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Research Papers

Optimal Synthesis of a Planar Reactionless Three-Degree-of-Freedom Parallel Mechanism

[+] Author and Article Information
Jean-François Collard1

Clément Gosselin

 Département de génie mécanique, Université Laval, Quebec (QC), G1V 0A6, Canadagosselin@gmc.ulaval.ca

1

Corresponding author.

J. Mechanisms Robotics 3(4), 041009 (Oct 24, 2011) (9 pages) doi:10.1115/1.4004897 History: Received December 14, 2010; Revised June 13, 2011; Published October 24, 2011; Online October 24, 2011

A reactionless mechanism is one in which no reaction forces nor moments are transmitted to the base for any arbitrary motion. This interesting property often requires to increase the total mass and the moments of inertia, leading to reduced dynamical performances. Therefore, this paper presents an optimization approach to synthesize and improve the dynamical performance of a reactionless three-degree-of-freedom planar mechanism. The three legs of this original mechanism are composed of reactionless four-bar mechanisms dynamically balanced with only one counter-rotation at the base. The optimization variables are the geometric and inertial parameters, whereas the goal is to minimize the global moment of inertia of each leg. This will reduce the power consumption of the three actuators and increase the agility. To meet physical and realistic requirements, the optimization problem is also constrained with bounds on the parameters, with the reachability of a given workspace and with a given range on a kinematic sensitivity index. Since different initial guesses of the optimization process lead to similar objective results, it is proposed to search for several local solutions (morphologies). A methodology is therefore developed to explore the design space and group the results after refinement. The final choice among the obtained solutions is made using additional design criteria based on the sensitivity in terms of dynamic balancing and power consumption with respect to the design parameters.

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Copyright © 2011 by American Society of Mechanical Engineers
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Figures

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Figure 1

A reactionless three-degree-of-freedom planar parallel mechanism with nine generalized coordinates

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Figure 2

Design parameters of a leg of the mechanism

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Figure 3

Two assembly modes of the three-degree-of-freedom planar parallel mechanism

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Figure 4

Equivalence between a disk platform and three point masses with six constraint forces

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Figure 5

Actuation power during the proposed simulation at 0.5 Hz

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Figure 6

The reachable workspace is the intersection of the three outer disks

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Figure 7

The kinematic sensitivity index is computed in ten points over the required workspace

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Figure 8

Evolution of the objective function and the mass along the optimization process

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Figure 9

Comparison between initial and optimal mechanisms (first optimization)

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Figure 10

Power consumption of the first actuator of the optimum mechanisms during the proposed simulation at 0.5 Hz. The power consumption of the other two actuators is phase-shifted by ±120 deg with respect to the first one.

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Figure 11

Comparison between initial and optimal mechanisms (second optimization). Only the first leg is represented here for clarity, the other two are obtained by rotations of ± 120 deg of the first one.

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Figure 12

Nine first locally-optimum mechanisms sorted from the best to the worst

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Figure 13

Analysis of 12 local optima with similar parameters

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Figure 14

Position error of joints and center of mass of link j

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