Research Papers

Full-Mobility Three-CCC Parallel-Kinematics Machines: Kinematics and Isotropic Design

[+] 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

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.

2R, P, H, C denote revolute, prismatic, screw and cylindrical joints, respectively, underlined symbols denoting actuated joints.

Manuscript received July 23, 2017; final manuscript received October 18, 2017; published online December 22, 2017. Assoc. Editor: Shaoping Bai.

J. Mechanisms Robotics 10(1), 011011 (Dec 22, 2017) (11 pages) Paper No: JMR-17-1217; doi: 10.1115/1.4038306 History: Received July 23, 2017; Revised October 18, 2017

The subject of this paper is twofold: the kinematics and the isotropic design of six degrees-of-freedom (DOF), three-CCC parallel-kinematics machines (PKMs). Upon proper embodiment and dimensioning, the PKMs discussed here, with all actuators mounted on the base, exhibit interesting features, not found elsewhere. One is the existence of an isotropy locus, as opposed to isolated isotropy points in the workspace, thereby guaranteeing the accuracy and the homogeneity of the motion of the moving platform (MP) along different directions within a significantly large region of their workspace. The conditions leading to such a locus are discussed in depth; several typical isotropic designs are brought to the limelight. Moreover, the kinematic analysis shows that rotation and translation of the MP are decoupled, which greatly simplifies not only the kinetostatic analysis but also, most importantly, their control. Moreover, it is shown that the singularity loci of this class of mechanism are determined only by the orientation of their MP, which also simplifies locus evaluation and eases its representation.

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Fig. 2

An embodiment of the C-drive

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Fig. 1

An example of a three-CCC PKM

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Fig. 3

The determination of the BP and MP using di, c0, and pi

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Fig. 4

The surface of feasible points of isotropy within a cube of edge length

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Fig. 5

The surface of feasible points of isotropy within a cube of edge length 1.5

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Fig. 6

An example of an isotropic design for layout I

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Fig. 7

An example of an isotropic design for layout II

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Fig. 9

An example of an isotropic design for layout IV

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Fig. 8

An example of an isotropic design for layout III



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