete solution to the problem of transmission angle control. This paper is an extension of the recent works [1–3] where partial solutions of input-link rotatability and transmission angle control were considered. It is shown how to eliminate the branch defect from the designed linkages.     

The Bennett,Goldberg and Myard linkages—in perspectiveLes mecanismes de Bennet,de Goldberg et de Myard — en perspective

The linkages due to Bennett, Goldberg and Myard have passed into the classical literature, despite the considerable misconceptions still associated with them. Modern linkage analysis increasingly touches on these loops, or actually depends on them, as researchers extend their range of operations. The three groups of linkages are strongly inter-related, so that it is convenient, if not necessary, to treat them all at once. The paper sets out to completely clarify the linkages and the various relationships, including the derivation of comprehensive closure equations, something not previously attempted.     

Optimum design of high-speed flexible mechanismsCalcul optimum de mecanismes flexibles de grande vitesse

In recent years, considerable attention has been given to the analysis of flexible mechanisms. Analysis procedures often involve representing members of a particular mechanism by finite elements, and solving the derived system of governing equations for deflections and stresses. The inverse problem, which is one of design rather than analysis, is more difficult, and only a limited amount of work has been carried out in this area. In design, one must determine mechanism parameters that will satisfy specified stress and/or deflection conditions. In this paper a new procedure is presented for designing flexible mechanisms, and it is illustrated by an example of a planar 4-bar mechanism driven at a constant input rotational speed. Results for the example problem, using this new procedure, are found to converge to the optimum solution in fewer iterations than that required for previously published optimization techniques.     

Dynamic analysis of mechanisms via vector network modelAnalyse dynamique des mecanismes via le modele du reseau vectoriel

The Vector Network Model has already been defined both for problems in dynamics as well as for kinematics. For the latter, the model was developed for a sequential determination of position, velocity and acceleration variables associated with mechanisms. This paper deals with the next phase of kinematic analysis, namely, the dynamic analysis of mechanisms. Again, Vector Network Models have been invoked for the study and the method of analysis lends itself to generalizations which are deemed necessary for the analysis of complex mechanisms, both in terms of the number of linkages as well as the types of joints that are encountered. This model along with the one dealing with static analysis have already been incorporated into software for computer aided analysis including graphics.     

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.     

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.     

Self-osculating coupler curvesSelbstoskulierende koppelkurven

Coupler curves, generated by a planar four-bar linkage and possessing the peculiarity of self-osculation, are generally discussed. Condition formulas characterizing appropriate linkages are developed.     

Mechanics and adaptation systems in robotsLa mecanique et les systemes d'adaptation dans les robots

Modern requirements for industrial robots as a main means of the automatization of technological and transport operations are accuracy, efficiency, universality and the possibility of readjusting easily to manufacturing. Above mentioned robots' performances are determined by the characteristics of their motor system, mechanics, drive and system of adaptation. Some ways of developing the mechanics and adaptation of industrial robots based on the modern level of technical ideas and satisfying the increased demands are discussed in this paper.     

Linear state-feedback control of manipulatorsControle des manipulateurs par asservissements lineaires

The control of rigid-link manipulators with n single-degree-of-freedom joints is considered. Linearization of the nonlinear dynamics leads to stability and controllability conclusions, some valid also for the nonlinear system. Several methods for assigning closed-loop poles using centralized control are presented. Decentralized (independent joint) control is shown to be feasible by solving a set of nonlinear algebraic equations. For n = 2, existence of a solution is proven by construction, and nonuniqueness is established. Design examples show some pitfalls of decentralized designs and conditions for avoiding them are given. The final illustrative designs, using both centralized and decentralized control, show no outstanding advantage of the former.