Dexterous workspace optimization of an asymmetric six-degree of freedom Stewart–Gough platform type manipulator

Toz, Metin; Küçük, Serdar

doi:10.1016/j.robot.2013.07.004

Cited by 40 publications

(28 citation statements)

References 37 publications

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“…Gao et al [2] used these distance and angular constraints for categorizing GSP mechanisms into 4 classes, namely 6D, 5D1A, 4D2A, and 3D3A. Toz and Kucuk [9] ignored the constraints defined by means of the plane geometric primitives due to their inconvenience [9]. They used the remaining constraints (1 angular and 4 distance constraints) to design 6-DOF of GSP mechanisms.…”

Section: Gsp Mechanismsmentioning

confidence: 99%

“…These constraints were named D 1 , D 2 , D 3 , D 4 , and A 1 for the point-point distance constraint, line-point distance constraint, point-line distance constraint, line-line distance constraint, and lineline angular constraint, respectively. According to these constraint types, Toz and Kucuk [9] reduced the possible combinations of GSP mechanisms from 3850 to 195 using the same combination formula used by Gao et al [2]. They also grouped 195 GSP mechanisms into 6D, 5D1A, 4D2A, and 3D3A classes [9].…”

Section: Gsp Mechanismsmentioning

confidence: 99%

“…In this section, the methodology for building the inverse Jacobian matrix of 195 GSP mechanisms is described by 2 examples: a symmetrical D 3 GSP mechanism given in Figure 5 is a member of the 6D class given in [9]. It has 6 D 3 type constraints between the base and the moving platforms.…”

Section: Building Inverse Jacobian Matrices For 195 Gsp Mechanismsmentioning

confidence: 99%

“…On the other hand, Toz and Kucuk [9] proposed a criterion to achieve feasible structures among the 3850 GSP mechanisms. This criterion disregards planar joints, which are not used in practical applications [9]. Thus, 3850 GSP mechanisms are reduced to 195 GSPs, which include 191 asymmetrical and 4 symmetrical GSP mechanisms.…”

Section: Introductionmentioning

confidence: 99%

“…It is well known that the inverse Jacobian matrix provides an instantaneous transformation between joint velocities and linear and angular velocities of the end-effector [5]. It can be used in several analysis processes of these mechanisms, such as the performance evaluation [9][10][11][12][13][14] and dynamical analysis [15]. A condition number based on the maximum and minimum singular values of the inverse Jacobian matrix is computed in general for performance evaluation of parallel manipulators [16][17][18][19].…”

Section: Introductionmentioning

confidence: 99%

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Development of derivation of inverse Jacobian matrices for 195 6-DOF GSP mechanisms

Toz¹,

Küçük²

2016

Turk J Elec Eng & Comp Sci

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Abstract:One of the key issues in robotics is finding high-performance manipulator structures. To evaluate the performance of a parallel manipulator, researchers mostly use kinematic performance indices (such as condition number, minimum singular value, dexterity, and manipulability), which are based on inverse Jacobian matrices. Driving the inverse Jacobian matrix of even one parallel manipulator is a very cumbersome process. However, in this paper, general equations for the inverse Jacobian matrices of 195 GSP mechanisms are symbolically derived by considering 4 basic leg types having 1 angular and 4 distance constraints. With the help of these general equations, the development of the inverse Jacobian matrix for a GSP mechanism can be achieved by defining only the leg connection points on the base and moving platforms with minimum cost. Having derived the inverse Jacobian matrices, one can directly compute kinematic performance indices to measure and compare the manipulator performance of the 195 GSP mechanism. These analyses may yield new high-performance GSP mechanisms for use in engineering, medical device design, and other applied branches. Two different mechanisms (symmetrical and asymmetrical) are given as examples to describe the methodology for deriving the inverse Jacobian matrices. Finally, 2 numerical examples are given for illustrating the practical applications of the procedure.

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Section: Gsp Mechanismsmentioning

confidence: 99%

Section: Gsp Mechanismsmentioning

confidence: 99%

Section: Building Inverse Jacobian Matrices For 195 Gsp Mechanismsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Development of derivation of inverse Jacobian matrices for 195 6-DOF GSP mechanisms

Toz¹,

Küçük²

2016

Turk J Elec Eng & Comp Sci

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Parallel manipulator software tool for design, analysis, and simulation of 195 GSP mechanisms

Toz

Küçük

2015

Comp Applic In Engineering

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ABSTRACT:In this paper, a new parallel manipulator software tool based on the MATLAB Graphical User Interface (GUI) is developed for design, analysis and simulation of 195 6-DOF General Stewart Platform mechanisms (GSP). The new proposed tool called as GSPDAP uses four basic leg types (SPS, SPC, CPS, and CCC) to design GSP mechanisms. Point or line coordinates required for leg connections are sufficient for GSPDAP to design a GSP mechanism. Once the design of a GSP mechanism is completed, GSPDAP provides the user with several analyses such as inverse kinematics, Jacobian matrix, workspace, and dexterity. It is not necessary for the user to have preliminary knowledge to obtain the inverse kinematics or Jacobian matrix etc. Additionally, GSPDAP generates symbolic equations for the inverse kinematics and the inverse Jacobian matrices of 195 GSP mechanisms. Including 195 parallel manipulator in its library, GSPDAP provides the educational users to profoundly improve the understanding of parallel manipulator fundamentals through interactive simulation. Parallel manipulators are more complex structures than their serial counterparts. Therefore, designing even one parallel manipulator is very cumbersome and expensive issue. In this condition GSPDAP may provide educators and students to design their manipulators in a computer environment with minimum cost. ß 2015 Wiley Periodicals, Inc. Comput Appl Eng Educ 23:931-946, 2015; View this article online at wileyonlinelibrary.com/journal/ cae;

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Using Standard Components in Evolutionary Robotics to Produce an Inexpensive Robot Arm

Louwrens

Plessis

Greyling

2015

Advances in Intelligent Systems and Computing

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Dexterous workspace optimization of an asymmetric six-degree of freedom Stewart–Gough platform type manipulator

Cited by 40 publications

References 37 publications

Development of derivation of inverse Jacobian matrices for 195 6-DOF GSP mechanisms

Development of derivation of inverse Jacobian matrices for 195 6-DOF GSP mechanisms

Parallel manipulator software tool for design, analysis, and simulation of 195 GSP mechanisms

Using Standard Components in Evolutionary Robotics to Produce an Inexpensive Robot Arm

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