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Research Papers

Unified Kinematics and Singularity Analysis of a Metamorphic Parallel Mechanism With Bifurcated Motion

[+] Author and Article Information
Dongming Gan

Robotics Institute,
Khalifa University of Science,
Technology and Research,
Abu Dhabi 127788, UAE
e-mail: dongming.gan@kustar.ac.ae

Jian S. Dai

School of Natural and Mathematical Sciences,
King's College London,
University of London,
London WC2R2LS, UK

Jorge Dias

Robotics Institute,
Khalifa University of Science,
Technology and Research,
Abu Dhabi 127788, UAE;
Faculty of Science and Technology,
University of Coimbra,
Coimbra 3000-315, Portugal

Lakmal Seneviratne

Robotics Institute,
Khalifa University of Science,
Technology and Research,
Abu Dhabi 127788, UAE;
School of Natural and Mathematical Sciences,
King's College London,
University of London,
London WC2R2LS, UK

1Corresponding author.

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANISMS AND ROBOTICS. Manuscript received July 18, 2012; final manuscript received March 28, 2013; published online June 10, 2013. Assoc. Editor: Qiaode Jeffrey Ge.

J. Mechanisms Robotics 5(3), 031004 (Jun 24, 2013) (11 pages) Paper No: JMR-12-1101; doi: 10.1115/1.4024292 History: Received July 18, 2012; Revised March 28, 2013

This paper introduces a new metamorphic parallel mechanism consisting of four reconfigurable rTPS limbs. Based on the reconfigurability of the reconfigurable Hooke (rT) joint, the rTPS limb has two phases while in one phase the limb has no constraint to the platform, in the other it constrains the spherical joint center to lie on a plane. This results in the mechanism to have ability of reconfiguration between different topologies with variable mobility. Geometric constraint equations of the platform rotation matrix and translation vector are set up based on the point-plane constraint, which reveals the bifurcated motion property in the topology with mobility 2 and the geometric condition with mobility change in altering to other mechanism topologies. Following this, a unified kinematics limb modeling is proposed considering the difference between the two phases of the reconfigurable rTPS limb. This is further applied for the mechanism modeling and both the inverse and forward kinematics is analytically solved by combining phases of the four limbs covering all the mechanism topologies. Based on these, a unified singularity modeling is proposed by defining the geometric constraint forces and actuation forces in the Jacobian matrix with their change in the variable topologies in terms of constraint screws. Analysis of workspace with singularity distribution is carried out using this model and corresponding singularity loci are obtained with special singular configurations illustrated.

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Figures

Grahic Jump Location
Fig. 1

Two phases of the rTPS limb (a) (rT)1PS and (b) (rT)2PS

Grahic Jump Location
Fig. 2

The 4(rT)2PS MPM with bifurcated motion

Grahic Jump Location
Fig. 3

Variable topologies of the 4(rT)PS MPM (a) 3(rT)2PS-1(rT)1PS (1T2R), (b) 2(rT)2PS-2(rT)1PS (2T2R), (c) 1(rT)2PS-3(rT)1PS (2T3R), and (d) 4(rT)1PS (3T3R)

Grahic Jump Location
Fig. 4

Unified limb modeling

Grahic Jump Location
Fig. 5

Workspace and singular configurations of 4(rT)2PS (2DOF) (a) workspace with singularity distribution, (b) singularity 1, (c) singularity 2, and (d) singularity 3

Grahic Jump Location
Fig. 6

Workspace and singularity locus of the 3(rT)2PS-1(rT)1PS (3DOF) (a) workspace with singularities (3D view), (b) workspace with singularities (top view), (c) singularity locus, (d) singularity 4

Grahic Jump Location
Fig. 8

Singularity 6 in two different configurations (a) home position (b) a general configuration (px = −4, py = 2, and pz = 8)

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