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Research Papers

# Multiobjective Optimum Design of a Symmetric Parallel Schönflies-Motion Generator

[+] Author and Article Information
O. Altuzarra, A. Hernandez

Department of Mechanical Engineering, University of the Basque Country, Alameda de Urquijo s/n, Bilbao 48013, Spain

Ikerlan S. Coop., Paseo Jose Maria Arizmendiarrieta 2, Arrasate 20500, Spain

J. Angeles

Department of Mechanical Engineering, Centre of Intelligent Machines, 817 Sherbrooke Street West, Montreal, QC, H3A 2K6, Canada

The parallelogram is regarded as a kinematic pair that allows for a pure translation of the parallelogram link at $Cj$ along a circle of radius $BjCj¯$.

Plots of the volume function can seem contradictory, as one can expect the plot corresponding to $a/d=1$ between the other ones. This is because the complete definition of the plots would require the definition of the relations among parameters $a$, $d$, and $r$.

The dexterity index $ϵg$ was evaluated discretizing the workspace in 199,927 points.

J. Mech. Des 131(3), 031002 (Jan 26, 2009) (11 pages) doi:10.1115/1.3066659 History: Received January 31, 2008; Revised November 25, 2008; Published January 26, 2009

## Abstract

The multiobjective optimization of a four-degree-of-freedom symmetric parallel manipulator for Schönflies-motion generation is the subject of this paper. First, the inverse positioning problem is discussed, along with its velocity analysis. The workspace is then analyzed, thereby deriving a closed-form expression of the workspace volume, which depends on the orientation of the moving platform. Next, the isotropic design of the manipulator is obtained. Then, the dexterity analysis of the manipulator is conducted, which is one objective of the optimum design of the manipulator, a second objective being a normalized workspace volume. Finally, the results of the optimization process are reported in terms of a set of Pareto-optimum pairs of the design parameters.

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## Figures

Figure 1

4DOF fully symmetric Schönflies-motion generator

Figure 2

Top view of both the MP and the BP

Figure 3

Workspace of the manipulator for a defined orientation angle, with a/r=0.1, d/r=0.15, and θ=−π/4

Figure 4

Top views of the workspace of the manipulator for different values of angle θ

Figure 5

Volume of the robot workspace for different values of the ratio a/d

Figure 6

Isotropic posture of the manipulator for Jacobian matrices J¯v and Jq for a/r=3/15 and d/r=23/15

Figure 7

Dexterity maps corresponding to constant-orientation workspaces of the manipulator with proportions a/r=0.1375 and d/r=0.05

Figure 8

Design space

Figure 9

Requirement space

Figure 10

Prototype of the SMG: (a) a CAD rendering and (b) a photograph

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