Kinematic analysis of geared robotic mechanism using Matroid and T–T graph methods

Amirinezhad, S. Vahid; Uyguroğlu, M.

doi:10.1016/j.mechmachtheory.2015.02.002

Cited by 9 publications

(6 citation statements)

References 22 publications

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“…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.…”

Section: Graphic Theory and Kinematic Analysismentioning

confidence: 99%

“…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.…”

Section: Graphic Theory and Kinematic Analysismentioning

confidence: 99%

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

Hong

Jabran

Ren

2018

Advances in Mechanical Engineering

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Research on the cable-driven mechanism has greatly developed with the booming of the robots in the past 30 years, and a range of corresponding theoretical studies have been published on them. The large-scale robot or manipulator with the complex cable-driven mechanism can be reconfigured. However, more theoretical studies are required on their topological architecture design and optimization to achieve this. Therefore, the applied cable-driven architectures and the corresponding theoretical studies are reviewed and summarized here. The parallel, serial, and differential architecture are illustrated, as well as their theories and methods, such as the workspace analysis based on the Jacobian matrix, particle swarm optimization and genetic algorithm, and kinematic design based on the graph theory are described. The features of the architecture and the theory studies are concluded. It is hoped that this study will help with design of future studies.

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Section: Graphic Theory and Kinematic Analysismentioning

confidence: 99%

Section: Graphic Theory and Kinematic Analysismentioning

confidence: 99%

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

Hong

Jabran

Ren

2018

Advances in Mechanical Engineering

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“…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.…”

Section: Introductionmentioning

confidence: 99%

Advances in Robot Kinematics 2016

Lenarčič¹,

Merlet²

2018

Springer Proceedings in Advanced Robotics

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By incorporating gearing into a planar 3R mechanism, one obtains a family of mechanisms in which the gear ratios play a central kinematic role. Special choices of these parameters result in interesting simplifications of the kinematic mapping. An explicit expression for the mapping can be derived using the 'matroid method' of Talpasanu et al [7]. We use this relatively simple mechanism to illustrate singularity analysis for geared mechanisms.

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“…This approach will provide us with a set called the design-configuration space (D-space). A family of manipulators consists of a fixed topology, referred to as the architecture of the family, which can be represented combinatorically by a graph in which the links are vertices and edges connect pairs of links that are connected by a joint [86,87,88]. Moreover, the edges are annotated by the type of joint, which also determines its degrees of freedom or constraints.…”

Section: Constraints Versus Freedomsmentioning

confidence: 99%

“…In order to enhance the computational effectiveness of the method, Talpasanu et al [87] 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 [88]. In this Chapter, 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.…”

Section: Planar Geared Manipulatorsmentioning

confidence: 99%

A Constraint-Based Approach to Manipulator Kinematics and Singularities

Amirinezhad¹

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<p>In this thesis, a differential-geometric approach to the kinematics of multibody mechanisms is introduced that enables analysis of singularities of both serial and parallel manipulators in a flexible and complete way. Existing approaches such as those of Gosselin and Angeles [1], Zlatanov et al. [2] and Park and Kim [3] make use of a combination of joint freedoms and constraints and so build in assumptions. In contrast, this new approach is solely constraint-based, avoiding some of the shortcomings of these earlier theories. The proposed representation has two core ingredients. First, it avoids direct reference to the choice of inputs and their associated joint freedoms and instead focuses on a kinematic constraint map (KCM), defined by the constraints imposed by all joints and not requiring consideration of closure conditions arising from closed loops in the design. The KCM is expressed in terms of pose (i.e. position and orientation) variables, which are the coordinates of all the manipulator’s links with respect to a reference frame. The kinematics of a given manipulator can be described by means of this representation, locally and globally. Also, for a family of manipulators defined by a specific architecture, the KCM will tell us how the choice of design parameters (e.g. link lengths) affects these kinematic properties within the family. At a global level, the KCM determines a subset in the space of all pose variables, known as the configuration space (C-space) of the manipulator, whose topology may vary across the set of design parameters. The Jacobian (matrix of first-order partial derivatives) of the KCM may become singular at some specific choices of pose variables. These conditions express a subset called the singular set of the C-space. It is shown that if a family of manipulators, parametrised by a manifold Rd of design parameters, is “well-behaved” then the pose variables can be eliminated from the KCM equations together with the conditions for singularities, to give conditions in terms of design parameters, that define a hypersurface in Rd of manipulators in the class that exhibit C-space singularities. These are referred to as Grashof-type conditions, as they generalise classically known inequalities classifying planar 4-bar mechanisms due to Grashof [4]. Secondly, we develop the theory to incorporate actuator space (A-space) and workspace (W-space), based on a choice of actuated joints or inputs and on the manipulator’s end-effector workspace or outputs. This will facilitate us with a framework for analysing singularities for forward and inverse kinematics via input and output mappings defined on the manipulator’s C-space. This provides new insight into the structure of the forward and inverse kinematics, especially for parallel manipulators. The theory is illustrated by a number of applications, some of which recapitulate classical or known results and some of which are new.</p>

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Kinematic analysis of geared robotic mechanism using Matroid and T–T graph methods

Cited by 9 publications

References 22 publications

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

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

Advances in Robot Kinematics 2016

A Constraint-Based Approach to Manipulator Kinematics and Singularities

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