Kinematic analysis of geared robotic mechanism using matroid and T-T graph methods

Abstract

A. ABSTRACTIn this paper, the kinematic structure of the geared robotic mechanism (GRM) is investigated with the aid of two different methods which are based on directed graphs and the methods are compared. One of the methods is Matroid Method developed by Talpasanu and the other method is Tsai-Tokad (T-T) Graph method developed by Uyguroglu and Demirel. It is shown that the kinematic structure of the geared robotic mechanism can be represented by directed graphs and angular velocity equations of the mechanisms can be systematically obtained from the graphs.The advantages and disadvantages of both methods are demonstrated relative to each other. B. INTRODUCTIONKinematic and dynamic analysis of mechanical systems have been well established by using graph theory in recent years. Non-oriented and oriented graphs were used for this purpose. Nonoriented graph technique is mainly used for the kinematic analysis of robotic bevel-gear trains [1]-[4]. The oriented graph technique has been used for electrical circuits and other types of lumped physical systems including mechanical systems in one-dimensional motion since the early sixties [5]-[8]. Chou et al. [9] used these techniques to three-dimensional systems. Recently, Tokad developed a systematic approach, the so called Network Model Approach, for the formulation of three dimensional mechanical systems [10], and Uyguroglu and Tokad extended this approach for the kinematic and dynamic analysis of spatial robotic bevel-gear trains [11]. Most recently the oriented and non-oriented graph techniques were compared by Uyguroglu and Demirel [12], and the advantages of the oriented graph over the non-oriented graph were demonstrated using the kinematic analysis of bevel-gear trains. In order to overcome the weaknesses of the methods developed by Tsai and Tokad, both method were combined and the so called T-T Graph method was introduced []. On the other hand, Talpasanu et al. [] developed Matroid Method for the kinematic analysis of geared mechanisms based on directed graph as well.In this paper the kinematic structures of the GRM is investigated with the aid of Matroid Method and T-T Graph method. Since both methods are used directed graph, the similarities and the differences are shown and the advantages of each system are indicated. C. Geared Robotic MechanismGRMs are closed-loop configurations which are used to reduce the mass and inertia of the actuators' loads. Gear trains in GRMs are employed such that actuators can be placed as closely as possible to the base. Figure 1 shows functional schematic of the GRM. It has 3 Degree of Freedom (i.e. it has 3 inputs) and the end-effector can have spatial motion (3 Dimensional) because this mechanism can generate two rotations about two intersected axes and one rotation of end-effector about its axis. In this mechanism 4, 5, and 6 are sun gears (input links), 1 and 2

A review on topological architecture and design methods of cable-driven mechanism

“…Network model, non-oriented and oriented graphs, and a few extended graphs models are applied to analyze the topological architecture and solve the kinematic relationships. [93][94][95][96][97][98][99] These theories and methods promote research of the cable-driven robots.…”

“…Therefore, the kinematic analysis may be easily processed based on such a table. After validating the bevel-gear trains, [93][94][95][96][97][98][99] the oriented-graph methods are utilized on the kinematic analysis of the tendon-driven mechanisms. The basic element, shown in Figure 11, is set up to present the cable-pulley unit, and the relationship between the graph and the tendon-driven mechanisms is established.…”

Kinematic Singularities of a 3-DoF Planar Geared Robot Manipulator

“…In order to enhance the computational effectiveness of the method, Talpasanu et al [6,7] refined and to some extent recast the approach, introducing the 'incidence and transfer method' that uses the cycle matroid of the mechanism's directed graph. A comparison of Talpasanu's method with that of Tsai-Tokad was made in [1]. In this paper, we illustrate Talpasanu's method for a simple geared version of a planar 3R mechanism in order to determine its kinematic mapping and thereby its singularities.…”