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Research Papers

Modeling and Analysis of Parallel Mechanisms With Both Kinematic and Actuation Redundancies Via Screw Theory

[+] Author and Article Information
Long Kang

Department of Electronic Systems Engineering,
Hanyang University,
Ansan 15588, Gyeonggi-do, South Korea
e-mail: hitjakie@gmail.com

Wheekuk Kim

Professor
Department of Electro-Mechanical System
Engineering,
Korea University,
2511, Sejong-ro,
Sejong 339-700, South Korea
e-mail: wheekuk@korea.ac.kr

Byung-Ju Yi

Professor
Department of Electronic Systems Engineering,
Hanyang University,
Ansan 15588, Gyeonggi-do, South Korea
e-mail: bj@hanyang.ac.kr

1Corresponding author.

Manuscript received April 13, 2017; final manuscript received August 22, 2017; published online September 20, 2017. Assoc. Editor: Clement Gosselin.

J. Mechanisms Robotics 9(6), 061007 (Sep 20, 2017) (12 pages) Paper No: JMR-17-1108; doi: 10.1115/1.4037805 History: Received April 13, 2017; Revised August 22, 2017

Two kinds of mechanical redundancies, namely kinematic redundancy and actuation redundancy, have been extensively studied due to their advantageous features in autonomous industry. Screw theory has been successfully applied to develop an analytical Jacobian of nonredundant parallel manipulators (PMs). However, to the best of our knowledge, screw theory has not been attempted for modeling of PMs with kinematic redundancies. Thus, first, through the mobility analysis of a simple nonredundant planar PM and its variations, this paper reviews kinematic and actuation redundancy systematically. Then, we demonstrated how to derive analytical Jacobian and also static force relationship for a PM with both kinematic and actuation redundancies by using the screw theory. Finally, simulations were performed to demonstrate the advantageous features of kinematic and actuation redundancies.

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References

Figures

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Fig. 1

Schematic diagram of the 3-RRR nonredundant manipulator

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Fig. 2

Schematic diagram of the 3-RPRR kinematically redundant manipulator

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Fig. 3

Schematic diagram of the RRR-RPRR-RPRRR kinematically redundant manipulator

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Fig. 4

Schematic diagram of the 4-RRR redundantly actuated manipulator

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Fig. 5

Flowchart of the hybrid resolution algorithm

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Fig. 6

Desired trajectory and initial configuration

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Fig. 7

Joint configurations during the trajectory: case of minimum norm solution

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Fig. 8

Link length variations of the three redundant prismatic joints: case of minimum norm solution

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Fig. 10

Link length variations of the three redundant prismatic joints: case of optimized null-space solution

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Fig. 11

Variations of det(AAT) for two different inverse kinematic solutions of 3-RPRR PM

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Fig. 9

Joint configurations during the trajectory: case of optimized null-space solution

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Fig. 12

Comparison of 2-norm of the actuation torque/force of the 3-RPRR PM with that of the 3-RPRR PM

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