Kinematic Analysis Of Spatial Mechanisms Research Articles

Kinematic solution of spherical Stephenson-III six-bar mechanism

A closed-form solution can be obtained for kinematic analysis of spatial mechanisms by using analytical method. However, extra solutions would occur when solving the constraint equations of mechanism kinematics unless the constraint equations are established with a proper method and the solving approach is appropriate. In order to obtain a kinematic solution of the spherical Stephenson-III six-bar mechanism, spherical analytical theory is employed to construct the constraint equations. Firstly, the mechanism is divided into a four-bar loop and a two-bar unit. On the basis of the decomposition, vectors of the mechanism nodes are derived according to spherical analytical theory and the principle of coordinate transformation. Secondly, the structural constraint equations are constructed by applying cosine formula of spherical triangles to the top platform of the mechanism. Thirdly, the constraint equations are solved by using Bezout’s elimination method for forward analysis and Sylvester’s resultant elimination method for inverse kinematics respectively. By the aid of computer symbolic systems, Mathematica and Maple, symbolic closed-form solution of forward and inverse displacement analysis of spherical Stephenson-III six-bar mechanism are obtained. Finally, numerical examples of forward and inverse analysis are presented to illustrate the proposed approach. The results indicate that the constraint equations established with the proposed method are much simpler than those reported by previous literature, and can be readily eliminated and solved.

On Displacement Analysis of the RSSR-SS Mechanism

This article presents a method for performing (RSSR-SS) mechanism displacement analysis. The benefit of this method is that it provides a practical alternative for performing RSSR-SS mechanism displacement analysis and is fully applicable with today's mathematics software. This method is an extension of the adjustable RSSR-SS synthesis method developed by the authors (Suh, C. H., Radcliffe, C. W. (1978). Kinematic analysis of spatial mechanisms. In: Kinematics and Mechanism Design. New York: John Wiley and Sons, pp. 179–183). By utilizing the passive degree of freedom of the coupler of the RSSR mechanism and its design equations (Sandor, G. N., Erdman, A. G. (1984). Spatial mechanisms with an introduction to robotics. In: Advanced Mechanism Design Analysis and Synthesis. Englewood Cliffs: Prentice-Hall, pp. 635–641), the design equation for the remaining (S-S) link of the RSSR-SS mechanism was developed using spatial transformation matrices under the constant length condition of the remaining S-S link. The angular rotation about the coupler of the RSSR mechanism, satisfying the constant length equation of this remaining S-S link, was calculated, numerically (Allen M. B. III, Isaacson, E. L. (1998). Solution of non-linear equations. In: Numerical Analysis for Applied Science. New York: John Wiley and Sons, pp. 177–187). As an example, the displacement of a series of rigid body points on the coupler of an adjustable RSSR-SS mechanism was calculated for a range of prescribed crank angles.

A NUMERICAL METHOD FOR THE KINEMATIC ANALYSIS OF SPATIAL MECHANISMS USING POINT COORDINATES

A numerical method for the kinematic analysis of spatial mechanisms with lower pairs is presented. The kinematic analysis is carried out in terms of the rectangular Cartesian coordinates of some defined points in the links and at the kinematic joints. The formulation in terms of this system of coordinates is simple and it involves elementary mathematics. The method suggests a new approach for choosing and classifying the different points and links in the mechanisms. Two examples are used to demonstrate the simplicity and efficiency of the proposed method.

Extraneous roots and kinematic analysis of spatial mechanisms and robots

A systematic algorithm, for the complete position analysis of “any” single loop spatial mechanism, is introduced. The method yields four non-linear equations, with the least possible total degree. These equations are transformed into algebraic ones, which may be solved, analytically, based upon the concept of resultants. The solutions are free from extraneous roots, since such roots are identified and extracted by the proposed techniques. An algorithm, for the efficient position analysis of mechanisms with parallel or perpendicular joint axes and/or zero link lengths and offsets, is also given.

The Joint Displacement Method for Multiloop Kinematic Analysis

We present a kinematic formulation, referred to as the joint displacement method. In the kinematic analysis, the closed-loop kinematic chain of interest must be transformed into several open-loop chains by imagining that some joints are relaxed (disconnected), and by replacing them as physical entities with a set of constraint equations. This formulation requires only a minimal number of generalized coordinates, hence it provides a highly efficient approach for real-time kinematic analysis of spatial mechanisms, heretofore unseen in the literature. For example, the Jacobian matrix for the RSCR mechanism is 3×3 and the CPU time required to perform Gauss elimination is 182 times shorter than that in the traditional link-coordinate method which requires a 17×17 Jacobian matrix. This method is applicable to both single loop and multiloop spatial mechanisms with revolute, cylindrical, translational, spherical and universal joints. A general-purpose computer program that implements the joint displacement method has been developed and tested on a variety of mechanisms.

