Research Papers

A Novel Kinematically Redundant Planar Parallel Robot Manipulator With Full Rotatability

[+] Author and Article Information
Nicholas Baron

School of Engineering and Informatics,
University of Sussex,
Brighton BN1 9RH, UK
e-mail: n.baron@sussex.ac.uk

Andrew Philippides

School of Engineering and Informatics,
University of Sussex,
Brighton BN1 9RH, UK
e-mail: andrewop@sussex.ac.uk

Nicolas Rojas

Dyson School of Design Engineering,
Imperial College London,
London SW7 2DB, UK
e-mail: n.rojas@imperial.ac.uk

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANISMS AND ROBOTICS. Manuscript received May 25, 2018; final manuscript received September 26, 2018; published online November 13, 2018. Assoc. Editor: Damien Chablat.

J. Mechanisms Robotics 11(1), 011008 (Nov 13, 2018) (8 pages) Paper No: JMR-18-1151; doi: 10.1115/1.4041698 History: Received May 25, 2018; Revised September 26, 2018

This paper presents a novel kinematically redundant planar parallel robot manipulator, which has full rotatability. The proposed robot manipulator has an architecture that corresponds to a fundamental truss, meaning that it does not contain internal rigid structures when the actuators are locked. This also implies that its rigidity is not inherited from more general architectures or resulting from the combination of other fundamental structures. The introduced topology is a departure from the standard 3-RPR (or 3-RRR) mechanism on which most kinematically redundant planar parallel robot manipulators are based. The robot manipulator consists of a moving platform that is connected to the base via two RRR legs and connected to a ternary link, which is joined to the base by a passive revolute joint, via two other RRR legs. The resulting robot mechanism is kinematically redundant, being able to avoid the production of singularities and having unlimited rotational capability. The inverse and forward kinematics analyses of this novel robot manipulator are derived using distance-based techniques, and the singularity analysis is performed using a geometric method based on the properties of instantaneous centers of rotation. An example robot mechanism is analyzed numerically and physically tested; and a test trajectory where the end effector completes a full cycle rotation is reported. A link to an online video recording of such a capability, along with the avoidance of singularities and a potential application, is also provided.

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Fig. 1

Kinematic diagram of the proposed robot mechanism. The architecture consists of a moving platform connected directly to the base via two RRR legs and connected to a ternary link, which is joined to the base by a passive revolute joint, via two other RRR legs.

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Fig. 2

Equivalent kinematic model used for solving the forward kinematics; it corresponds to the mechanism obtained when the robot actuators are fixed at particular values. This model also applies for a robot manipulator with type RPR legs.

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Fig. 3

Resulting configurations of the example used in the forward kinematic analysis

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Fig. 4

Kinematic diagram of 3-RPR mechanism with the links numbered and with the ICRs of the M = 1 sub-mechanisms shown (links 1, 2, 3, and 5; links 1, 2, 4, and 5; and links 1, 3, 4, and 5)

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Fig. 5

Circle diagram for M = 1 submechanism with link 4 removed (left) and link 3 removed (right) for the case of the 3-RPR robot manipulator. See text for details.

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Fig. 6

Kinematic diagram of proposed mechanism with links numbered. ICR(1,7) for the submechanisms (ii) and (iii) is shown.

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Fig. 7

Circle diagram for M = 1 submechanism with link 5 removed (left) and link 4 removed (right) for the case of the introduced kinematically redundant architecture

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Fig. 8

A comparison between d and the inverse of the condition number of the Jacobian, 1/k(J), of the proposed mechanism with RPR legs

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Fig. 9

Prototype of the novel kinematically redundant planar parallel robot manipulator. An online video of this prototype completing a 2π rotation about a single point, avoiding singularities, and performing a pick-and-place trajectory of full rotation can be seen.1

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Fig. 10

Graph displaying d, the distance between the two ICR (1,7)s, against ϕ, the angular displacement of the end-effector along the rotation trajectory



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