Six-link Mechanism Research Articles

Analysis and synthesis of a three-dimensional six-link mechanism

The structure and kinematics of a three-dimensional six-link mechanism with two input links are analyzed. Such mechanisms are widely used in the food industry.

Synthesis of Planar Stephenson III Six-Link Mechanism for Function Generation Based on Hyper-Chaos Newton Downhill Method

The problem synthesis of planar Stephenson Ⅲ six-link mechanism for function generation all the while is a research difficult puzzle in mechanism fields. The hyper-chaos Newton downhill method finding all real solutions of nonlinear equations was proposed that is based on utilizing hyper-chaotic discrete system to obtain locate initial points to find all real solutions of the nonlinear questions. The numerical example of synthesis of planar Stephenson Ⅲ six-link mechanism for function generation with 11 accurate points was given. The result shows that most real solutions have been quickly obtained. The number of solutions is the most and the time-spending is the less than existing any other method and it proves the correctness and validity of the proposed method.

Synthesis of lever transmissions with approximate rest at the extreme positions

A new method of synthesis is considered for lever transmissions with approximate rest at the extreme positions. The example of a six-link mechanism with approximate rest based on two hinged four-link systems and a slide-block mechanism with two approximate rests in series is discussed.

Kinematic Analysis of MacPherson Strut Mechanism

In this paper, we derive the closed-loop equations of the MacPherson strut mechanism as the spatial six-link mechanism of two degrees of freedom. With given values of steering and strut displacements, the formulas for analyzing the attitude of the strut are established. The results of analysis are verified experimentally. The static analysis is done under the several conditions, for example, the angle of the lower arm and the position of the steering rack are varied. By this analysis, it can be shown how the force transmitted through the rod is needed to steer the tires. From the results of analysis, we can know how the force preventing the smooth sliding of the strut occurs. We analyzed the sensitivities to show how the error of the assembling and processing had an effect on the kinematics of this mechanism. The sensitivities can be derived from partially differentiating the closed-loop equations with respect to the kinematic constants. A few of them are verified experimentally. Comparing with result of static analysis, we investigate if the cause of error involve in transmissibility.

Grashof's Condition of Stephenson-type Planar Six-Link Mechanisms

There exist two, four or six solutions of the output angle of the Stephenson six-link mechanism of type III, which is composed of the constituent four-link mechanism and the driving two-link chain, for any value of the input angle. These solutions correspond to link-chain configurations in different domains of motion of the driving link. Domains of motion are corresponded to either parts of the coupler curve of the constituent four-link mechanism which are separated by two limit points or connections of two parts separated by limit and turning points, or the coupler curve or its parts separated by two turning points. So, domains of motion are mapped on four number-lines of the input angle which are discriminated by the sign of the determinant of the equations of the velocity analysis and the sign of the sine of the relative angle of the driving two-link chain. Consequently, all relationships between input and output angles are calculated as a continuous function. In this paper, the identification method of the domains of motion is expanded the grashof's condition, that is, the algorithm for judging whether the driving link can make a continuous rotation in one direction or not.

Identification of motion domains of planar six-link mechanisms of the Stephenson-type

Analytical solutions of the output displacement of the Stephenson-3 six-link mechanism for a value of the input displacement contain solutions corresponding to link-chain configurations in different domains of motion of the driving link. These domains of motion correspond to either parts of the coupler curve separated by two limit points or connections of two parts separated by limit and turning points, or the coupler curve or its parts separated by two turning points. In this paper, these domains of motion are mapped on four number lines, which are discriminated by the sign of the determinant of the Jacobian matrix and the sign of the sine of the relative angle between two links of the external dyad. Consequently, every relationship between input and output displacements is calculated as a continuous function. Moreover, the relationships between the domain of motion of the driving and the circuit, the branch are made clear.

Design of a Six-link Mechanism for a Micro Air Vehicle

Micro air vehicle (MAV) is a small flight vehicle that uses lift-generating mechanism different from the mechanism used for a larger aircraft. The MAV may require configurations that are more unusual and approaches, ranging from low aspect ratio fixed wings to rotary wings, or even flapping wings. One of the most efficient lift-generating mechanism in small geometries is observed in the one species of insects Encarsia formosa, as reported by Weis Fogh. This is achieved by generating lift prior to setting up of net circulation. In this paper, the design of a flapping mechanism used to realise the Weis Fogh mechanism of lift generation is described. A single-drive design using concepts of motion synthesis by kinematic inversion technique, followed by dynamic analysis, is presented. This simplification opens the way for future miniaturisation of these devices at economic costs.

