Dynamics of Parallel Robots

Briot, Sébastien; Khalil, Wisama

doi:10.1007/978-3-319-19788-3

Cited by 72 publications

(42 citation statements)

References 40 publications

(51 reference statements)

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“…where H is the homogeneous transformation matrix [55] and ZYX sequence of Euler angles is assumed to calculate the rotation matrix ξ ξ ξ (see Eq. (23)).…”

Section: Conversely We May Writementioning

confidence: 99%

Optomechanics of a stable diffractive axicon light sail

Srivastava

Swartzlander

2020

Eur. Phys. J. Plus

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Beamed propulsion of a light sail based on radiation pressure benefits from a passively self-stabilizing "beam riding" diffractive film. We describe the optomechanics of a rigid non-spinning light sail that mitigates catastrophic sail walk-off and tumbling by use of a flat axicon diffraction grating. A linear stability analysis and numerical integration of the coupled translational and rotational equations of motion are examined. Stability is traded against longitudinal acceleration. The examined system achieves 90% of the theoretical longitudinal force limit and stability against a relative sail translation up to 30% of the sail radius when the payload is attached to a long boom. Administration (NASA, Innovative Advanced Concepts Office), Award Number 80NSSC18K0867. We are grateful to Ying-Ju Lucy Chu and Amber Dubill, Rochester Institute of Technology, for discussions related to radiation pressure and rigid body dynamics, and to Les Johnson and Andy Heaton, NASA Marshall Space Flight Center, for discussions on light sailing.

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“…where H is the homogeneous transformation matrix [55] and ZYX sequence of Euler angles is assumed to calculate the rotation matrix ξ ξ ξ (see Eq. (23)).…”

Section: Conversely We May Writementioning

confidence: 99%

Optomechanics of a stable diffractive axicon light sail

Srivastava

Swartzlander

2020

Eur. Phys. J. Plus

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“…10(b). Once all the three regions {W i } 3 1 are available, their intersection yields the fixed-orientation workspace sought. Researchers usually discretize one of the three coordinates, e.g., the Z-coordinate, then find the workspace shape on different layers.…”

Section: Workpace Analysismentioning

confidence: 99%

“…a parallel-kinematics machine (PKM), is defined as a multi-degree-of-freedom (multi-dof) articulated mechanical system composed of one moving platform (MP) and one base platform (BP), connected by at least two serial limbs [1]. Compared with their serial counterparts, PKMs offer many attractive features, as per the pertinent literature [1][2][3]. On the other hand, PKMs suffer of limited workspace, multiple singularities and coupled motion 1 , which makes their control especially challenging.…”

Section: Introductionmentioning

confidence: 99%

A Novel Three-Loop Parallel Robot With Full Mobility: Kinematics, Singularity, Workspace, and Dexterity Analysis

Ángeles

2017

Journal of Mechanisms and Robotics

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A novel parallel robot, dubbed the SDelta, is the subject of this paper. SDelta is a simpler alternative to both the well-known Stewart–Gough platform (SGP) and current three-limb, full-mobility parallel robots, as it contains fewer components and all its motors are located on the base. This reduces the inertial load on the system, making it a good candidate for high-speed operations. SDelta features a symmetric structure; its forward-displacement analysis leads to a system of three quadratic equations in three unknowns, which admits up to eight solutions, or half the number of those admitted by the SGP. The kinematic analysis, undertaken with a geometrical method based on screw theory, leads to two Jacobian matrices, whose singularity conditions are investigated. Instead of using the determinant of a 6 × 6 matrix, we derive one simple expression that characterizes the singularity condition. This approach is also applicable to a large number of parallel robots whose six actuation wrench axes intersect pairwise, such as all three-limb parallel robots whose limbs include, each, a passive spherical joint. The workspace is analyzed via a geometric method, while the dexterity analysis is conducted via discretization. Both show that the given robot has the potential to offer both large workspace and good dexterity with a proper choice of design variables.

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“…While any formulation for modeling general multibody systems can be applied, the robotics community needs tailored modeling approaches, in particular such that take into account the modularity inherent to the majority of PKM. There are basically two formulations reported in the literature that respond to this demand; one is the formulation by Angeles [1] and the other that by Briot and Khalil [2]. Both yield equations of motion (EOM) in terms of joint coordinates.…”

Section: Introductionmentioning

confidence: 99%

“…The latter makes explicit use of the modularity of PKM, and supports a modular modeling. For details, and for a short discussion of the methods in [1,2], the reader is referred to [7].…”

Section: Introductionmentioning

confidence: 99%

A Modular Geometric Approach to Dynamics Modeling of Fully-Parallel PKM by Example of a Planar 3RPR Mechanism

Müller

2020

Mechanisms and Machine Science

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The modeling of parallel kinematic machines (PKM) has been a topic of ongoing research since PKM started to gain popularity more than twenty years ago. Due to the modular setup of most PKM, research has been conducted towards modular modeling paradigms. This applies in particular to so-called fully parallel PKM. Recently, a general modeling approach was introduced for such PKM, which rests on a Lie group formulation of the kinematics and dynamics. Therein, the PKM kinematics is described by means of screw coordinates, which makes this a user-friendly approach free from restrictive modeling conventions. In this paper, application of the method is demonstrated for a simple planar 3RPR PKM.

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Dynamics of Parallel Robots

Cited by 72 publications

References 40 publications

Optomechanics of a stable diffractive axicon light sail

Optomechanics of a stable diffractive axicon light sail

A Novel Three-Loop Parallel Robot With Full Mobility: Kinematics, Singularity, Workspace, and Dexterity Analysis

A Modular Geometric Approach to Dynamics Modeling of Fully-Parallel PKM by Example of a Planar 3RPR Mechanism

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