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Research Papers

Design of Planar Parallel Robots With Preloaded Flexures for Guaranteed Backlash Prevention

[+] Author and Article Information
Wei Wei

Department of Mechanical Engineering, Advanced Robotics and Mechanisms Applications Laboratory (ARMA Lab), Columbia University, New York, NY 10027ww2161@columbia.edu

Nabil Simaan1

Department of Mechanical Engineering, Advanced Robotics and Mechanisms Applications Laboratory (ARMA Lab), Columbia University, New York, NY 10027ns2236@columbia.edu

Throughout this paper, a twist is defined as a three- or six-dimensional column vector with linear velocity preceding the angular velocity.

1

Corresponding author.

J. Mechanisms Robotics 2(1), 011012 (Jan 11, 2010) (10 pages) doi:10.1115/1.4000522 History: Received December 16, 2008; Revised July 23, 2009; Published January 11, 2010

The precision of parallel robots is limited by backlash in their joints. This paper investigates algorithms for designing inexpensive planar parallel robots with prescribed backlash-free workspace. The method of closing the backlash of the actuators uses preloaded flexible joints to replace the passive joints. These flexible joints may be made using standard joints with preloaded springs or by using preloaded flexure joints. Given a norm-bounded wrench acting on the robot, an algorithm is presented for determining the required preload for the flexible joints in order to guarantee backlash-free operation along a path or within a prescribed workspace. An investigation of the effects of the preloaded flexible joints on the stiffness is carried out using performance measures comparing the same robot with or without preloaded joints. These performance measures use an extended stiffness definition based on three noncollinear vertices on the moving platform. This paper presents simulations of the statics, stiffness, and backlash prevention algorithm, followed by experimental validations.

Copyright © 2010 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

A 3DOF planar parallel robot with preloaded flexures

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Figure 2

Explanation of backlash-free condition

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Figure 3

Kinematic relationship of the planar parallel robot

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Figure 4

Designed path from configuration A to configuration B where configuration B approaches singularity

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Figure 5

Statics ellipses along the path of Fig. 4

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Figure 6

Manipulability ratio and inverse of condition number along the path from configuration A to configuration B of Fig. 4

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Figure 7

Actuation force plots as the robot traces a circular path

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Figure 8

Actuation force plots with different wrenches of (a) [0 N, 0 N, 1.73 N m]T, (b) [0 N, 0 N, 2.29 N m]T, and (c) [0 N, 0 N, 3 N m]T. The shaded region has the actuator backlash onset.

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Figure 9

Actuation force plots. The shaded region has the actuator backlash onset.

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Figure 10

Stiffness comparison between robots with and without flexures. The ratio of stiffness constants KP/KS is 400.

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Figure 11

Stiffness performance improvement plots of the robot while preloaded with flexures. Comparisons are along the circular path in Fig. 1.

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Figure 12

Structure of the planar parallel robot: (a) CAD model; (b) exploded view of the robot’s leg to show the artificial backlash

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Figure 13

Experimental setups: (a) position tracking system; (b) optical marker illustration and externally loaded robot setup

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Figure 14

Top view of spring angles: (a) no load; (b) preloaded

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Figure 15

Plots for tracing the 10 mm circle: (a) tracing plot with spring preloads; (b) tracing plot without spring preloads. In both plots, dashed curves represent the theoretical path and solid curves represent the actual tracing positions.

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Figure 16

Tracing error plots. The shaded transparent region represents the upper bound of the tracker errors.

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Figure 17

Tracing error plots for different external loads. The transparent regions represent the upper bound of the tracker errors.

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Figure 18

Helical path plots. The shaded transparent regions show backlash-free target workspace for the corresponding external load.

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Figure 19

Position errors when the robot traced the helical path with different loads. The transparent regions represent the upper bound of the tracker errors.

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