Tensor-matrix method in the kinematical analysis of spatial mechanisms as seen from the point of view of equivalency of mechanisms

D. Mangeron and K. Dregan have laid the foundations of the tensor-matrix method for the kinematic analysis of spatial mechanisms. However, in their presentation there are quite a lot of inaccuracies and inadequate analyses. In their paper, for the purpose of a more simple analysis, a type of equivalency mechanism is used. In the first part of the present paper an analytical proof is brought forth to show that the type of mechanism equivalency mentioned above is incorrect in principle, and that the analysis must be carried out on a real mechanism. In the second part of this paper, theoretical statements of the method given correctly in the paper by Mangeron and Dregan are presented. Here they are supplemented with a proof of the tensorial nature of the “position tensor”. Finally, the tensor-matrix method is illustrated by the analysis of a planetary mechanism.

The principle of transference: History, statement and proof

The principle of transference has been, since the last century, the center of many controversies. Despite its importance in the kinematic analysis of spatial mechanisms, and in instantaneous kinematics, no complete proof of the principle is currently available. This work presents a review of the history of the principle, then shows a clear statement of the principle, as well as a thorough proof.

A Simple Numerical Method for the Kinematic Analysis of Spatial Mechanisms

In this paper we present a new numerical method for the computer analysis of spatial mechanisms. This study is limited to the analysis of velocities and accelerations. Results are obtained in the form of a set of velocities and accelerations of different points of the mechanism. The position of all points of the mechanism is considered as known. The velocities and accelerations of as many input links as the system has degrees of freedom must also be specified. The result is the velocity and acceleration of points on the remaining links.

Kinematic Analysis of Spatial Mechanisms Using Train Components

A useful method for the kinematic analysis of spatial mechanisms is presented. For the purpose of kinematic analysis, the mechanism is treated as a consist of a number of master train components. For each master train component, geometric constitutive equations for use in kinematic analysis of mechanisms are developed. The kinematic analysis of all train components consisting the mechanism are performed as parts of the master components using a mathematical programming procedure. The analysis is followed in sequence from one train component to another as they form the entire mechanism. Numerical examples are presented to illustrate the proposed technique.

Kinematic Analysis of Spatial Mechanisms Via Successive Screw Displacements

A new, unified method is proposed and demonstrated to conduct kinematic analysis of spatial mechanisms involving revolute, cylindrical, prismatic, helical and spherical pairs. The paper derives the equations for the successive screw displacements, and the equations for pair constraints. Using these equations, closed-form relationships for displacement, velocity and acceleration of single or multi-loop spatial mechanisms are obtained by (1) breaking the mechanism at a critical joint (2) unfolding the mechanism along a straight line (3) providing successive screw displacement at each joint and (4) reassembling the mechanism to form a closed loop. The application of this newly developed approach is demonstrated by considering an example of a two-loop spatial mechanism with revolute, cylindrical and spherical pairs.

Kinematic Analysis of Spatial Mechanisms by Means of Constant-Distance Equations

The concept and use of constant-distance equations for the kinematic analysis of linkages are presented. The procedure is based on the fact that a constant-distance equation is formulated, wherever the distance between two pair-centers of a rigid link remains constant throughout its motion. This results in a much simpler kinematic analysis of the linkage. To illustrate the procedure and the feasibility of the method, the cases of spatial RRRR– and RGCR-mechanisms with coupler points are considered. The technique is well suited to digital computer analysis of complex mechanisms; extensions to dimensional synthesis as well as to dynamic and mobility analysis are possible.

Kinematic Analysis of Spatial Mechanisms by Means of Screw Coordinates. Part 1—Screw Coordinates

The concept of screw coordinates is developed in terms of motor algebra, and applied to the kinematics and statics of rigid bodies, in particular to the computer-aided motion analysis of spatial mechanisms. The laws of the composition and transformation of screw coordinates and their application to the kinematics and statics of rigid bodies are developed. These results form the basis for the development of numerical methods for the kinematic analysis of spatial mechanisms.

Kinematic Analysis of Spatial Mechanisms by Means of Screw Coordinates. Part 2—Analysis of Spatial Mechanisms

The basic concepts of screw coordinates described in Part I are applied to the numerical kinematic analysis of spatial mechanisms. The techniques are illustrated with reference to the displacement, velocity, and static-force-and-torque analysis of a general, single-degree-of-freedom spatial mechanism: a seven-link mechanism with screw pairs (H)7. By specialization the associated computer program is capable of analyzing many other single-loop spatial mechanisms. Numerical examples illustrate the results.