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Research Papers

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

[+] Author and Article Information
Wei Li

Department of Mechanical Engineering,
Centre for Intelligent Machines,
McGill University,
Montreal, QC H3A 0C3, Canada
e-mail: livey@cim.mcgill.ca

Jorge Angeles

Professor
Fellow ASME
Department of Mechanical Engineering,
Centre for Intelligent Machines,
McGill University,
Montreal, QC H3A 0C3, Canada
e-mail: angeles@cim.mcgill.ca

1Corresponding author.

Manuscript received October 3, 2016; final manuscript received June 10, 2017; published online August 4, 2017. Assoc. Editor: Andreas Mueller.

J. Mechanisms Robotics 9(5), 051003 (Aug 04, 2017) (10 pages) Paper No: JMR-16-1286; doi: 10.1115/1.4037112 History: Received October 03, 2016; Revised June 10, 2017

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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References

Figures

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Fig. 1

Topology of the SDelta robot

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Fig. 2

Topology of the C-drive

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Fig. 3

Architecture of the SDelta robot

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Fig. 4

An embodiment of the C-drive

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Fig. 5

Notation for the kinematic chain of the jth limb of the SDelta robot

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Fig. 6

The reference posture of the MP

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Fig. 7

The workspace and singularity of the SDelta under the reference orientation: (a) design I and (b) design II

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Fig. 8

The workspace and singularity of the SDelta with the orientation e=[0,0,1]T and ϕ=15 deg: (a) design I and (b) design II

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Fig. 9

The workspace and singularity of the SDelta with the orientation e=[0,1,0]T and ϕ=15 deg: (a) design I and (b) design II

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Fig. 10

Illustration of the workspace formulation based on the geometric method

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Fig. 11

The workspace of the Sdelta under the reference orientation: (a) design I and (b) design II

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Fig. 12

The workspace of the SDelta with the orientation e=[0,0,1]T and ϕ=15 deg: (a) design I and (b) design II

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Fig. 13

The workspace of the SDelta with the orientation e=[0,1,0]T and ϕ=15 deg: (a) design I and (b) design II

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Fig. 14

The workspace volume with respect to the ratio of a/b, under different orientations

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Fig. 15

The dexterity of the SDelta on the layers of z=0.3,0.6,0.9,1.2, with the orientation e=[0,0,1]T and ϕ=15 deg: (a) design I and (b) design II

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Fig. 16

The dexterity of the SDelta on the layers of z=0.3,0.6,0.9,1.2, with the orientation e=[0,1,0]T and ϕ=15 deg: (a) design I and (b) design II

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