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Research Papers

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

[+] Author and Article Information
Kristan Marlow

Centre for Intelligent Systems Research,
Deakin University,
Geelong, VIC 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

Saeid Nahavandi

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

1Corresponding author.

Manuscript received September 29, 2015; final manuscript received March 13, 2016; published online April 19, 2016. Assoc. Editor: Jian S. Dai.

J. Mechanisms Robotics 8(4), 041019 (Apr 19, 2016) (11 pages) Paper No: JMR-15-1285; doi: 10.1115/1.4033158 History: Received September 29, 2015; Revised March 13, 2016

Singularities are one of the most important issues affecting the performance of parallel mechanisms. Therefore, analysis of their locations and closeness is essential for the development of a high-performance mechanism. The screw theory based motion/force transmission analysis provides such a closeness measure in terms of the work performed between specific mechanism twists and wrenches. As such, this technique has been applied to many serial chain parallel mechanisms. However, the motion/force transmission performance of parallel mechanisms with mixed topology chains is yet to be examined. These chains include linkages in both series and parallel, where the parallel portion is termed a closed-loop subchain (CLSC). This paper provides an analysis of such chains, where the CLSC is a planar four-bar linkage. In order to completely define the motion/force transmission abilities of these mechanisms, adapted wrench definitions are introduced. The proposed methodology is applied to a family of two degrees-of-freedom planar axis-symmetric parallel mechanisms, each with a different CLSC configuration. The presented analysis provides the first complete motion/force transmission analysis of such mechanisms.

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Figures

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Fig. 1

Two variants of the 2DOF planar axis-symmetric parallel mechanism with a CLSC: (a) the obtuse trapezium variant and (b) the triangular variant. The terms utilized to identify the different bodies within the mechanisms are labeled in (a).

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Fig. 2

Parametrization of a general variant of the studied 2DOF planar axis-symmetric parallel mechanisms

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Fig. 3

The two solutions to the mobile platform's α angle for qR2 with the same X position. The unit direction vector ŝ1 is shown from joint B2,1 to C2,1, along with ŝ2 from joint C2,1 to C2,2, for both solutions.

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Fig. 4

Planar CLSC constraints: (a) the constraint generating wrenches and (b) the equivalent constraint wrench

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Fig. 5

Actuation wrench of a serial RRR chain

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Fig. 6

Instantaneous center of the output link P for a four-bar closed-loop

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Fig. 7

The generalized forces that a planar four-bar closed-loop can transmit through its output link, given the opposite link is fixed, for (a) parallel and (b) nonparallel distal links

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Fig. 8

The ITS and OTS actuation wrenches of a general planar 2DOF axis-symmetric parallel mechanism with a CLSC

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Fig. 9

The CLSC variants utilized in the analysis with the ITI and OTI actuation wrenches overlaid. The subchain arrangements are termed (a) parallelogram, (b) obtuse trapezium, (c) acute trapezium, (d) crossed, and (e) triangular.

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Fig. 10

The planar annulus-shaped workspace of the studied 2DOF planar axis-symmetric parallel mechanisms

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Fig. 11

The ITI, OTI, and ICCI distribution plots at y = 0, x ≥ 0 for the planar 2DOF axis-symmetric parallel mechanisms with various CLSCs, using the parameters in Tables 2 and 3. The vertical axis ρ specifies the value of the indices from zero to unity. The distribution plots are for the (a) parallelogram, (b) obtuse trapezium, (c) acute trapezium, (d) crossed, and (e) triangular. The legend for the index plots is given in (g). The overall minimum of the ITI and OTI cropped with an ICCI lower bound of 0.64 is illustrated in (f) for each CLSC, and are labeled according to Fig. 9.

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Fig. 12

OTS configurations for the (a) obtuse trapezium and (b) acute trapezium variants. The OTI actuation wrench of each chain is labeled and illustrated by a thick arrow, while the instantaneous output motion of the mobile platform, due to the respective output twist, is shown by a thin arrow.

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Fig. 13

Optimal OTI configurations for the (a) obtuse trapezium and (b) acute trapezium variants. The OTI actuation wrench of each chain is labeled and illustrated by a thick arrow. The instantaneous output motions of the mobile platform, due to the respective output twist, are collinear to the respective wrenches and are shown by the thin arrows.

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Fig. 14

(a) The deviation of the mobile platform's parasitic yaw angle from its mean for each variant, labeled according to Figs. 9 and 11(f). (b) The CLSC variants ordered in terms of the gradient of their respective plots.

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