車輪操舵・懸架機構の運動特性解析(S46-1 機構の開発とシミュレーション(I),S46 機構の開発とシミュレーション)

The independent suspension system is adopted in the automobiles to make the driving be comfortable and maneuverable. Especially, the MacPherson strut mechanism is the one of the most commonly used mechanisms in front suspension because of a small number of component parts. But that reduces parameters to draw the ideal trajectory of the wheel spindle and limit the freedom of design. It is difficult to estimate the trajectory of the wheel spindle comparing the ideal one in three dimensional space. In this paper, we derive the closed-loop equations of the MacPherson strut mechanism as the spatial six-link mechanism of two degrees of freedom. With given values of steering and strut displacements, the formulas for analyzing the attitude of the strut are established. And sensitivity analyses were done using the closed-loop equations with respect to the coordinets of the spherical pair connecting the strut and the frame. The results of analysis is verified experimentally.

スティーブンソン形6節リンク機構のブランチおよびサーキット(OS3, OS5 機構の開発とシミュレーション, 機械設計における情報共有)

The Stephenson-3 six-link mechanism consists of the planar four-bar linkage and the external dyad. All relationships between the input and output angles are analyzed by solving the algebraic equation of sixth degree. The solutions are mutually contained in different branches or circuits. The branches are the parts of the coupler curves separated by two limit points. A circuit of a linkage is defined as all possible orientations of the links which can be realized without disconnecting any of the joints. In this paper, it is shown that these branches and circuits can be mapped on four number lines which are discriminated by the sign of the determinant of the Jacobian matrix and the sign of the sine of the relative angular displacement between two links of the external dyad. So the motion domains of the driving Link of the Stephenson-3 six-link mechanism are identified.

Circuits and Branches of Stephenson-Type Planar Six-Link Mechanisms with the Driving Slider.

The Stephenson III six-bar linkage consists of the planar four-bar linkage and the external dyad. All relationships between the input and output angles are analyzed by determining the points of intersection of the coupler curve of the constituent four-bar linkage and the end pairing point circle of the second link of the external dyad. The number of points of intersection (solutions) is even and less than six. The solutions are mutually contained in different branches or circuits. The branches are the domains on the coupler curves separated by two limit points or limit and turning points. The circuits are the coupler curve or its domains separated by two turning points. In this paper, it is shown that if the driving link is the slider, these branches and circuits can be mapped on four number lines discriminated by the sign of the determinant of the Jacobian matrix and the sign of the cosine of the angular displacement of the connecting link. So the motion domains of the driving link of the Stephenson III six-bar linkage are identified.

2331 スティーブンソン形平面 6 節リンク機構の運動領域識別アルゴリズム

2331 スティーブンソン形平面 6 節リンク機構の運動領域識別アルゴリズム

212 スティーブンソン形平面6節リンク機構における運動領域識別(機械要素)

212 スティーブンソン形平面6節リンク機構における運動領域識別(機械要素)

Mechanism Design of Wrist Joint for an Articulated Manipulator.

Motion transform mechanisms are designed for driving the wrist joint of a manipulator whose power sources(motors)are installed on the base in order to reduce masses and moments of inertia of arms. The wrist joint is composed of a spherical five-link mechanism of 2 DOF(degrees of freedom)and two linear-rotational motion transforms of Stephenson six-link mechanisms. Rotational motions of motors are transformed to linear motions by means of ball screw mechanisms, and then these motions become inputs of linear-rotational motion transformers which are driving the spherical five-link mechanism. Kinematic constants of the linear-rotational motion transformer are determined by means of a random search of the Stephenson six-link mechanism of its structural errors and forces acting on pairing elements. It is shown experimentally that the linear-rotational motion transformer is useful for the mechanism to drive the wrist joint.

Numerical evaluation of periodic transverse vibration of elastic connecting rods in a six-link mechanism

Application of the substructure method and d'Alembert's principle to deriving the differential equation of motion of a six-link mechanism with two elastic connecting rods is presented. In the case of stationary motion, the generalized Ritz's method has been applied to obtain system of linear differential equations with periodic coefficients. We have written computer programs to check conditions of dynamic stability and to find periodic solutions of the obtained equations. Numerical examples are given and from which the effect of elastic factors on articulation reactions is evaluated.

