1986
DOI: 10.1177/027836498600500207
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A New Method for the Singularity Analysis of Simple Six-link Manipulators

Abstract: This paper presents a new method for identifying conditions governing all singular configurations of simple six-link manipulators whose inverse kinematic position problems have closed-form solutions. The method is developed based on the concepts of service sphere, free service region, and dextrous wrist. For a simple six-link manipulator, we identify its singular state with finite internal degrees of freedom by using the conditions that cause the manipulator's inverse solutions to be indeterminate. Meanwhile i… Show more

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Cited by 58 publications
(19 citation statements)
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“…D. Gottlieb [19] proved their observation while D. Baker [20] used topological argument to confirm them. Inter alia method, analytical approach by dividing the Jacobian matrix in four distinct square matrix [21],identification method by developing equation on the sphere [22], algebraic based on screw theory and it reciprocal [23,25,30],forward and inverse kinematic equation approach [24,31,32,34,35], singularity isolation or removing the degenerate part method [26,36], geometric classification method [27][28][29], quaternion based on geometry algebra [38,39],constraint and actuated force method [33]etc … Although, singular configuration of serial robot could be detected by software simulation [37], the large expressions of det( ) t J is still a challenge for researchers. In this scope J.…”
Section: Introductionmentioning
confidence: 99%
“…D. Gottlieb [19] proved their observation while D. Baker [20] used topological argument to confirm them. Inter alia method, analytical approach by dividing the Jacobian matrix in four distinct square matrix [21],identification method by developing equation on the sphere [22], algebraic based on screw theory and it reciprocal [23,25,30],forward and inverse kinematic equation approach [24,31,32,34,35], singularity isolation or removing the degenerate part method [26,36], geometric classification method [27][28][29], quaternion based on geometry algebra [38,39],constraint and actuated force method [33]etc … Although, singular configuration of serial robot could be detected by software simulation [37], the large expressions of det( ) t J is still a challenge for researchers. In this scope J.…”
Section: Introductionmentioning
confidence: 99%
“…However, the problem of determining the smooth path trajectories has only marginally been addressed in the literature. Delineation of singular behavior where the manipulator may or may not be able to cross a barrier was addressed by many researchers and is typically based on a null-space criterion of the manipulator's Jacobian [35,23,33,34,8,24,29,36]. Those barriers have traditionally been calculated using numerical methods that do not lend themselves to further study, or for designing the path to avoid encountering a barrier.…”
Section: Introductionmentioning
confidence: 99%
“…The analytic method was presented as analytical formulations for a specific class of manipulators based on a Jacobian's singularity, such as the methods reported in Refs. [4][5][6][7].…”
Section: Introductionmentioning
confidence: 99%