Singular Phenomena in Kinematics

Donelan, Peter; Gibson, C. G.

doi:10.1017/cbo9780511569265.024

Cited by 4 publications

(3 citation statements)

References 40 publications

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“…However, there is still much work to do before having definitive geometric conditions for general 6-R robots. Resorting to some transversality theorems used by singularity theorists would help going further, providing that we remain in the generic case (Pai and Leu, 1991), (Donelan and Gibson, 1999), (Donelan and Müller, 2010). So the first step would be to enumerate all 6-R generic robots.…”

Section: Discussionmentioning

confidence: 99%

Cuspidal Robots

Wenger¹

2019

Singular Configurations of Mechanisms and Manipulators

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This chapter is dedicated to the so-called cuspidal robots, i.e. those robots that can move from one inverse geometric solution to another without meeting a singular confuguration. This feature was discovered quite recently and has then been fascinating a lot of researchers. After a brief history of cuspidal robots, the chapter provides the main features of cuspidal robots: explanation of the non-singular change of posture, uniqueness domains, regions of feasible paths, identification and classification of cuspidal robots. The chapter focuses on 3-R orthogonal serial robots. The case of 6-dof robots and parallel robots is discussed in the end of this chapter.

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Section: Discussionmentioning

confidence: 99%

Cuspidal Robots

Wenger¹

2019

Singular Configurations of Mechanisms and Manipulators

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“…However, there is still much work to do before having definitive geometric conditions for general 6R robots. Resorting to some transversality theorems used by singularity theorists would help going further, providing that we remain in the generic case 16,49 . So the first step would be to enumerate all 6R generic manipulators.…”

Section: Discussionmentioning

confidence: 99%

Cuspidal and noncuspidal robot manipulators

Wenger¹

2007

Robotica

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This article synthezises the most important results on the kinematics of cuspidal manipulators i.e. nonredundant manipulators that can change posture without meeting a singularity. The characteristic surfaces, the uniqueness domains and the regions of feasible paths in the workspace are defined. Then, several sufficient geometric conditions for a manipulator to be noncuspidal are enumerated and a general necessary and sufficient condition for a manipulator to be cuspidal is provided. An explicit DH-parameter-based condition for an orthogonal manipulator to be cuspidal is derived. The full classification of 3R orthogonal manipulators is provided and all types of cuspidal and noncuspidal orthogonal manipulators are enumerated. Finally, some facts about cuspidal and noncuspidal 6R manipulators are reported.

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“…Hence, the condition for a singular constraint Jacobian is the linear dependence of more than n-r m of the instantaneous joint screws. Finding the condition that a set of given screws forms a screw system of certain rank is a very difficult problem that has been addressed in series of publications (Gibson 1999;Gibson and Hunt 1990a, b;Hunt 1986;Karger 1996;Kieffer 1992Kieffer , 1994Lipkin and Pohl 1991;Litvin et al 1986;McCarthy 2000;Rico and Duffy 1992a, b;Rico et al 1995).…”

Section: Forward Kinematic Singularities Of Serial Manipulatorsmentioning

confidence: 99%

Manipulator Velocities and Static Forces

Zhang¹,

Zhang²,

Müller³

2014

Handbook of Manufacturing Engineering and Technology

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Robotic manipulators are mechanisms that are used to transmit motions and forces. Their kinematic and static properties are thus basic characteristics that must be analyzed when controlling them but also within the design phase. Such kinematic properties are the transmission of joint rates to the end-effector velocities. The dual property is the transformation of end-effector forces to joint forces. This requires adequate modeling of the manipulators, where serial and parallel manipulators must be distinguished. Special situations where these transformation properties change drastically are so-called singularities.In this chapter, the kinematic modeling is reviewed making use of recursive frame transformation. The velocity and force transformation relation is derived and explained for several manipulators, serial as well as parallel manipulators. The phenomenon of singularities is discussed, and the conditions for the existence of singularities are presented.The motion planning and control requires the solution of the inverse kinematic problem. This is also discussed in this paper. In particular, kinematic redundancy and redundant actuation are introduced, and the inverse problem discussed.where V is the platform velocity and _ q are the actuator joint rates. This kinematic model involves two Jacobians, each of which can become singular. This has been first addressed in (Gosselin and Angeles 1990). Configurations where B becomes singular are called type I singularities, and when Handbook of Manufacturing Engineering and Technology

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Singular Phenomena in Kinematics

Cited by 4 publications

References 40 publications

Cuspidal Robots

Cuspidal Robots

Cuspidal and noncuspidal robot manipulators

Manipulator Velocities and Static Forces

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