Spherical Linkages Research Articles

408 球面連鎖を用いた小型関節機構に関する研究 : 第 1 報 : 変形ヒンジ適用の検討

408 球面連鎖を用いた小型関節機構に関する研究 : 第 1 報 : 変形ヒンジ適用の検討

508 リンク形状誤差を含む球面連鎖関節機構の挙動解析(加工・生産機器)

508 リンク形状誤差を含む球面連鎖関節機構の挙動解析(加工・生産機器)

THE KINEMATIC SYNTHESIS OF STEERING MECHANISMS

We propose a computational-kinematics approach based on elimination procedures to synthesize a steering four-bar linkage. In this regard, we aim at minimizing the root-mean square error of the synthesized linkage in meeting the steering condition over a number of linkage configurations within the linkage range of motion. A minimization problem is thus formulated, whose normality conditions lead to two polynomial equations in two unknown design variables. Upon eliminating one of these two variables, a monovariate polynomial equation is obtained, whose roots yield all locally-optimum linkages. From these roots, the global optimum, as well as unfeasible local optima, are readily identified. The global optimum, however, turns out to be impractical because of the large differences in its link lengths, which we refer to as dimensional unbalance. To cope with this drawback, we use a kinematically-equivalent focal mechanism, i.e., a six-bar linkage with an input-output function identical to that of the four-bar linkage. Given that the synthesized linkage requires a rotational input, as opposed to most existing steering linkages, which require a translational input, we propose a spherical four-bar linkage to drive the steering linkage. The spherical linkage is synthesized so as to yield a speed reduction as close as possible to 2:1 and to have a maximum transmission quality.

On the Moduli Space of a Spherical Polygonal Linkage

AbstractWe give a “wall-crossing” formula for computing the topology of the moduli space of a closed n-gon linkage on 𝕊2. We do this by determining the Morse theory of the function ρn on the moduli space of n-gon linkages which is given by the length of the last side—the length of the last side is allowed to vary, the first (n − 1) side-lengths are fixed. We obtain a Morse function on the (n − 2)-torus with level sets moduli spaces of n-gon linkages. The critical points of ρn are the linkages which are contained in a great circle. We give a formula for the signature of the Hessian of ρn at such a linkage in terms of the number of back-tracks and the winding number. We use our formula to determine the moduli spaces of all regular pentagonal spherical linkages.

Spherical four-bar linkages with symmetrical coupler-curves

In this paper we present analogies between planar and spherical four-bar linkages with symmetrical coupler-curves. Three types of planar four-bar linkages with symmetrical coupler-curves are investigated. For spherical linkages in contrast to these planar four-bar linkages, two types of them generate symmetrical coupler-curves, and so does the remaining one if it has special dimensions.

Wrist Joint Mechanism Using Triple Spherical Linkage.

Using the theory of degrees of freedom, we have developed a constant velocity joint mechanism which has triple spherical linkages and applied it to the wrist joint of manipulators. The wrist joint mechanism features are as follows: revolute type lower pairs only; singularity-freemotion; pitch and yaw angles greater than 180 degrees; 360-degrees continuous roll motion; internal cable routing passage; high precision; high rigidity; remote driveability; back driveability. In this paper, the process of the mechanism development is described, the performance of the mechanism is discussed, and the practical design conditions are explained. Trial wrist models have been designed and built, and one was mounted on an industrial robot.

On the Rotatability of Spherical N-Bar Chains

This paper established the spherical counterparts of Ting’s rotatability laws of planar linkages. Generally speaking, similar rotatability properties exist between a pair of adjoining links in planar and spherical linkages and the concept of invariant link rotatability is valid for spherical linkage only if it is referred to that between adjoining links. The established spherical rotatability criteria are also valid for single and multiple degree of freedom nR3C, nR2C1P, nR1C2P and nR3P spatial linkages.

Optimization of Planar, Spherical and Spatial Function Generators Using Input-Output Curve Planning

A general scheme for the optimization of planar, spherical and spatial bimodal linkages for function generation is proposed. The problem is solved here following two basic steps: (i) planning input-output ((I/O) curves based on design requirements and selecting data from the planned curve; and (ii) setting up an optimization procedure to minimize a performance index.

Kinematic Geometry of Spherical Evolutes

In this paper, we define spherical evolutes corresponding to the trajectory of a point in spherical kinematics. We derive general expressions for the curvature properties of the nth spherical evolute in terms of the geodesic curvature and the derivative of the geodesic curvature for the (n-1)the spherical evolute. The results are illustrated by numerical examples for the motion of a circular cone rolling on a fixed circular cone, of a spherical turning-block linkage, and of a spherical four-bar linkage.

A generalised study of three multiply separated positions in spherical kinematics

Spatial motion problems such as transfer mechanisms in automatic processing equipment, function generation between non-parallel axes and certain classes of path generation problems cannot be solved by planar mechanisms. The significance of spherical linkages could be dramatically increased by bringing the synthesis techniques of these linkages up to the level of coplanar synthesis. The work of Sandor in terms of complex numbers and Tesar using an algebraic formulation has increased the breadth in coplanar synthesis of the analytical treatment particularly with regard to multiply separated positions. It is shown in this paper that the multiply separated position concept may be extended to spherical kinematics. The establishment of Burmester theory incorporating this concept enables the 4-bar spherical mechanism to be designed with the ease of its planar counterpart.

Higher-Order Path Curvature in Spherical Kinematics

Characteristic numbers are derived which define a spherical curve, within a stretch rotation, to a given order. The loci of all points, which have the same characteristic numbers, under rigid body spherical motion are studied. These results are useful for synthesis and analysis of spherical linkages. The theory is illustrated by numerical examples for the motion of rolling cones and a spherical turning-block linkage.

Mathematical Analysis of Finger Positions of a Spherical Linkage Metamorphic Robot Palm

Grasping is the main function performed by the mechanical hand. Mechanisms with more functionality are needed for secure grasping of different and complex objects. With the advancement of the field of robotics it is important to think of mechanisms of multifingered robot hand with added functionality. The metamorphic mechanism with spherical linkage opens a wide opportunity to design a multi fingered robot hand with spherical palm, which can achieve human like dexterity. On the basis of an intensive study of literature, this paper focuses on the development of a geometrical model and mathematical analysis of spherical robot palm with fingers attached to it. To develop the generalised mathematical model, the co-ordinate transformation matrices of the joint axis position and the finger position have been derived. The transformation matrices have been derived with the position and orientation of the links and finger positions. So the co-ordinate points of a point of interest in the three dimensional space can be described at different configuration state of the mechanism. The detail analysis has been done through this mathematical and geometrical modelling of five-bar spherical metamorphic linkage robotic palm. This mathematical and geometrical model can be used to inspect the feasibility of the mechanism design for a multi fingered robot palm. Journal of Mechanical Engineering Vol.36 Dec. 2006 pp.18-26DOI = 10.3329/jme.v36i0.807

Synthesis of Spherical Linkages With Use of the Displacement Matrix

Equations of synthesis are derived which are based upon rigid body motion expressed as a displacement matrix. Applications are shown in spherical rigid body guidance, function generation, and path generation.