Synthesis of Watt's six-link mechanism for manipulation action in relative space

A method for dimensional synthesis of symmetrical six-link Watt's mechanism is presented. The method is based on Chebyshev's best approximation theory. The dimensions of the links are determined by partial synthesis, which involves independent solutions for the crank, and the two dyads. The synthesis problem requires a path generator, since the point of interest moves along a symmetrical trajectory with given symmetrically changing velocity, as well as a necessary symmetrical orientation of the output link. In order to satisfy the conditions of the symmetry, a special topology (e.g. the Galloway's basic four-bar mechanism) is chosen. The method provides possibilities for pre-estimation of the structural error.

Type Synthesis of Spatial Mechanisms with Consideration of General Constraint.

In the design of non-uniform motion mechanisms with pairs of multiple degrees of freedom, the influence of components of motion upon the allocation of degree of freedom of pairs is one of the important problems which must be solved for improvement of the output precision of mechanisms. In this paper, similarly to spatial mechanisms which are constructed with multiple closed circuits, a systematic synthesis of spatial mechanisms is carried out with consideration of general constraints of mechanisms. Namely, constraint conditions required to construct the pair in mechnisms with multiple closed circuits are formulated. Moreover, Structures of mechanisms with multiple closed circuits are represented accurately with incidence matrices whose components are the degrees of freedom of each pair, to obtain optimum allocation of degree of freedom of pairs. Based on the above analytical results, a systematic system for the spatial mechanism is proposed which determines the optimum allocation of degree of freedom of pairs. Finally, the spatial six-link mechanism which satisfies requirements of the above-mentioned conditions is synthesized to verity the method.

Evaluation of Motion-Transmission Characteristics of Planar Six-Link Mechanisms with a Prismatic Pair

An index of motion-transmission characteristics τ of the planar six-link mechanism with a prismatic pair is presented through investigations of the sensitivities of the angular and linear displacements of the links to the deviations of the kinematic constants and the forces acting on the pairs due to the external forces on the links. Generally speaking, the average of the sensitivities S and the average of the forces acting on the pairs F decrease rapidly in the interval [0, 0.3] and slowly in the [0.3, 1]as τ increases. The τ-S and τ-F relations are approximated to the regions bounded by two rectangular hyperbolas. Consequently, it is possible to estimate the values of S and F for any mechanism at the given crank angle by means of τ.

Remarks on the motion of link in the dwell-position

It has been found that the path of every point on a moving plane has a cusp in the T-position of the second kind, which is in nature an instantaneous dwell-position. In this paper, cases which violate such a property are found, hence the motion of a moving plane in the vicinity of the instantaneous dwell-position is investigated. Interesting properties and their interrelationships are obtained, such as the number of consecutive contact points between the fixed polode and the moving polode, the paths of points on the moving plane, path tangent at the cusp, etc. The instant center of a link in the instantaneous dwell-position, in general, cannot be determined by the existing methods. However, based on the current properties, the instant center can be determined analytically. A geometric procedure presented here is able to determine the instant center of the stationary link of six-link mechanisms in the limit position.

Evaluation of Motion-Transmission Characteristics of Planar Six-Link Mechanisms with a Prismatic Pair.

An index of motion-transmission characteristics τ of the planar six-link mechanism with a prismatic pair is presented through investigations of the sensitivities of the angular and linear displacements of the links to the deviations of the kinematic constants and the forces acting at the pairs to the external forces on the links. Generally speaking, the average of the sensitivities S and the average of the forces acting at the pairs F decrease rapidly in the interval [0, 0.3] and slowly in [0.3, 1] as τ increases. The τ-S and τ-F relations are approximated by the regions bounded by two rectangular hyperbolas. Consequently, it is possible to estimate the values of S and F of any mechanism at the given crank angle by means of τ.

Automatic classification of coupler curves of planar six-link mechanisms of the Watt-type. (2nd Report. Classification of curves).

The preceding paper proposed a method for determining the nodes, the inflection points, and the maximum-and minimum-curvature points of the coupler curves. In this paper, each of the solutions of the relative angle of the compound three-link chain for determining the double points of the coupler curves of W23 mechanisms is expressed as a function of the angular displacement of the driving link. The conditions that the driving links of W22 and W23 mechanisms can make a complete rotation, are formulated in two inequalities respect to the kinematic constants. According to the numbers of the nodes, the inflection points, the maximum-curvature points and the number of rotations of the curve, the coupler curves of W22 and W23 mechanisms are automatically classified into 166 and 163 kinds. These curves are illustrated schematically together with their appearance frequencies.