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Research Papers: Design of Mechanisms and Robotic Systems

Motion/Force Transmission Analysis of Parallel Mechanisms With Planar Closed-Loop Subchains

[+] Author and Article Information
Kristan Marlow

Centre for Intelligent Systems Research,
Deakin University,
Geelong, Victoria 3217, Australia
e-mail: kristan.marlow@research.deakin.edu.au

Mats Isaksson

Department of Electrical and Computer
Engineering,
Colorado State University,
Fort Collins, CO 80523-1373
e-mail: mats.isaksson@gmail.com

Jian S. Dai

Centre for Robotics Research,
King's College,
University of London,
Strand, London WC2R 2LS, UK
e-mail: jian.dai@kcl.ac.uk

Saeid Nahavandi

Centre for Intelligent Systems Research,
Deakin University,
Geelong, Victoria 3217, Australia
e-mail: saeid.nahavandi@deakin.edu.au

1Corresponding author.

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received July 20, 2015; final manuscript received March 29, 2016; published online April 29, 2016. Assoc. Editor: Oscar Altuzarra.

J. Mech. Des 138(6), 062302 (Apr 29, 2016) (11 pages) Paper No: MD-15-1514; doi: 10.1115/1.4033338 History: Received July 20, 2015; Revised March 29, 2016

Singularities are one of the most important issues affecting the performance of parallel mechanisms. A parallel mechanism with less than six degrees of freedom (6DOF) is classed as having lower mobility. In addition to input–output singularities, such mechanisms potentially suffer from singularities among their constraints. Furthermore, the utilization of closed-loop subchains (CLSCs) may introduce additional singularities, which can strongly affect the motion/force transmission ability of the entire mechanism. In this paper, we propose a technique for the analysis of singularities occurring within planar CLSCs, along with a finite, dimensionless, frame invariant index, based on screw theory, for examining the closeness to these singularities. The integration of the proposed index with existing performance measures is discussed in detail and exemplified on a prototype industrial parallel mechanism.

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References

Figures

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Fig. 1

CLSC in a parallel mechanism

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Fig. 2

Representation of a wrench of actuation for a common RSS (RUS, RUU, RRR, etc.) serial chain

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Fig. 3

(a) The vectors associated with the wrenches of the (SS)2 four-bar closed-loop and (b) the common R(SS)2 chain with various (SS)2 orientations

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Fig. 4

(a) The physical prototype of the SCARA-Tau parallel mechanism and (b) its kinematic parameters

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Fig. 5

ITI distribution throughout the SCARA-Tau's workspace. Shaded from dark at singular locations to light when furthest from singular locations according to (a). (a) Index mapping, (b) ITI1, (c) ITI2, (d) ITI3, and (e) min(ITI1,ITI2,ITI3).

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Fig. 6

OTI distribution throughout the SCARA-Tau's workspace. Shaded as per Fig. 5(a), ranging from dark at singular locations to light when furthest from singular locations. (a) OTI1, (b) OTI2, (c) OTI3, and (d) min(OTI1,OTI2,OTI3).

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Fig. 7

OTI overall minimum distribution for the SCARA-Tau with a poor parameter choice, where h3,1 = 0.400, while the other parameters are identical to those in Table 1. Shaded as per Fig. 5(a), ranging from dark at singular locations to light when furthest from singular locations.

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Fig. 8

CTI distribution throughout the SCARA-Tau's workspace. Shaded as per Fig. 5(a), ranging from dark at singular locations to light when furthest from singular locations. (a) CTI1,1, (b) CTI2,1, (c) CTI2,2, and (d) min(CTI1,1,CTI2,1,CTI2,2).

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Fig. 9

ICCI distribution throughout the SCARA-Tau's workspace. Shaded as per Fig. 5(a), ranging from dark at singular locations to light when furthest from singular locations. (a) ICCI1,11, (b) ICCI2,11, (c) ICCI2,21, and (d) min(ICCI1,11,ICCI2,11,ICCI2,21).

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Fig. 10

The SCARA-Tau mechanism in a singularity free location, [x, y, z] = [1.4, 0, 0], from (a) an angled and (b) top view and close to an ICCS of the yaw constraining parallelogram at point [x, y, z] = [0.5, 0, 0], from (c) an angled and (d) top view. The point of analysis is indicated by the cross.

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Fig. 11

(a) The OSI distribution throughout the SCARA-Tau's workspace and (b) with a lower acceptable bound on the ICCI of 0.64 applied. Shaded as per Fig. 5(a), ranging from dark at singular locations to light when furthest from singular locations.

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